2eb21d5 · laop · git.iko.soy

git.iko.soy/laop

Added relational shrinking and overriding.

Added relational McCarthy's Conditional.

commit2eb21d5698cc4ae71d7323f27b8d9e7cc0fdac3e authorArmando Santos <armandoifsantos@gmail.com> dateTue 28 Jan 2020, 19:35 (7 years ago) parent59f3ebc

66 files changed+4548−1

compare with master

unifiedsplit

.ghc.environment.x86_64-linux-8.6.5new file+17

@@ -0,0 +1,17 @@

1+-- This is a GHC environment file written by cabal. This means you can

2+-- run ghc or ghci and get the environment of the project as a whole.

3+-- But you still need to use cabal repl $target to get the environment

4+-- of specific components (libs, exes, tests etc) because each one can

5+-- have its own source dirs, cpp flags etc.

6+--

7+clear-package-db

8+global-package-db

9+package-db /home/bolt/.cabal/store/ghc-8.6.5/package.db

10+package-db packagedb/ghc-8.6.5

11+package-id laop-0.1.0.0-inplace

12+package-id base-4.12.0.0

13+package-id ghc-prim-0.5.3

14+package-id rts

15+package-id integer-gmp-1.0.2.0

16+package-id deepseq-1.4.4.0

17+package-id array-0.5.3.0

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/build/autogen/Paths_laop.hsnew file+50

@@ -0,0 +1,50 @@

1+{-# LANGUAGE CPP #-}

2+{-# LANGUAGE NoRebindableSyntax #-}

3+{-# OPTIONS_GHC -fno-warn-missing-import-lists #-}

4+module Paths_laop (

5+ version,

6+ getBinDir, getLibDir, getDynLibDir, getDataDir, getLibexecDir,

7+ getDataFileName, getSysconfDir

8+ ) where

10+import qualified Control.Exception as Exception

11+import Data.Version (Version(..))

12+import System.Environment (getEnv)

13+import Prelude

14+

15+#if defined(VERSION_base)

16+

17+#if MIN_VERSION_base(4,0,0)

18+catchIO :: IO a -> (Exception.IOException -> IO a) -> IO a

19+#else

20+catchIO :: IO a -> (Exception.Exception -> IO a) -> IO a

21+#endif

22+

23+#else

24+catchIO :: IO a -> (Exception.IOException -> IO a) -> IO a

25+#endif

26+catchIO = Exception.catch

27+

28+version :: Version

29+version = Version [0,1,0,0] []

30+bindir, libdir, dynlibdir, datadir, libexecdir, sysconfdir :: FilePath

31+

32+bindir = "/home/bolt/.cabal/bin"

33+libdir = "/home/bolt/.cabal/lib/x86_64-linux-ghc-8.6.5/laop-0.1.0.0-inplace"

34+dynlibdir = "/home/bolt/.cabal/lib/x86_64-linux-ghc-8.6.5"

35+datadir = "/home/bolt/.cabal/share/x86_64-linux-ghc-8.6.5/laop-0.1.0.0"

36+libexecdir = "/home/bolt/.cabal/libexec/x86_64-linux-ghc-8.6.5/laop-0.1.0.0"

37+sysconfdir = "/home/bolt/.cabal/etc"

38+

39+getBinDir, getLibDir, getDynLibDir, getDataDir, getLibexecDir, getSysconfDir :: IO FilePath

40+getBinDir = catchIO (getEnv "laop_bindir") (\_ -> return bindir)

41+getLibDir = catchIO (getEnv "laop_libdir") (\_ -> return libdir)

42+getDynLibDir = catchIO (getEnv "laop_dynlibdir") (\_ -> return dynlibdir)

43+getDataDir = catchIO (getEnv "laop_datadir") (\_ -> return datadir)

44+getLibexecDir = catchIO (getEnv "laop_libexecdir") (\_ -> return libexecdir)

45+getSysconfDir = catchIO (getEnv "laop_sysconfdir") (\_ -> return sysconfdir)

46+

47+getDataFileName :: FilePath -> IO FilePath

48+getDataFileName name = do

49+ dir <- getDataDir

50+ return (dir ++ "/" ++ name)

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/build/autogen/cabal_macros.hnew file+143

@@ -0,0 +1,143 @@

1+/* DO NOT EDIT: This file is automatically generated by Cabal */

3+/* package laop-0.1.0.0 */

4+#ifndef VERSION_laop

5+#define VERSION_laop "0.1.0.0"

6+#endif /* VERSION_laop */

7+#ifndef MIN_VERSION_laop

8+#define MIN_VERSION_laop(major1,major2,minor) (\

9+ (major1) < 0 || \

10+ (major1) == 0 && (major2) < 1 || \

11+ (major1) == 0 && (major2) == 1 && (minor) <= 0)

12+#endif /* MIN_VERSION_laop */

13+

14+/* package base-4.12.0.0 */

15+#ifndef VERSION_base

16+#define VERSION_base "4.12.0.0"

17+#endif /* VERSION_base */

18+#ifndef MIN_VERSION_base

19+#define MIN_VERSION_base(major1,major2,minor) (\

20+ (major1) < 4 || \

21+ (major1) == 4 && (major2) < 12 || \

22+ (major1) == 4 && (major2) == 12 && (minor) <= 0)

23+#endif /* MIN_VERSION_base */

24+

25+/* package deepseq-1.4.4.0 */

26+#ifndef VERSION_deepseq

27+#define VERSION_deepseq "1.4.4.0"

28+#endif /* VERSION_deepseq */

29+#ifndef MIN_VERSION_deepseq

30+#define MIN_VERSION_deepseq(major1,major2,minor) (\

31+ (major1) < 1 || \

32+ (major1) == 1 && (major2) < 4 || \

33+ (major1) == 1 && (major2) == 4 && (minor) <= 4)

34+#endif /* MIN_VERSION_deepseq */

35+

36+/* tool gcc-9.2.0 */

37+#ifndef TOOL_VERSION_gcc

38+#define TOOL_VERSION_gcc "9.2.0"

39+#endif /* TOOL_VERSION_gcc */

40+#ifndef MIN_TOOL_VERSION_gcc

41+#define MIN_TOOL_VERSION_gcc(major1,major2,minor) (\

42+ (major1) < 9 || \

43+ (major1) == 9 && (major2) < 2 || \

44+ (major1) == 9 && (major2) == 2 && (minor) <= 0)

45+#endif /* MIN_TOOL_VERSION_gcc */

46+

47+/* tool ghc-8.6.5 */

48+#ifndef TOOL_VERSION_ghc

49+#define TOOL_VERSION_ghc "8.6.5"

50+#endif /* TOOL_VERSION_ghc */

51+#ifndef MIN_TOOL_VERSION_ghc

52+#define MIN_TOOL_VERSION_ghc(major1,major2,minor) (\

53+ (major1) < 8 || \

54+ (major1) == 8 && (major2) < 6 || \

55+ (major1) == 8 && (major2) == 6 && (minor) <= 5)

56+#endif /* MIN_TOOL_VERSION_ghc */

57+

58+/* tool ghc-pkg-8.6.5 */

59+#ifndef TOOL_VERSION_ghc_pkg

60+#define TOOL_VERSION_ghc_pkg "8.6.5"

61+#endif /* TOOL_VERSION_ghc_pkg */

62+#ifndef MIN_TOOL_VERSION_ghc_pkg

63+#define MIN_TOOL_VERSION_ghc_pkg(major1,major2,minor) (\

64+ (major1) < 8 || \

65+ (major1) == 8 && (major2) < 6 || \

66+ (major1) == 8 && (major2) == 6 && (minor) <= 5)

67+#endif /* MIN_TOOL_VERSION_ghc_pkg */

68+

69+/* tool haddock-2.22.0 */

70+#ifndef TOOL_VERSION_haddock

71+#define TOOL_VERSION_haddock "2.22.0"

72+#endif /* TOOL_VERSION_haddock */

73+#ifndef MIN_TOOL_VERSION_haddock

74+#define MIN_TOOL_VERSION_haddock(major1,major2,minor) (\

75+ (major1) < 2 || \

76+ (major1) == 2 && (major2) < 22 || \

77+ (major1) == 2 && (major2) == 22 && (minor) <= 0)

78+#endif /* MIN_TOOL_VERSION_haddock */

79+

80+/* tool hpc-0.67 */

81+#ifndef TOOL_VERSION_hpc

82+#define TOOL_VERSION_hpc "0.67"

83+#endif /* TOOL_VERSION_hpc */

84+#ifndef MIN_TOOL_VERSION_hpc

85+#define MIN_TOOL_VERSION_hpc(major1,major2,minor) (\

86+ (major1) < 0 || \

87+ (major1) == 0 && (major2) < 67 || \

88+ (major1) == 0 && (major2) == 67 && (minor) <= 0)

89+#endif /* MIN_TOOL_VERSION_hpc */

90+

91+/* tool hsc2hs-0.68.5 */

92+#ifndef TOOL_VERSION_hsc2hs

93+#define TOOL_VERSION_hsc2hs "0.68.5"

94+#endif /* TOOL_VERSION_hsc2hs */

95+#ifndef MIN_TOOL_VERSION_hsc2hs

96+#define MIN_TOOL_VERSION_hsc2hs(major1,major2,minor) (\

97+ (major1) < 0 || \

98+ (major1) == 0 && (major2) < 68 || \

99+ (major1) == 0 && (major2) == 68 && (minor) <= 5)

100+#endif /* MIN_TOOL_VERSION_hsc2hs */

101+

102+/* tool pkg-config-1.6.3 */

103+#ifndef TOOL_VERSION_pkg_config

104+#define TOOL_VERSION_pkg_config "1.6.3"

105+#endif /* TOOL_VERSION_pkg_config */

106+#ifndef MIN_TOOL_VERSION_pkg_config

107+#define MIN_TOOL_VERSION_pkg_config(major1,major2,minor) (\

108+ (major1) < 1 || \

109+ (major1) == 1 && (major2) < 6 || \

110+ (major1) == 1 && (major2) == 6 && (minor) <= 3)

111+#endif /* MIN_TOOL_VERSION_pkg_config */

112+

113+/* tool runghc-8.6.5 */

114+#ifndef TOOL_VERSION_runghc

115+#define TOOL_VERSION_runghc "8.6.5"

116+#endif /* TOOL_VERSION_runghc */

117+#ifndef MIN_TOOL_VERSION_runghc

118+#define MIN_TOOL_VERSION_runghc(major1,major2,minor) (\

119+ (major1) < 8 || \

120+ (major1) == 8 && (major2) < 6 || \

121+ (major1) == 8 && (major2) == 6 && (minor) <= 5)

122+#endif /* MIN_TOOL_VERSION_runghc */

123+

124+/* tool strip-2.33 */

125+#ifndef TOOL_VERSION_strip

126+#define TOOL_VERSION_strip "2.33"

127+#endif /* TOOL_VERSION_strip */

128+#ifndef MIN_TOOL_VERSION_strip

129+#define MIN_TOOL_VERSION_strip(major1,major2,minor) (\

130+ (major1) < 2 || \

131+ (major1) == 2 && (major2) < 33 || \

132+ (major1) == 2 && (major2) == 33 && (minor) <= 0)

133+#endif /* MIN_TOOL_VERSION_strip */

134+

135+#ifndef CURRENT_PACKAGE_KEY

136+#define CURRENT_PACKAGE_KEY "laop-0.1.0.0-inplace"

137+#endif /* CURRENT_PACKAGE_KEY */

138+#ifndef CURRENT_COMPONENT_ID

139+#define CURRENT_COMPONENT_ID "laop-0.1.0.0-inplace"

140+#endif /* CURRENT_COMPONENT_ID */

141+#ifndef CURRENT_PACKAGE_VERSION

142+#define CURRENT_PACKAGE_VERSION "0.1.0.0"

143+#endif /* CURRENT_PACKAGE_VERSION */

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/cache/confignew file

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build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/Dist.htmlnew file+15

@@ -0,0 +1,15 @@

2+ in Haskell. See <a href="https://github.com/bolt12/master-thesis">my Msc Thesis</a> for the

3+ motivation behind the library, the underlying theory, and implementation details.This module exports a type synonym <code><a href="Dist.html#t:Dist" title="Dist">Dist</a></code>

4+ that represents a stochastic distribution

5+ matrix and several distribution construction

6+ functions.</div></div><div id="synopsis"><details id="syn"><summary>Synopsis</summary><ul class="details-toggle" data-details-id="syn"><li class="src short">newtype <a href="#t:Dist">Dist</a> a = <a href="#v:D">D</a> (<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () a)</li><li class="src short">type <a href="#t:Prob">Prob</a> = <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Double" title="Prelude">Double</a></li><li class="src short"><a href="#v:fmapD">fmapD</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => (a -> b) -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> b</li><li class="src short"><a href="#v:unitD">unitD</a> :: <a href="Dist.html#t:Dist" title="Dist">Dist</a> ()</li><li class="src short"><a href="#v:multD">multD</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> b -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> (a, b)</li><li class="src short"><a href="#v:selectD">selectD</a> :: (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b))) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> a b -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> b</li><li class="src short"><a href="#v:returnD">returnD</a> :: forall a. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a)) => a -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a</li><li class="src short"><a href="#v:bindD">bindD</a> :: <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> a b -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> b</li><li class="src short"><a href="#v:choose">choose</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => <a href="Dist.html#t:Prob" title="Dist">Prob</a> -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a</li><li class="src short"><a href="#v:shape">shape</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => (<a href="Dist.html#t:Prob" title="Dist">Prob</a> -> <a href="Dist.html#t:Prob" title="Dist">Prob</a>) -> [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a</li><li class="src short"><a href="#v:linear">linear</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a</li><li class="src short"><a href="#v:uniform">uniform</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a</li><li class="src short"><a href="#v:negExp">negExp</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a</li><li class="src short"><a href="#v:normal">normal</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a</li><li class="src short"><a href="#v:toValues">toValues</a> :: forall a. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> [(a, <a href="Dist.html#t:Prob" title="Dist">Prob</a>)]</li><li class="src short"><a href="#v:prettyDist">prettyDist</a> :: forall a. (<a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a></li><li class="src short"><a href="#v:prettyPrintDist">prettyPrintDist</a> :: forall a. (<a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="/package/base-4.12.0.0/docs/System-IO.html#t:IO" title="System.IO">IO</a> ()</li></ul></details></div><div id="interface"><h1>Documentation</h1><div class="doc">If the sum of the rows of a column matrix

7+ is equal to 1 then this stochastic matrix

8+ can be seen as a probability distribution.This module is still experimental but it's

9+ already possible to model probabilistic programming

10+ problems with it. Import <code><a href="Matrix.html#v:Nat" title="Matrix">Nat</a></code> or <code><a href="Matrix.html#v:Type" title="Matrix">Type</a></code>

11+ to access LAoP matrix combinators and then all you have

12+ to do is to define your sample space, either by creating a new data

13+ type or by abstracting it out via <code>Natural</code>.Write manipulation functions and promote them to matrices via

14+ <code>fromF</code> or <code>fromF'</code> and you're good to go!</div><a href="#g:1" id="g:1"><h1><code><a href="Dist.html#t:Dist" title="Dist">Dist</a></code> and <code><a href="Dist.html#t:Prob" title="Dist">Prob</a></code> type synonyms</h1></a><div class="top">newtype <a id="t:Dist" class="def">Dist</a> a <a href="src/Dist.Internal.html#Dist" class="link">Source</a> <a href="#t:Dist" class="selflink">#</a><div class="doc">Type synonym for column vector matrices. This represents a probability

15+ distribution.</div><div class="subs constructors">Constructors<table><tr><td class="src"><a id="v:D" class="def">D</a> (<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () a)</td><td class="doc empty"> </td></tr></table></div></div><div class="top">type <a id="t:Prob" class="def">Prob</a> = <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Double" title="Prelude">Double</a> <a href="src/Dist.Internal.html#Prob" class="link">Source</a> <a href="#t:Prob" class="selflink">#</a><div class="doc">Type synonym for probability value</div></div><a href="#g:2" id="g:2"><h1>Functor instance equivalent functions</h1></a><div class="top"><a id="v:fmapD" class="def">fmapD</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => (a -> b) -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> b <a href="src/Dist.Internal.html#fmapD" class="link">Source</a> <a href="#v:fmapD" class="selflink">#</a><div class="doc">Functor instance</div></div><a href="#g:3" id="g:3"><h1>Applicative equivalent functions</h1></a><div class="top"><a id="v:unitD" class="def">unitD</a> :: <a href="Dist.html#t:Dist" title="Dist">Dist</a> () <a href="src/Dist.Internal.html#unitD" class="link">Source</a> <a href="#v:unitD" class="selflink">#</a><div class="doc">Applicative/Monoidal instance <code>unit</code> function</div></div><div class="top"><a id="v:multD" class="def">multD</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> b -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> (a, b) <a href="src/Dist.Internal.html#multD" class="link">Source</a> <a href="#v:multD" class="selflink">#</a><div class="doc">Applicative/Monoidal instance <code>mult</code> function</div></div><a href="#g:4" id="g:4"><h1>Selective equivalent functions</h1></a><div class="top"><a id="v:selectD" class="def">selectD</a> :: (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b))) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> a b -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> b <a href="src/Dist.Internal.html#selectD" class="link">Source</a> <a href="#v:selectD" class="selflink">#</a><div class="doc">Selective instance function</div></div><a href="#g:5" id="g:5"><h1>Monad equivalent functions</h1></a><div class="top"><a id="v:returnD" class="def">returnD</a> :: forall a. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a)) => a -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a <a href="src/Dist.Internal.html#returnD" class="link">Source</a> <a href="#v:returnD" class="selflink">#</a><div class="doc">Monad instance <code><a href="/package/base-4.12.0.0/docs/Control-Monad.html#v:return" title="Control.Monad">return</a></code> function</div></div><div class="top"><a id="v:bindD" class="def">bindD</a> :: <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> a b -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> b <a href="src/Dist.Internal.html#bindD" class="link">Source</a> <a href="#v:bindD" class="selflink">#</a><div class="doc">Monad instance '(>>=)' function</div></div><a href="#g:6" id="g:6"><h1>Distribution construction functions</h1></a><div class="top"><a id="v:choose" class="def">choose</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => <a href="Dist.html#t:Prob" title="Dist">Prob</a> -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a <a href="src/Dist.Internal.html#choose" class="link">Source</a> <a href="#v:choose" class="selflink">#</a><div class="doc">Constructs a Bernoulli distribution</div></div><div class="top"><a id="v:shape" class="def">shape</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => (<a href="Dist.html#t:Prob" title="Dist">Prob</a> -> <a href="Dist.html#t:Prob" title="Dist">Prob</a>) -> [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a <a href="src/Dist.Internal.html#shape" class="link">Source</a> <a href="#v:shape" class="selflink">#</a><div class="doc">Creates a distribution given a shape function</div></div><div class="top"><a id="v:linear" class="def">linear</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a <a href="src/Dist.Internal.html#linear" class="link">Source</a> <a href="#v:linear" class="selflink">#</a><div class="doc">Constructs a Linear distribution</div></div><div class="top"><a id="v:uniform" class="def">uniform</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a <a href="src/Dist.Internal.html#uniform" class="link">Source</a> <a href="#v:uniform" class="selflink">#</a><div class="doc">Constructs an Uniform distribution</div></div><div class="top"><a id="v:negExp" class="def">negExp</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a <a href="src/Dist.Internal.html#negExp" class="link">Source</a> <a href="#v:negExp" class="selflink">#</a><div class="doc">Constructs an Negative Exponential distribution</div></div><div class="top"><a id="v:normal" class="def">normal</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) => [a] -> <a href="Dist.html#t:Dist" title="Dist">Dist</a> a <a href="src/Dist.Internal.html#normal" class="link">Source</a> <a href="#v:normal" class="selflink">#</a><div class="doc">Constructs an Normal distribution</div></div><a href="#g:7" id="g:7"><h1>Converto to list of pairs</h1></a><div class="top"><a id="v:toValues" class="def">toValues</a> :: forall a. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> [(a, <a href="Dist.html#t:Prob" title="Dist">Prob</a>)] <a href="src/Dist.Internal.html#toValues" class="link">Source</a> <a href="#v:toValues" class="selflink">#</a><div class="doc">Transforms a <code><a href="Dist.html#t:Dist" title="Dist">Dist</a></code> into a list of pairs.</div></div><a href="#g:8" id="g:8"><h1>Pretty print distribution</h1></a><div class="top"><a id="v:prettyDist" class="def">prettyDist</a> :: forall a. (<a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a> <a href="src/Dist.Internal.html#prettyDist" class="link">Source</a> <a href="#v:prettyDist" class="selflink">#</a><div class="doc">Pretty a distribution</div></div><div class="top"><a id="v:prettyPrintDist" class="def">prettyPrintDist</a> :: forall a. (<a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> <a href="Dist.html#t:Prob" title="Dist">Prob</a> () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => <a href="Dist.html#t:Dist" title="Dist">Dist</a> a -> <a href="/package/base-4.12.0.0/docs/System-IO.html#t:IO" title="System.IO">IO</a> () <a href="src/Dist.Internal.html#prettyPrintDist" class="link">Source</a> <a href="#v:prettyPrintDist" class="selflink">#</a><div class="doc">Pretty Print a distribution</div></div></div></div><div id="footer">Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.22.0</div></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/Matrix-Nat.htmlnew file+22

@@ -0,0 +1,22 @@

2+ Boolean matrices and in turn consider these as arrows.LAoP is a library for algebraic (inductive) construction and manipulation of matrices

3+ in Haskell. See <a href="https://github.com/bolt12/master-thesis">my Msc Thesis</a> for the

4+ motivation behind the library, the underlying theory, and implementation details.This module offers a newtype wrapper around <code><a href="Matrix-Type.html#v:Matrix" title="Matrix.Type">Matrix</a></code> that

5+ uses type level naturals instead of standard data types for the matrices

6+ dimensions.</div></div><div id="synopsis"><details id="syn"><summary>Synopsis</summary><ul class="details-toggle" data-details-id="syn"><li class="src short">newtype <a href="#t:Matrix">Matrix</a> e (cols :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) (rows :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) = <a href="#v:M">M</a> (Matrix e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))</li><li class="src short"><a href="#v:empty">empty</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e 0 0</li><li class="src short"><a href="#v:one">one</a> :: e -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e 1 1</li><li class="src short"><a href="#v:junc">junc</a> :: <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols2) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols1 rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols2 rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols3 rows</li><li class="src short"><a href="#v:split">split</a> :: <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows2) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows1 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows2 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows3</li><li class="src short">type family <a href="#t:FromNat">FromNat</a> (n :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> where ...</li><li class="src short">type family <a href="#t:Count">Count</a> (d :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a> where ...</li><li class="src short">type family <a href="#t:Normalize">Normalize</a> (d :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> where ...</li><li class="src short">class <a href="#t:FromLists">FromLists</a> e cols rows</li><li class="src short"><a href="#v:fromLists">fromLists</a> :: <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) => [[e]] -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:toLists">toLists</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> [[e]]</li><li class="src short"><a href="#v:toList">toList</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> [e]</li><li class="src short"><a href="#v:matrixBuilder">matrixBuilder</a> :: (<a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))) => ((<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>, <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> e) -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:row">row</a> :: <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) () => [e] -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols 1</li><li class="src short"><a href="#v:col">col</a> :: <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) => [e] -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e 1 rows</li><li class="src short"><a href="#v:zeros">zeros</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:ones">ones</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:bang">bang</a> :: forall e cols. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols 1</li><li class="src short"><a href="#v:constant">constant</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))) => e -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:columns">columns</a> :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></li><li class="src short"><a href="#v:rows">rows</a> :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></li><li class="src short"><a href="#v:tr">tr</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e rows cols</li><li class="src short"><a href="#v:select">select</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1)), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows2 ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1, <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols1 ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols2, <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols3) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols1 rows3 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols3 rows1 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols2 rows2</li><li class="src short"><a href="#v:cond">cond</a> :: (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols), <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e) => (a -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a>) -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:abideJS">abideJS</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:abideSJ">abideSJ</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:-61--61--61-">(===)</a> :: <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows2) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows1 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows2 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows3</li><li class="src short"><a href="#v:p1">p1</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) m</li><li class="src short"><a href="#v:p2">p2</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) n</li><li class="src short"><a href="#v:-124--124--124-">(|||)</a> :: <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols2) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols1 rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols2 rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols3 rows</li><li class="src short"><a href="#v:i1">i1</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (rows <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e rows (rows <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n)</li><li class="src short"><a href="#v:i2">i2</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> rows) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e rows (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> rows)</li><li class="src short"><a href="#v:-45--124--45-">(-|-)</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (n <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> m) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (k <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> j) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e n k -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e m j -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (n <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> m) (k <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> j)</li><li class="src short"><a href="#v:-62--60-">(><)</a> :: forall e m p n q. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> p)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> q)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n))), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q))), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> p), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> q), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> p) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> q))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e m p -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e n q -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n) (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q)</li><li class="src short"><a href="#v:kp1">kp1</a> :: forall e m k. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k))), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k) m</li><li class="src short"><a href="#v:kp2">kp2</a> :: forall e m k. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k))), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k) k</li><li class="src short"><a href="#v:khatri">khatri</a> :: forall e cols a b. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> b)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b))), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> a), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> b), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> a) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> b))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols a -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols b -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b)</li><li class="src short"><a href="#v:identity">identity</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols cols</li><li class="src short"><a href="#v:comp">comp</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cr rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols cr -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:fromF">fromF</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)) => (a -> b) -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows</li><li class="src short"><a href="#v:fromF-39-">fromF'</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> b)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> b) (<a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> a)) => (a -> b) -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> a) (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> b)</li><li class="src short"><a href="#v:pretty">pretty</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a></li><li class="src short"><a href="#v:prettyPrint">prettyPrint</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/System-IO.html#t:IO" title="System.IO">IO</a> ()</li></ul></details></div><div id="interface"><h1>Documentation</h1><div class="doc">LAoP (Linear Algebra of Programming) Inductive Matrix definition.LAoP generalises relations and functions treating them as

7+ Boolean matrices and in turn consider these as arrows.

8+ This library offers many of the combinators mentioned in the work of

9+ Macedo (2012) and Oliveira (2012).This definition is a wrapper around <code><a href="Matrix.html#v:Type" title="Matrix">Type</a></code> but

10+ dimensions are type level Naturals. Type inference might not

11+ be as desired.There exists two type families that make it easier to write

12+ matrix dimensions: <code>FromNat</code> and <code>Count</code>. This approach

13+ leads to a very straightforward implementation

14+ of LAoP combinators. </div><a href="#g:1" id="g:1"><h1>Type safe matrix representation</h1></a><div class="top">newtype <a id="t:Matrix" class="def">Matrix</a> e (cols :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) (rows :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) <a href="src/Matrix.Nat.html#Matrix" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a><div class="subs constructors">Constructors<table><tr><td class="src"><a id="v:M" class="def">M</a> (Matrix e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><details id="i:Matrix" open="open"><summary>Instances</summary><table><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="/package/base-4.12.0.0/docs/Control-Category.html#t:Category" title="Control.Category">Category</a> (<a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a> -> <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a> -> <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) <a href="src/Matrix.Nat.html#line-155" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc">It isn't possible to implement the <code><a href="/package/base-4.12.0.0/docs/Data-Function.html#v:id" title="Data.Function">id</a></code> function so it's

15+ implementation is <code><a href="/package/base-4.12.0.0/docs/Prelude.html#v:undefined" title="Prelude">undefined</a></code>. However <code><a href="Matrix-Nat.html#v:comp" title="Matrix.Nat">comp</a></code> can be and this partial

16+ class implementation exists just to make the code more readable.Please use <code><a href="Matrix-Nat.html#v:identity" title="Matrix.Nat">identity</a></code> instead.</td></tr><tr><td colspan="2"><details id="i:id:Matrix:Category:1"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Nat.html">Matrix.Nat</a> <div class="subs methods">Methods<a href="#v:id">id</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e a a <a href="#v:id" class="selflink">#</a><a href="#v:.">(.)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e b c -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e a b -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e a c <a href="#v:." class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> e => <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> (<a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows) <a href="src/Matrix.Nat.html#line-148" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:Eq:2"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Nat.html">Matrix.Nat</a> <div class="subs methods">Methods<a href="#v:-61--61-">(==)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a><a href="#v:-47--61-">(/=)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> (<a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows) <a href="src/Matrix.Nat.html#line-148" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:Num:3"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Nat.html">Matrix.Nat</a> <div class="subs methods">Methods<a href="#v:-43-">(+)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:-43-" class="selflink">#</a><a href="#v:-45-">(-)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:-45-" class="selflink">#</a><a href="#v:-42-">(*)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:-42-" class="selflink">#</a><a href="#v:negate">negate</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:negate" class="selflink">#</a><a href="#v:abs">abs</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:abs" class="selflink">#</a><a href="#v:signum">signum</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:signum" class="selflink">#</a><a href="#v:fromInteger">fromInteger</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Integer" title="Prelude">Integer</a> -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:fromInteger" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e => <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> (<a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows) <a href="src/Matrix.Nat.html#line-148" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:Ord:4"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Nat.html">Matrix.Nat</a> <div class="subs methods">Methods<a href="#v:compare">compare</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ordering" title="Data.Ord">Ordering</a> <a href="#v:compare" class="selflink">#</a><a href="#v:-60-">(<)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-60-" class="selflink">#</a><a href="#v:-60--61-">(<=)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-60--61-" class="selflink">#</a><a href="#v:-62-">(>)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-62-" class="selflink">#</a><a href="#v:-62--61-">(>=)</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-62--61-" class="selflink">#</a><a href="#v:max">max</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:max" class="selflink">#</a><a href="#v:min">min</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="#v:min" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e => <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> (<a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows) <a href="src/Matrix.Nat.html#line-148" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:Show:5"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Nat.html">Matrix.Nat</a> <div class="subs methods">Methods<a href="#v:showsPrec">showsPrec</a> :: <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:ShowS" title="Text.Show">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a><a href="#v:show">show</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a> <a href="#v:show" class="selflink">#</a><a href="#v:showList">showList</a> :: [<a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows] -> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:ShowS" title="Text.Show">ShowS</a> <a href="#v:showList" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/deepseq-1.4.4.0/docs/Control-DeepSeq.html#t:NFData" title="Control.DeepSeq">NFData</a> e => <a href="/package/deepseq-1.4.4.0/docs/Control-DeepSeq.html#t:NFData" title="Control.DeepSeq">NFData</a> (<a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows) <a href="src/Matrix.Nat.html#line-148" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:NFData:6"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Nat.html">Matrix.Nat</a> <div class="subs methods">Methods<a href="#v:rnf">rnf</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> () <a href="#v:rnf" class="selflink">#</a></div></details></td></tr></table></details></div></div><a href="#g:2" id="g:2"><h1>Primitives</h1></a><div class="top"><a id="v:empty" class="def">empty</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e 0 0 <a href="src/Matrix.Nat.html#empty" class="link">Source</a> <a href="#v:empty" class="selflink">#</a></div><div class="top"><a id="v:one" class="def">one</a> :: e -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e 1 1 <a href="src/Matrix.Nat.html#one" class="link">Source</a> <a href="#v:one" class="selflink">#</a></div><div class="top"><a id="v:junc" class="def">junc</a> :: <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols2) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols1 rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols2 rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols3 rows <a href="src/Matrix.Nat.html#junc" class="link">Source</a> <a href="#v:junc" class="selflink">#</a></div><div class="top"><a id="v:split" class="def">split</a> :: <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows2) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows1 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows2 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows3 <a href="src/Matrix.Nat.html#split" class="link">Source</a> <a href="#v:split" class="selflink">#</a></div><a href="#g:3" id="g:3"><h1>Auxiliary type families</h1></a><div class="top">type family <a id="t:FromNat" class="def">FromNat</a> (n :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> where ... <a href="src/Matrix.Internal.html#FromNat" class="link">Source</a> <a href="#t:FromNat" class="selflink">#</a><div class="doc">Type family that computes of a given type dimension from a given naturalThanks to Li-Yao Xia this type family is super fast.</div><div class="subs equations">Equations<table><tr><td class="src"><a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> 0 = <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> 1 = ()</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n = FromNat' (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Mod" title="GHC.TypeNats">Mod</a> n 2 <a href="/package/base-4.12.0.0/docs/Data-Type-Equality.html#t:-61--61-" title="Data.Type.Equality">==</a> 0) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Div" title="GHC.TypeNats">Div</a> n 2))</td><td class="doc empty"> </td></tr></table></div></div><div class="top">type family <a id="t:Count" class="def">Count</a> (d :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a> where ... <a href="src/Matrix.Internal.html#Count" class="link">Source</a> <a href="#t:Count" class="selflink">#</a><div class="doc">Type family that computes the cardinality of a given type dimension.It can also count the cardinality of custom types that implement the

17+ <code><a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:Generic" title="GHC.Generics">Generic</a></code> instance.</div><div class="subs equations">Equations<table><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m) = (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-45-" title="GHC.TypeNats">-</a> n) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> 1</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) = <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">(+)</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> a) (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> b)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (a, b) = <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> a) (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> b)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (a -> b) = <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-94-" title="GHC.TypeNats">(^)</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> b) (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:M1" title="GHC.Generics">M1</a> _ _ f p) = <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (f p)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:K1" title="GHC.Generics">K1</a> _ _ _) = 1</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:V1" title="GHC.Generics">V1</a> _) = 0</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:U1" title="GHC.Generics">U1</a> _) = 1</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t::-42-:" title="GHC.Generics">(:*:)</a> a b p) = <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (a p) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (b p)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t::-43-:" title="GHC.Generics">(:+:)</a> a b p) = <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (a p) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (b p)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> d = <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:Rep" title="GHC.Generics">Rep</a> d <a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:R" title="GHC.Generics">R</a>)</td><td class="doc empty"> </td></tr></table></div></div><div class="top">type family <a id="t:Normalize" class="def">Normalize</a> (d :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> where ... <a href="src/Matrix.Internal.html#Normalize" class="link">Source</a> <a href="#t:Normalize" class="selflink">#</a><div class="doc">Type family that normalizes the representation of a given data

18+ structure</div><div class="subs equations">Equations<table><tr><td class="src"><a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> d = <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> d)</td><td class="doc empty"> </td></tr></table></div></div><a href="#g:4" id="g:4"><h1>Matrix construction and conversion</h1></a><div class="top">class <a id="t:FromLists" class="def">FromLists</a> e cols rows <a href="src/Matrix.Internal.html#FromLists" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a><div class="doc">Type class for defining the <code>fromList</code> conversion function.Given that it is not possible to branch on types at the term level type

19+ classes are needed bery much like an inductive definition but on types.</div><div class="subs minimal">Minimal complete definitionfromLists</div><div class="subs instances"><details id="i:FromLists" open="open"><summary>Instances</summary><table><tr><td class="src clearfix"> <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () () <a href="src/Matrix.Internal.html#line-311" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:1"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e () ()</div></details></td></tr><tr><td class="src clearfix"> <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a> <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a> <a href="src/Matrix.Internal.html#line-307" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:2"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a> <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a></div></details></td></tr><tr><td class="src clearfix"> (<a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () a, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () b, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> a)) => <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) <a href="src/Matrix.Internal.html#line-329" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:3"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e () (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b)</div></details></td></tr><tr><td class="src clearfix"> <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () rows => <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> () rows) <a href="src/Matrix.Internal.html#line-325" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:4"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e () (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> () rows)</div></details></td></tr><tr><td class="src clearfix"> (<a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e a (), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e b (), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> a)) => <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) () <a href="src/Matrix.Internal.html#line-319" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:5"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ()</div></details></td></tr><tr><td class="src clearfix"> <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e cols () => <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> () cols) () <a href="src/Matrix.Internal.html#line-315" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:6"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> () cols) ()</div></details></td></tr><tr><td class="src clearfix"> (<a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) c, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) d, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> c)) => <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> c d) <a href="src/Matrix.Internal.html#line-335" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:7"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> c d)</div></details></td></tr></table></details></div></div><div class="top"><a id="v:fromLists" class="def">fromLists</a> :: <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) => [[e]] -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#fromLists" class="link">Source</a> <a href="#v:fromLists" class="selflink">#</a></div><div class="top"><a id="v:toLists" class="def">toLists</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> [[e]] <a href="src/Matrix.Nat.html#toLists" class="link">Source</a> <a href="#v:toLists" class="selflink">#</a></div><div class="top"><a id="v:toList" class="def">toList</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> [e] <a href="src/Matrix.Nat.html#toList" class="link">Source</a> <a href="#v:toList" class="selflink">#</a></div><div class="top"><a id="v:matrixBuilder" class="def">matrixBuilder</a> :: (<a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))) => ((<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>, <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> e) -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#matrixBuilder" class="link">Source</a> <a href="#v:matrixBuilder" class="selflink">#</a></div><div class="top"><a id="v:row" class="def">row</a> :: <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) () => [e] -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols 1 <a href="src/Matrix.Nat.html#row" class="link">Source</a> <a href="#v:row" class="selflink">#</a></div><div class="top"><a id="v:col" class="def">col</a> :: <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) => [e] -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e 1 rows <a href="src/Matrix.Nat.html#col" class="link">Source</a> <a href="#v:col" class="selflink">#</a></div><div class="top"><a id="v:zeros" class="def">zeros</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#zeros" class="link">Source</a> <a href="#v:zeros" class="selflink">#</a></div><div class="top"><a id="v:ones" class="def">ones</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#ones" class="link">Source</a> <a href="#v:ones" class="selflink">#</a></div><div class="top"><a id="v:bang" class="def">bang</a> :: forall e cols. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols 1 <a href="src/Matrix.Nat.html#bang" class="link">Source</a> <a href="#v:bang" class="selflink">#</a></div><div class="top"><a id="v:constant" class="def">constant</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows))) => e -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#constant" class="link">Source</a> <a href="#v:constant" class="selflink">#</a></div><a href="#g:5" id="g:5"><h1>Misc</h1></a><a href="#g:6" id="g:6"><h2>Get dimensions</h2></a><div class="top"><a id="v:columns" class="def">columns</a> :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> <a href="src/Matrix.Nat.html#columns" class="link">Source</a> <a href="#v:columns" class="selflink">#</a></div><div class="top"><a id="v:rows" class="def">rows</a> :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> <a href="src/Matrix.Nat.html#rows" class="link">Source</a> <a href="#v:rows" class="selflink">#</a></div><a href="#g:7" id="g:7"><h2>Matrix Transposition</h2></a><div class="top"><a id="v:tr" class="def">tr</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e rows cols <a href="src/Matrix.Nat.html#tr" class="link">Source</a> <a href="#v:tr" class="selflink">#</a></div><a href="#g:8" id="g:8"><h2>Selective operator</h2></a><div class="top"><a id="v:select" class="def">select</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1)), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows2 ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1, <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols1 ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols2, <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols3) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols1 rows3 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols3 rows1 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols2 rows2 <a href="src/Matrix.Nat.html#select" class="link">Source</a> <a href="#v:select" class="selflink">#</a></div><a href="#g:9" id="g:9"><h2>McCarthy's Conditional</h2></a><div class="top"><a id="v:cond" class="def">cond</a> :: (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e () (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols), <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e) => (a -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a>) -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#cond" class="link">Source</a> <a href="#v:cond" class="selflink">#</a></div><a href="#g:10" id="g:10"><h2>Matrix "abiding"</h2></a><div class="top"><a id="v:abideJS" class="def">abideJS</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#abideJS" class="link">Source</a> <a href="#v:abideJS" class="selflink">#</a></div><div class="top"><a id="v:abideSJ" class="def">abideSJ</a> :: <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#abideSJ" class="link">Source</a> <a href="#v:abideSJ" class="selflink">#</a></div><a href="#g:11" id="g:11"><h1>Biproduct approach</h1></a><a href="#g:12" id="g:12"><h2>Split</h2></a><div class="top"><a id="v:-61--61--61-" class="def">(===)</a> :: <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows2) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows1 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows2 -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows3 infixl 2 <a href="src/Matrix.Nat.html#%3D%3D%3D" class="link">Source</a> <a href="#v:-61--61--61-" class="selflink">#</a></div><a href="#g:13" id="g:13"><h3>Projections</h3></a><div class="top"><a id="v:p1" class="def">p1</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) m <a href="src/Matrix.Nat.html#p1" class="link">Source</a> <a href="#v:p1" class="selflink">#</a></div><div class="top"><a id="v:p2" class="def">p2</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) n <a href="src/Matrix.Nat.html#p2" class="link">Source</a> <a href="#v:p2" class="selflink">#</a></div><a href="#g:14" id="g:14"><h2>Junc</h2></a><div class="top"><a id="v:-124--124--124-" class="def">(|||)</a> :: <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols3 ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols1) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols2) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols1 rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols2 rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols3 rows infixl 3 <a href="src/Matrix.Nat.html#%7C%7C%7C" class="link">Source</a> <a href="#v:-124--124--124-" class="selflink">#</a></div><a href="#g:15" id="g:15"><h3>Injections</h3></a><div class="top"><a id="v:i1" class="def">i1</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (rows <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e rows (rows <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> n) <a href="src/Matrix.Nat.html#i1" class="link">Source</a> <a href="#v:i1" class="selflink">#</a></div><div class="top"><a id="v:i2" class="def">i2</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> rows) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e rows (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> rows) <a href="src/Matrix.Nat.html#i2" class="link">Source</a> <a href="#v:i2" class="selflink">#</a></div><a href="#g:16" id="g:16"><h2>Bifunctors</h2></a><div class="top"><a id="v:-45--124--45-" class="def">(-|-)</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (n <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> m) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (k <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> j) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> j)) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e n k -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e m j -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (n <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> m) (k <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> j) infixl 5 <a href="src/Matrix.Nat.html#-%7C-" class="link">Source</a> <a href="#v:-45--124--45-" class="selflink">#</a></div><div class="top"><a id="v:-62--60-" class="def">(><)</a> :: forall e m p n q. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> p)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> q)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n))), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q))), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> p), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> q), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> n)), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> p) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> q))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e m p -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e n q -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> n) (p <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> q) infixl 4 <a href="src/Matrix.Nat.html#%3E%3C" class="link">Source</a> <a href="#v:-62--60-" class="selflink">#</a></div><a href="#g:17" id="g:17"><h2>Applicative matrix combinators</h2></a><div class="doc">Note that given the restrictions imposed it is not possible to

20+ implement the standard type classes present in standard Haskell.

21+ *** Matrix pairing projections</div><div class="top"><a id="v:kp1" class="def">kp1</a> :: forall e m k. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k))), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k) m <a href="src/Matrix.Nat.html#kp1" class="link">Source</a> <a href="#v:kp1" class="selflink">#</a></div><div class="top"><a id="v:kp2" class="def">kp2</a> :: forall e m k. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k))), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> m) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> k))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> k) k <a href="src/Matrix.Nat.html#kp2" class="link">Source</a> <a href="#v:kp2" class="selflink">#</a></div><a href="#g:18" id="g:18"><h3>Matrix pairing</h3></a><div class="top"><a id="v:khatri" class="def">khatri</a> :: forall e cols a b. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> b)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b))), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> a), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b)) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> b), <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b) ~ <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> a) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> b))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols a -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols b -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols (a <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> b) <a href="src/Matrix.Nat.html#khatri" class="link">Source</a> <a href="#v:khatri" class="selflink">#</a></div><a href="#g:19" id="g:19"><h1>Matrix composition and lifting</h1></a><a href="#g:20" id="g:20"><h2>Arrow matrix combinators</h2></a><div class="doc">Note that given the restrictions imposed it is not possible to

22+ implement the standard type classes present in standard Haskell.</div><div class="top"><a id="v:identity" class="def">identity</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols))) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols cols <a href="src/Matrix.Nat.html#identity" class="link">Source</a> <a href="#v:identity" class="selflink">#</a></div><div class="top"><a id="v:comp" class="def">comp</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cr rows -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols cr -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#comp" class="link">Source</a> <a href="#v:comp" class="selflink">#</a></div><div class="top"><a id="v:fromF" class="def">fromF</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> rows) (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)) => (a -> b) -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows <a href="src/Matrix.Nat.html#fromF" class="link">Source</a> <a href="#v:fromF" class="selflink">#</a></div><div class="top"><a id="v:fromF-39-" class="def">fromF'</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> b)), <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">FromLists</a> e (<a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> b) (<a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Normalize</a> a)) => (a -> b) -> <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> a) (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> b) <a href="src/Matrix.Nat.html#fromF%27" class="link">Source</a> <a href="#v:fromF-39-" class="selflink">#</a></div><a href="#g:21" id="g:21"><h1>Matrix printing</h1></a><div class="top"><a id="v:pretty" class="def">pretty</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a> <a href="src/Matrix.Nat.html#pretty" class="link">Source</a> <a href="#v:pretty" class="selflink">#</a></div><div class="top"><a id="v:prettyPrint" class="def">prettyPrint</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Count</a> (<a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">FromNat</a> cols)), <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e) => <a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/System-IO.html#t:IO" title="System.IO">IO</a> () <a href="src/Matrix.Nat.html#prettyPrint" class="link">Source</a> <a href="#v:prettyPrint" class="selflink">#</a></div></div></div><div id="footer">Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.22.0</div></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/Matrix-Type.htmlnew file+36

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2+ Boolean matrices and in turn consider these as arrows.LAoP is a library for algebraic (inductive) construction and manipulation of matrices

3+ in Haskell. See <a href="https://github.com/bolt12/master-thesis">my Msc Thesis</a> for the

4+ motivation behind the library, the underlying theory, and implementation details.This module offers a newtype wrapper around <code><a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a></code> that

5+ uses arbitrary types instead of canonical data types for the matrices

6+ dimensions.NOTE: If the types in the dimensions are custom they must need to

7+ implement a <code>Generic</code> instance.</div></div><div id="synopsis"><details id="syn"><summary>Synopsis</summary><ul class="details-toggle" data-details-id="syn"><li class="src short">newtype <a href="#t:Matrix">Matrix</a> e (cols :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) (rows :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) = <a href="#v:M">M</a> (Matrix e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))</li><li class="src short">type <a href="#t:Zero">Zero</a> = <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a></li><li class="src short">type <a href="#t:One">One</a> = ()</li><li class="src short"><a href="#v:empty">empty</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e <a href="Matrix-Type.html#t:Zero" title="Matrix.Type">Zero</a> <a href="Matrix-Type.html#t:Zero" title="Matrix.Type">Zero</a></li><li class="src short"><a href="#v:one">one</a> :: e -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a></li><li class="src short"><a href="#v:junc">junc</a> :: <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e b rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) rows</li><li class="src short"><a href="#v:split">split</a> :: <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b)</li><li class="src short">type family <a href="#t:FromNat">FromNat</a> (n :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> where ...</li><li class="src short">type family <a href="#t:Count">Count</a> (d :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a> where ...</li><li class="src short">type family <a href="#t:Normalize">Normalize</a> (d :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> where ...</li><li class="src short">class <a href="#t:FromLists">FromLists</a> e cols rows</li><li class="src short"><a href="#v:fromLists">fromLists</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows) => [[e]] -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:toLists">toLists</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> [[e]]</li><li class="src short"><a href="#v:toList">toList</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> [e]</li><li class="src short"><a href="#v:matrixBuilder">matrixBuilder</a> :: (<a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))) => ((<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>, <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> e) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:row">row</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) () => [e] -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a></li><li class="src short"><a href="#v:col">col</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows) => [e] -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> rows</li><li class="src short"><a href="#v:zeros">zeros</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:ones">ones</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:bang">bang</a> :: forall e cols. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols))) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a></li><li class="src short"><a href="#v:constant">constant</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))) => e -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:fmapM">fmapM</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => (a -> b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c b</li><li class="src short"><a href="#v:unitM">unitM</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e () ()</li><li class="src short"><a href="#v:multM">multM</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b))), <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c (a, b)</li><li class="src short"><a href="#v:selectM">selectM</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols b</li><li class="src short"><a href="#v:returnM">returnM</a> :: forall e a. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> e, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a)) => a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> a</li><li class="src short"><a href="#v:bindM">bindM</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e b c -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a c</li><li class="src short"><a href="#v:columns">columns</a> :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></li><li class="src short"><a href="#v:rows">rows</a> :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></li><li class="src short"><a href="#v:tr">tr</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e rows cols</li><li class="src short"><a href="#v:cond">cond</a> :: (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e) => (a -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a>) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b</li><li class="src short"><a href="#v:abideJS">abideJS</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:abideSJ">abideSJ</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:-61--61--61-">(===)</a> :: <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b)</li><li class="src short"><a href="#v:p1">p1</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) m</li><li class="src short"><a href="#v:p2">p2</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) n</li><li class="src short"><a href="#v:-124--124--124-">(|||)</a> :: <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e b rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) rows</li><li class="src short"><a href="#v:i1">i1</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e m (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n)</li><li class="src short"><a href="#v:i2">i2</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e n (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n)</li><li class="src short"><a href="#v:-45--124--45-">(-|-)</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> n m) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> k j) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e n k -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e m j -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> n m) (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> k j)</li><li class="src short"><a href="#v:-62--60-">(><)</a> :: forall e m p n q. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> p)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> q)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, n))), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (p, q))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, n)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, n)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (p, q)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> p), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (p, q)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> q), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, n) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (p, q) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> p, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> q)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e m p -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e n q -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (m, n) (p, q)</li><li class="src short"><a href="#v:kp1">kp1</a> :: forall e m k. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (m, k) m</li><li class="src short"><a href="#v:kp2">kp2</a> :: forall e m k. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (m, k) k</li><li class="src short"><a href="#v:khatri">khatri</a> :: forall e cols a b. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols (a, b)</li><li class="src short"><a href="#v:identity">identity</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a))) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a a</li><li class="src short"><a href="#v:comp">comp</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cr rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols cr -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:fromF">fromF</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)) => (a -> b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows</li><li class="src short"><a href="#v:fromF-39-">fromF'</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => (a -> b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b</li><li class="src short"><a href="#v:pretty">pretty</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a></li><li class="src short"><a href="#v:prettyPrint">prettyPrint</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/System-IO.html#t:IO" title="System.IO">IO</a> ()</li></ul></details></div><div id="interface"><h1>Documentation</h1><div class="doc">LAoP (Linear Algebra of Programming) Inductive Matrix definition.LAoP generalises relations and functions treating them as

8+ Boolean matrices and in turn consider these as arrows.

9+ This library offers many of the combinators mentioned in the work of

10+ Macedo (2012) and Oliveira (2012).This definition is a wrapper around <code><a href="Matrix.html#v:Type" title="Matrix">Type</a></code> but

11+ dimensions are arbitrary data types. Type inference might not

12+ be as desired.</div><a href="#g:1" id="g:1"><h1>Type safe matrix representation</h1></a><div class="top">newtype <a id="t:Matrix" class="def">Matrix</a> e (cols :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) (rows :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) <a href="src/Matrix.Type.html#Matrix" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a><div class="subs constructors">Constructors<table><tr><td class="src"><a id="v:M" class="def">M</a> (Matrix e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><details id="i:Matrix" open="open"><summary>Instances</summary><table><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="/package/base-4.12.0.0/docs/Control-Category.html#t:Category" title="Control.Category">Category</a> (<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> -> <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> -> <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) <a href="src/Matrix.Type.html#line-174" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc">It isn't possible to implement the <code><a href="/package/base-4.12.0.0/docs/Data-Function.html#v:id" title="Data.Function">id</a></code> function so it's

13+ implementation is <code><a href="/package/base-4.12.0.0/docs/Prelude.html#v:undefined" title="Prelude">undefined</a></code>. However <code><a href="Matrix-Type.html#v:comp" title="Matrix.Type">comp</a></code> can be and this partial

14+ class implementation exists just to make the code more readable.Please use <code><a href="Matrix-Type.html#v:identity" title="Matrix.Type">identity</a></code> instead.</td></tr><tr><td colspan="2"><details id="i:id:Matrix:Category:1"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Type.html">Matrix.Type</a> <div class="subs methods">Methods<a href="#v:id">id</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a a <a href="#v:id" class="selflink">#</a><a href="#v:.">(.)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e b c -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a c <a href="#v:." class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> e => <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> (<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows) <a href="src/Matrix.Type.html#line-167" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:Eq:2"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Type.html">Matrix.Type</a> <div class="subs methods">Methods<a href="#v:-61--61-">(==)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a><a href="#v:-47--61-">(/=)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> (<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows) <a href="src/Matrix.Type.html#line-167" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:Num:3"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Type.html">Matrix.Type</a> <div class="subs methods">Methods<a href="#v:-43-">(+)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:-43-" class="selflink">#</a><a href="#v:-45-">(-)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:-45-" class="selflink">#</a><a href="#v:-42-">(*)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:-42-" class="selflink">#</a><a href="#v:negate">negate</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:negate" class="selflink">#</a><a href="#v:abs">abs</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:abs" class="selflink">#</a><a href="#v:signum">signum</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:signum" class="selflink">#</a><a href="#v:fromInteger">fromInteger</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Integer" title="Prelude">Integer</a> -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:fromInteger" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e => <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> (<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows) <a href="src/Matrix.Type.html#line-167" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:Ord:4"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Type.html">Matrix.Type</a> <div class="subs methods">Methods<a href="#v:compare">compare</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ordering" title="Data.Ord">Ordering</a> <a href="#v:compare" class="selflink">#</a><a href="#v:-60-">(<)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-60-" class="selflink">#</a><a href="#v:-60--61-">(<=)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-60--61-" class="selflink">#</a><a href="#v:-62-">(>)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-62-" class="selflink">#</a><a href="#v:-62--61-">(>=)</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-62--61-" class="selflink">#</a><a href="#v:max">max</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:max" class="selflink">#</a><a href="#v:min">min</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="#v:min" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e => <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> (<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows) <a href="src/Matrix.Type.html#line-167" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:Show:5"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Type.html">Matrix.Type</a> <div class="subs methods">Methods<a href="#v:showsPrec">showsPrec</a> :: <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:ShowS" title="Text.Show">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a><a href="#v:show">show</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a> <a href="#v:show" class="selflink">#</a><a href="#v:showList">showList</a> :: [<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows] -> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:ShowS" title="Text.Show">ShowS</a> <a href="#v:showList" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/deepseq-1.4.4.0/docs/Control-DeepSeq.html#t:NFData" title="Control.DeepSeq">NFData</a> e => <a href="/package/deepseq-1.4.4.0/docs/Control-DeepSeq.html#t:NFData" title="Control.DeepSeq">NFData</a> (<a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows) <a href="src/Matrix.Type.html#line-167" class="link">Source</a> <a href="#t:Matrix" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Matrix:NFData:6"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Type.html">Matrix.Type</a> <div class="subs methods">Methods<a href="#v:rnf">rnf</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> () <a href="#v:rnf" class="selflink">#</a></div></details></td></tr></table></details></div></div><a href="#g:2" id="g:2"><h1>Type aliases</h1></a><div class="top">type <a id="t:Zero" class="def">Zero</a> = <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a> <a href="src/Matrix.Type.html#Zero" class="link">Source</a> <a href="#t:Zero" class="selflink">#</a><div class="doc">Zero type alias</div></div><div class="top">type <a id="t:One" class="def">One</a> = () <a href="src/Matrix.Type.html#One" class="link">Source</a> <a href="#t:One" class="selflink">#</a><div class="doc">One type alias</div></div><a href="#g:3" id="g:3"><h1>Primitives</h1></a><div class="top"><a id="v:empty" class="def">empty</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e <a href="Matrix-Type.html#t:Zero" title="Matrix.Type">Zero</a> <a href="Matrix-Type.html#t:Zero" title="Matrix.Type">Zero</a> <a href="src/Matrix.Type.html#empty" class="link">Source</a> <a href="#v:empty" class="selflink">#</a><div class="doc">Empty matrix constructor</div></div><div class="top"><a id="v:one" class="def">one</a> :: e -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> <a href="src/Matrix.Type.html#one" class="link">Source</a> <a href="#v:one" class="selflink">#</a><div class="doc">Unit matrix constructor</div></div><div class="top"><a id="v:junc" class="def">junc</a> :: <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e b rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) rows <a href="src/Matrix.Type.html#junc" class="link">Source</a> <a href="#v:junc" class="selflink">#</a><div class="doc">Matrix <code>Junc</code> constructor</div></div><div class="top"><a id="v:split" class="def">split</a> :: <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) <a href="src/Matrix.Type.html#split" class="link">Source</a> <a href="#v:split" class="selflink">#</a><div class="doc">Matrix <code>Split</code> constructor</div></div><a href="#g:4" id="g:4"><h1>Auxiliary type families</h1></a><div class="top">type family <a id="t:FromNat" class="def">FromNat</a> (n :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> where ... <a href="src/Matrix.Internal.html#FromNat" class="link">Source</a> <a href="#t:FromNat" class="selflink">#</a><div class="doc">Type family that computes of a given type dimension from a given naturalThanks to Li-Yao Xia this type family is super fast.</div><div class="subs equations">Equations<table><tr><td class="src"><a href="Matrix-Type.html#t:FromNat" title="Matrix.Type">FromNat</a> 0 = <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:FromNat" title="Matrix.Type">FromNat</a> 1 = ()</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:FromNat" title="Matrix.Type">FromNat</a> n = FromNat' (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Mod" title="GHC.TypeNats">Mod</a> n 2 <a href="/package/base-4.12.0.0/docs/Data-Type-Equality.html#t:-61--61-" title="Data.Type.Equality">==</a> 0) (<a href="Matrix-Type.html#t:FromNat" title="Matrix.Type">FromNat</a> (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Div" title="GHC.TypeNats">Div</a> n 2))</td><td class="doc empty"> </td></tr></table></div></div><div class="top">type family <a id="t:Count" class="def">Count</a> (d :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a> where ... <a href="src/Matrix.Internal.html#Count" class="link">Source</a> <a href="#t:Count" class="selflink">#</a><div class="doc">Type family that computes the cardinality of a given type dimension.It can also count the cardinality of custom types that implement the

15+ <code><a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:Generic" title="GHC.Generics">Generic</a></code> instance.</div><div class="subs equations">Equations<table><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m) = (m <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-45-" title="GHC.TypeNats">-</a> n) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> 1</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) = <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">(+)</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a) (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> b)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (a, b) = <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a) (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> b)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (a -> b) = <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-94-" title="GHC.TypeNats">(^)</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> b) (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:M1" title="GHC.Generics">M1</a> _ _ f p) = <a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (f p)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:K1" title="GHC.Generics">K1</a> _ _ _) = 1</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:V1" title="GHC.Generics">V1</a> _) = 0</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:U1" title="GHC.Generics">U1</a> _) = 1</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t::-42-:" title="GHC.Generics">(:*:)</a> a b p) = <a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (a p) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-" title="GHC.TypeNats">*</a> <a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (b p)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t::-43-:" title="GHC.Generics">(:+:)</a> a b p) = <a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (a p) <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-" title="GHC.TypeNats">+</a> <a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (b p)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> d = <a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:Rep" title="GHC.Generics">Rep</a> d <a href="/package/base-4.12.0.0/docs/GHC-Generics.html#t:R" title="GHC.Generics">R</a>)</td><td class="doc empty"> </td></tr></table></div></div><div class="top">type family <a id="t:Normalize" class="def">Normalize</a> (d :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a>) :: <a href="/package/base-4.12.0.0/docs/Data-Kind.html#t:Type" title="Data.Kind">Type</a> where ... <a href="src/Matrix.Internal.html#Normalize" class="link">Source</a> <a href="#t:Normalize" class="selflink">#</a><div class="doc">Type family that normalizes the representation of a given data

16+ structure</div><div class="subs equations">Equations<table><tr><td class="src"><a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> d = <a href="Matrix-Type.html#t:FromNat" title="Matrix.Type">FromNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> d)</td><td class="doc empty"> </td></tr></table></div></div><a href="#g:5" id="g:5"><h1>Matrix construction and conversion</h1></a><div class="top">class <a id="t:FromLists" class="def">FromLists</a> e cols rows <a href="src/Matrix.Internal.html#FromLists" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a><div class="doc">Type class for defining the <code>fromList</code> conversion function.Given that it is not possible to branch on types at the term level type

17+ classes are needed bery much like an inductive definition but on types.</div><div class="subs minimal">Minimal complete definitionfromLists</div><div class="subs instances"><details id="i:FromLists" open="open"><summary>Instances</summary><table><tr><td class="src clearfix"> <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () () <a href="src/Matrix.Internal.html#line-311" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:1"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e () ()</div></details></td></tr><tr><td class="src clearfix"> <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a> <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a> <a href="src/Matrix.Internal.html#line-307" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:2"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a> <a href="/package/base-4.12.0.0/docs/Data-Void.html#t:Void" title="Data.Void">Void</a></div></details></td></tr><tr><td class="src clearfix"> (<a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () a, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () b, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a)) => <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) <a href="src/Matrix.Internal.html#line-329" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:3"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e () (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b)</div></details></td></tr><tr><td class="src clearfix"> <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () rows => <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> () rows) <a href="src/Matrix.Internal.html#line-325" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:4"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e () (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> () rows)</div></details></td></tr><tr><td class="src clearfix"> (<a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e a (), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e b (), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a)) => <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) () <a href="src/Matrix.Internal.html#line-319" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:5"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ()</div></details></td></tr><tr><td class="src clearfix"> <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e cols () => <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> () cols) () <a href="src/Matrix.Internal.html#line-315" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:6"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> () cols) ()</div></details></td></tr><tr><td class="src clearfix"> (<a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) c, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) d, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> c)) => <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> c d) <a href="src/Matrix.Internal.html#line-335" class="link">Source</a> <a href="#t:FromLists" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:ic:FromLists:FromLists:7"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Matrix-Internal.html">Matrix.Internal</a> <div class="subs methods">Methods<a href="#v:fromLists">fromLists</a> :: [[e]] -> Matrix e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> c d)</div></details></td></tr></table></details></div></div><div class="top"><a id="v:fromLists" class="def">fromLists</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows) => [[e]] -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#fromLists" class="link">Source</a> <a href="#v:fromLists" class="selflink">#</a><div class="doc">Build a matrix out of a list of list of elements. Throws a runtime

18+ error if the dimensions do not match.</div></div><div class="top"><a id="v:toLists" class="def">toLists</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> [[e]] <a href="src/Matrix.Type.html#toLists" class="link">Source</a> <a href="#v:toLists" class="selflink">#</a><div class="doc">Converts a matrix to a list of lists of elements.</div></div><div class="top"><a id="v:toList" class="def">toList</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> [e] <a href="src/Matrix.Type.html#toList" class="link">Source</a> <a href="#v:toList" class="selflink">#</a><div class="doc">Converts a matrix to a list of elements.</div></div><div class="top"><a id="v:matrixBuilder" class="def">matrixBuilder</a> :: (<a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))) => ((<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>, <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> e) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#matrixBuilder" class="link">Source</a> <a href="#v:matrixBuilder" class="selflink">#</a><div class="doc">Matrix builder function. Constructs a matrix provided with

19+ a construction function.</div></div><div class="top"><a id="v:row" class="def">row</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) () => [e] -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> <a href="src/Matrix.Type.html#row" class="link">Source</a> <a href="#v:row" class="selflink">#</a><div class="doc">Constructs a row vector matrix</div></div><div class="top"><a id="v:col" class="def">col</a> :: <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows) => [e] -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> rows <a href="src/Matrix.Type.html#col" class="link">Source</a> <a href="#v:col" class="selflink">#</a><div class="doc">Constructs a column vector matrix</div></div><div class="top"><a id="v:zeros" class="def">zeros</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#zeros" class="link">Source</a> <a href="#v:zeros" class="selflink">#</a><div class="doc">The zero matrix. A matrix wholly filled with zeros.</div></div><div class="top"><a id="v:ones" class="def">ones</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#ones" class="link">Source</a> <a href="#v:ones" class="selflink">#</a><div class="doc">The ones matrix. A matrix wholly filled with ones.Also known as T (Top) matrix.</div></div><div class="top"><a id="v:bang" class="def">bang</a> :: forall e cols. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols))) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> <a href="src/Matrix.Type.html#bang" class="link">Source</a> <a href="#v:bang" class="selflink">#</a><div class="doc">The T (Top) row vector matrix.</div></div><div class="top"><a id="v:constant" class="def">constant</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows))) => e -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#constant" class="link">Source</a> <a href="#v:constant" class="selflink">#</a><div class="doc">The constant matrix constructor. A matrix wholly filled with a given

20+ value.</div></div><a href="#g:6" id="g:6"><h1>Functor instance equivalent function</h1></a><div class="top"><a id="v:fmapM" class="def">fmapM</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => (a -> b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c b <a href="src/Matrix.Type.html#fmapM" class="link">Source</a> <a href="#v:fmapM" class="selflink">#</a><div class="doc">Functor instance equivalent function</div></div><a href="#g:7" id="g:7"><h1>Applicative/Monoidal instance equivalent functions</h1></a><div class="top"><a id="v:unitM" class="def">unitM</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e () () <a href="src/Matrix.Type.html#unitM" class="link">Source</a> <a href="#v:unitM" class="selflink">#</a><div class="doc">Applicative instance equivalent <code>unit</code> function,</div></div><div class="top"><a id="v:multM" class="def">multM</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b))), <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e c (a, b) <a href="src/Matrix.Type.html#multM" class="link">Source</a> <a href="#v:multM" class="selflink">#</a><div class="doc">Applicative instance equivalent <code>unit</code> function,</div></div><a href="#g:8" id="g:8"><h1>Selective equivalent instance function</h1></a><div class="top"><a id="v:selectM" class="def">selectM</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols b <a href="src/Matrix.Type.html#selectM" class="link">Source</a> <a href="#v:selectM" class="selflink">#</a><div class="doc">Selective functors <code>select</code> operator equivalent inspired by the

21+ ArrowMonad solution presented in the paper.</div></div><a href="#g:9" id="g:9"><h1>Monad equivalent instance function</h1></a><div class="top"><a id="v:returnM" class="def">returnM</a> :: forall e a. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> e, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> a)) => a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e <a href="Matrix-Type.html#t:One" title="Matrix.Type">One</a> a <a href="src/Matrix.Type.html#returnM" class="link">Source</a> <a href="#v:returnM" class="selflink">#</a><div class="doc">Monad instance equivalent <code><a href="/package/base-4.12.0.0/docs/Control-Monad.html#v:return" title="Control.Monad">return</a></code> function,</div></div><div class="top"><a id="v:bindM" class="def">bindM</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e b c -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a c <a href="src/Matrix.Type.html#bindM" class="link">Source</a> <a href="#v:bindM" class="selflink">#</a><div class="doc">Monad instance equivalent '(>>=)' function,</div></div><a href="#g:10" id="g:10"><h1>Misc</h1></a><a href="#g:11" id="g:11"><h2>Get dimensions</h2></a><div class="top"><a id="v:columns" class="def">columns</a> :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> <a href="src/Matrix.Type.html#columns" class="link">Source</a> <a href="#v:columns" class="selflink">#</a><div class="doc">Obtain the number of columns.NOTE: The <code><a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a></code> constaint is needed in order to obtain the

22+ dimensions in constant time.TODO: A <code><a href="Matrix-Type.html#v:columns" title="Matrix.Type">columns</a></code> function that does not need the <code><a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a></code> constraint in

23+ exchange for performance.</div></div><div class="top"><a id="v:rows" class="def">rows</a> :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> <a href="src/Matrix.Type.html#rows" class="link">Source</a> <a href="#v:rows" class="selflink">#</a><div class="doc">Obtain the number of rows.NOTE: The <code><a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a></code> constaint is needed in order to obtain the

24+ dimensions in constant time.TODO: A <code><a href="Matrix-Type.html#v:rows" title="Matrix.Type">rows</a></code> function that does not need the <code><a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a></code> constraint in

25+ exchange for performance.</div></div><a href="#g:12" id="g:12"><h2>Matrix Transposition</h2></a><div class="top"><a id="v:tr" class="def">tr</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e rows cols <a href="src/Matrix.Type.html#tr" class="link">Source</a> <a href="#v:tr" class="selflink">#</a><div class="doc">Matrix transposition.</div></div><a href="#g:13" id="g:13"><h2>McCarthy's Conditional</h2></a><div class="top"><a id="v:cond" class="def">cond</a> :: (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e () (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e) => (a -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a>) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b <a href="src/Matrix.Type.html#cond" class="link">Source</a> <a href="#v:cond" class="selflink">#</a><div class="doc">McCarthy's Conditional expresses probabilistic choice.</div></div><a href="#g:14" id="g:14"><h2>Matrix "abiding"</h2></a><div class="top"><a id="v:abideJS" class="def">abideJS</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#abideJS" class="link">Source</a> <a href="#v:abideJS" class="selflink">#</a><div class="doc">Matrix "abiding" followin the 'Junc'-'Split' abide law.Law:<pre><code>Junc</code> (<code>Split</code> a c) (<code>Split</code> b d) == <code>Split</code> (<code>Junc</code> a b) (<code>Junc</code> c d)

26+</pre></div></div><div class="top"><a id="v:abideSJ" class="def">abideSJ</a> :: <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#abideSJ" class="link">Source</a> <a href="#v:abideSJ" class="selflink">#</a><div class="doc">Matrix "abiding" followin the 'Split'-'Junc' abide law.Law:<pre><code>Split</code> (<code>Junc</code> a b) (<code>Junc</code> c d) == <code>Junc</code> (<code>Split</code> a c) (<code>Split</code> b d)

27+</pre></div></div><a href="#g:15" id="g:15"><h1>Biproduct approach</h1></a><a href="#g:16" id="g:16"><h2>Split</h2></a><div class="top"><a id="v:-61--61--61-" class="def">(===)</a> :: <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) infixl 2 <a href="src/Matrix.Type.html#%3D%3D%3D" class="link">Source</a> <a href="#v:-61--61--61-" class="selflink">#</a><div class="doc">Matrix <code>Split</code> constructor</div></div><a href="#g:17" id="g:17"><h3>Projections</h3></a><div class="top"><a id="v:p1" class="def">p1</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) m <a href="src/Matrix.Type.html#p1" class="link">Source</a> <a href="#v:p1" class="selflink">#</a><div class="doc">Biproduct first component projection</div></div><div class="top"><a id="v:p2" class="def">p2</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) n <a href="src/Matrix.Type.html#p2" class="link">Source</a> <a href="#v:p2" class="selflink">#</a><div class="doc">Biproduct second component projection</div></div><a href="#g:18" id="g:18"><h2>Junc</h2></a><div class="top"><a id="v:-124--124--124-" class="def">(|||)</a> :: <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e b rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> a b) rows infixl 3 <a href="src/Matrix.Type.html#%7C%7C%7C" class="link">Source</a> <a href="#v:-124--124--124-" class="selflink">#</a><div class="doc">Matrix <code>Junc</code> constructor</div></div><a href="#g:19" id="g:19"><h3>Injections</h3></a><div class="top"><a id="v:i1" class="def">i1</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e m (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) <a href="src/Matrix.Type.html#i1" class="link">Source</a> <a href="#v:i1" class="selflink">#</a><div class="doc">Biproduct first component injection</div></div><div class="top"><a id="v:i2" class="def">i2</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e n (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> m n) <a href="src/Matrix.Type.html#i2" class="link">Source</a> <a href="#v:i2" class="selflink">#</a><div class="doc">Biproduct second component injection</div></div><a href="#g:20" id="g:20"><h2>Bifunctors</h2></a><div class="top"><a id="v:-45--124--45-" class="def">(-|-)</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> n m) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> k j) ~ <a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> j)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e n k -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e m j -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> n m) (<a href="/package/base-4.12.0.0/docs/Data-Either.html#t:Either" title="Data.Either">Either</a> k j) infixl 5 <a href="src/Matrix.Type.html#-%7C-" class="link">Source</a> <a href="#v:-45--124--45-" class="selflink">#</a><div class="doc">Matrix coproduct functor also known as matrix direct sum.</div></div><div class="top"><a id="v:-62--60-" class="def">(><)</a> :: forall e m p n q. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> p)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> q)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, n))), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (p, q))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, n)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, n)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (p, q)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> p), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (p, q)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> q), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, n) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> n), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (p, q) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> p, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> q)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e m p -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e n q -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (m, n) (p, q) infixl 4 <a href="src/Matrix.Type.html#%3E%3C" class="link">Source</a> <a href="#v:-62--60-" class="selflink">#</a><div class="doc">Matrix product functor also known as kronecker product</div></div><a href="#g:21" id="g:21"><h2>Applicative matrix combinators</h2></a><div class="doc">Note that given the restrictions imposed it is not possible to

28+ implement the standard type classes present in standard Haskell.

29+ *** Matrix pairing projections</div><div class="top"><a id="v:kp1" class="def">kp1</a> :: forall e m k. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (m, k) m <a href="src/Matrix.Type.html#kp1" class="link">Source</a> <a href="#v:kp1" class="selflink">#</a><div class="doc">Khatri Rao product first component projection matrix.</div></div><div class="top"><a id="v:kp2" class="def">kp2</a> :: forall e m k. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (m, k) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> m, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> k)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e (m, k) k <a href="src/Matrix.Type.html#kp2" class="link">Source</a> <a href="#v:kp2" class="selflink">#</a><div class="doc">Khatri Rao product second component projection matrix.</div></div><a href="#g:22" id="g:22"><h3>Matrix pairing</h3></a><div class="top"><a id="v:khatri" class="def">khatri</a> :: forall e cols a b. (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b))), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b)) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b), <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (a, b) ~ <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a, <a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols a -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols b -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols (a, b) <a href="src/Matrix.Type.html#khatri" class="link">Source</a> <a href="#v:khatri" class="selflink">#</a><div class="doc">Khatri Rao Matrix product also known as matrix pairing.NOTE: That this is not a true categorical product, see for instance:<pre> | kp1 <code><a href="Matrix-Type.html#v:comp" title="Matrix.Type">comp</a></code> khatri a b == a

30+khatri a b ==> |

31+ | kp2 <code><a href="Matrix-Type.html#v:comp" title="Matrix.Type">comp</a></code> khatri a b == b

32+</pre>Emphasis on the implication symbol.</div></div><a href="#g:23" id="g:23"><h1>Matrix composition and lifting</h1></a><a href="#g:24" id="g:24"><h2>Arrow matrix combinators</h2></a><div class="doc">Note that given the restrictions imposed it is not possible to

33+ implement the standard type classes present in standard Haskell.</div><div class="top"><a id="v:identity" class="def">identity</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a))) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a a <a href="src/Matrix.Type.html#identity" class="link">Source</a> <a href="#v:identity" class="selflink">#</a><div class="doc">Identity matrix</div></div><div class="top"><a id="v:comp" class="def">comp</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cr rows -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols cr -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#comp" class="link">Source</a> <a href="#v:comp" class="selflink">#</a><div class="doc">Matrix composition. Equivalent to matrix-matrix multiplication.This definition takes advantage of divide-and-conquer and fusion laws

34+ from LAoP.</div></div><div class="top"><a id="v:fromF" class="def">fromF</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> rows) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)) => (a -> b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows <a href="src/Matrix.Type.html#fromF" class="link">Source</a> <a href="#v:fromF" class="selflink">#</a><div class="doc">Lifts functions to matrices with arbitrary dimensions.NOTE: Be careful to not ask for a matrix bigger than the cardinality of

35+ types <code>a</code> or <code>b</code> allows.</div></div><div class="top"><a id="v:fromF-39-" class="def">fromF'</a> :: (<a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> a, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> b, <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> b, <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> e, <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> e, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)), <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b)), <a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">FromLists</a> e (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> b) (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> a)) => (a -> b) -> <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e a b <a href="src/Matrix.Type.html#fromF%27" class="link">Source</a> <a href="#v:fromF-39-" class="selflink">#</a><div class="doc">Lifts functions to matrices with dimensions matching <code>a</code> and <code>b</code>

36+ cardinality's.</div></div><a href="#g:25" id="g:25"><h1>Matrix printing</h1></a><div class="top"><a id="v:pretty" class="def">pretty</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a> <a href="src/Matrix.Type.html#pretty" class="link">Source</a> <a href="#v:pretty" class="selflink">#</a><div class="doc">Matrix pretty printer</div></div><div class="top"><a id="v:prettyPrint" class="def">prettyPrint</a> :: (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> (<a href="Matrix-Type.html#t:Count" title="Matrix.Type">Count</a> (<a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Normalize</a> cols)), <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> e) => <a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix</a> e cols rows -> <a href="/package/base-4.12.0.0/docs/System-IO.html#t:IO" title="System.IO">IO</a> () <a href="src/Matrix.Type.html#prettyPrint" class="link">Source</a> <a href="#v:prettyPrint" class="selflink">#</a><div class="doc">Matrix pretty printer</div></div></div></div><div id="footer">Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.22.0</div></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/Utils.htmlnew file+52

@@ -0,0 +1,52 @@

2+ in Haskell. See <a href="https://github.com/bolt12/master-thesis">my Msc Thesis</a> for the

3+ motivation behind the library, the underlying theory, and implementation details.This module provides the <code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code> data type.

4+ The semantic associated with this data type is that

5+ it's meant to be a restricted <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code> value.</div></div><div id="synopsis"><details id="syn"><summary>Synopsis</summary><ul class="details-toggle" data-details-id="syn"><li class="src short">data <a href="#t:Natural">Natural</a> (start :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) (end :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>)</li><li class="src short"><a href="#v:nat">nat</a> :: forall n m. (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> n, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> m) => <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m</li><li class="src short"><a href="#v:coerceNat">coerceNat</a> :: (<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> a a' -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> b b' -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> c c'</li><li class="src short"><a href="#v:coerceNat2">coerceNat2</a> :: ((<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>, <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> a a', <a href="Utils.html#t:Natural" title="Utils">Natural</a> b b') -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> c c' -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> d d'</li><li class="src short"><a href="#v:coerceNat3">coerceNat3</a> :: (<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> a) -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> b b' -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> c c' -> a</li></ul></details></div><div id="interface"><h1>Documentation</h1><div class="doc">Utility module that provides the <code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code> data type.

6+ The semantic associated with this data type is that

7+ it's meant to be a restricted <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code> value. For example

8+ the type <code>Natural 1 6</code> can only be instanciated with <code>nat n</code>

9+ where <code>1 <= n <= 6</code>. Why, You might ask, because with normal

10+ <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code>s it is not possible to have a decent <code>Enum (Int, Int)</code>

11+ instance. See the following probabilistic programming model as and

12+ example:We want to calculate the probability of the sum of two dice throws.

13+ To do this we start by defining the sample space: <pre>type SampleSpace = Int -- We think <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code> are enough

14+

15+die :: Dist Int 6

16+die = unifrom [1..6]

17+

18+-- Promote <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code> addition to a matrix

19+addM = fromF (uncurry (+)) -- Impossible

20+</pre>The last line is impossible because <code>(Int, Int)</code> does not have

21+ a good <code><a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a></code> instance: <code>[(0, 1), (0, 2), .. (0, maxBound), (1, 0),

22+ ..]</code>. And we'd like the addition matrix to be of 36 columns by 12

23+ rows but limited to integers up to <code>6</code>!One way to solve this issue is by defining and auxilary data type to

24+ represent the sample space:<pre>data SampleSpace = S1 | S2 | S3 | S4 | S5 | S6

25+ deriving (Show, Eq, Enum, Bounded) -- Enum and Bounded are

26+ important

27+</pre>And write the sample space addition function:<pre>ssAdd :: SampleSpace -> SampleSpace -> Int

28+ssAdd a b = (fromEnum a + 1) + (fromEnum b + 1)

29+</pre>And then promote that function to matrix and everything is alright:<pre>ssAddM = fromF' (uncurry ssAdd)

30+

31+dieSumProb = ssAddM <code>comp</code> (khatri die die)

32+</pre>This is a nice solution for small sample spaces. But for larger ones

33+ it is not feasible to write a data type with hundreds of constructors

34+ and then write manipulation functions that need to deal with them.

35+ To mitigate this limitation the <code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code> type comes a long way and

36+ allows one to model the sample in an easier way. See for instance:<pre>ssAdd :: Natural 1 6 -> Natural 1 6 -> Natural 1 12

37+ssAdd = coerceNat (+)

38+

39+ssAddM = fromF' (uncurry sumSS)

40+

41+die :: Dist (Natural 1 6) 6

42+die = uniform [nat <code>1 </code>6 1 .. nat 6]

43+

44+dieSumProb = ssAddM <code>comp</code> (khatri die die)

45+</pre><ul><li><code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code> data type</li></ul></div><div class="top">data <a id="t:Natural" class="def">Natural</a> (start :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) (end :: <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat" title="GHC.TypeNats">Nat</a>) <a href="src/Utils.Internal.html#Natural" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a><div class="doc">Wrapper around <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code>s that have a restrictive semantic associated.

46+ A value of type <code><code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code> n m</code> can only be instanciated with some <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code>

47+ <code>i</code> that's <code>n <= i <= m</code>.</div><div class="subs instances"><details id="i:Natural" open="open"><summary>Instances</summary><table><tr><td class="src clearfix"> (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> n, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> m) => <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Bounded" title="Prelude">Bounded</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m) <a href="src/Utils.Internal.html#line-138" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Natural:Bounded:1"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Utils-Internal.html">Utils.Internal</a> <div class="subs methods">Methods<a href="#v:minBound">minBound</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:minBound" class="selflink">#</a><a href="#v:maxBound">maxBound</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:maxBound" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> n, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> m) => <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Enum" title="Prelude">Enum</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m) <a href="src/Utils.Internal.html#line-142" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Natural:Enum:2"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Utils-Internal.html">Utils.Internal</a> <div class="subs methods">Methods<a href="#v:succ">succ</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:succ" class="selflink">#</a><a href="#v:pred">pred</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:pred" class="selflink">#</a><a href="#v:toEnum">toEnum</a> :: <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:toEnum" class="selflink">#</a><a href="#v:fromEnum">fromEnum</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> <a href="#v:fromEnum" class="selflink">#</a><a href="#v:enumFrom">enumFrom</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> [<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m] <a href="#v:enumFrom" class="selflink">#</a><a href="#v:enumFromThen">enumFromThen</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> [<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m] <a href="#v:enumFromThen" class="selflink">#</a><a href="#v:enumFromTo">enumFromTo</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> [<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m] <a href="#v:enumFromTo" class="selflink">#</a><a href="#v:enumFromThenTo">enumFromThenTo</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> [<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m] <a href="#v:enumFromThenTo" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq" title="Data.Eq">Eq</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end) <a href="src/Utils.Internal.html#line-101" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Natural:Eq:3"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Utils-Internal.html">Utils.Internal</a> <div class="subs methods">Methods<a href="#v:-61--61-">(==)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-61--61-" class="selflink">#</a><a href="#v:-47--61-">(/=)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-47--61-" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> n, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> m) => <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Num" title="Prelude">Num</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> n m) <a href="src/Utils.Internal.html#line-105" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a></td><td class="doc">Throws a runtime error if any of the operations overflows or

48+ underflows.</td></tr><tr><td colspan="2"><details id="i:id:Natural:Num:4"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Utils-Internal.html">Utils.Internal</a> <div class="subs methods">Methods<a href="#v:-43-">(+)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:-43-" class="selflink">#</a><a href="#v:-45-">(-)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:-45-" class="selflink">#</a><a href="#v:-42-">(*)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:-42-" class="selflink">#</a><a href="#v:negate">negate</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:negate" class="selflink">#</a><a href="#v:abs">abs</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:abs" class="selflink">#</a><a href="#v:signum">signum</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:signum" class="selflink">#</a><a href="#v:fromInteger">fromInteger</a> :: <a href="/package/base-4.12.0.0/docs/Prelude.html#t:Integer" title="Prelude">Integer</a> -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="#v:fromInteger" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord" title="Data.Ord">Ord</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end) <a href="src/Utils.Internal.html#line-101" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Natural:Ord:5"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Utils-Internal.html">Utils.Internal</a> <div class="subs methods">Methods<a href="#v:compare">compare</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Data-Ord.html#t:Ordering" title="Data.Ord">Ordering</a> <a href="#v:compare" class="selflink">#</a><a href="#v:-60-">(<)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-60-" class="selflink">#</a><a href="#v:-60--61-">(<=)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-60--61-" class="selflink">#</a><a href="#v:-62-">(>)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-62-" class="selflink">#</a><a href="#v:-62--61-">(>=)</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool" title="Data.Bool">Bool</a> <a href="#v:-62--61-" class="selflink">#</a><a href="#v:max">max</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end <a href="#v:max" class="selflink">#</a><a href="#v:min">min</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end <a href="#v:min" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Text-Read.html#t:Read" title="Text.Read">Read</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end) <a href="src/Utils.Internal.html#line-101" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Natural:Read:6"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Utils-Internal.html">Utils.Internal</a> <div class="subs methods">Methods<a href="#v:readsPrec">readsPrec</a> :: <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Text-ParserCombinators-ReadP.html#t:ReadS" title="Text.ParserCombinators.ReadP">ReadS</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end) <a href="#v:readsPrec" class="selflink">#</a><a href="#v:readList">readList</a> :: <a href="/package/base-4.12.0.0/docs/Text-ParserCombinators-ReadP.html#t:ReadS" title="Text.ParserCombinators.ReadP">ReadS</a> [<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end] <a href="#v:readList" class="selflink">#</a><a href="#v:readPrec">readPrec</a> :: <a href="/package/base-4.12.0.0/docs/Text-ParserCombinators-ReadPrec.html#t:ReadPrec" title="Text.ParserCombinators.ReadPrec">ReadPrec</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end) <a href="#v:readPrec" class="selflink">#</a><a href="#v:readListPrec">readListPrec</a> :: <a href="/package/base-4.12.0.0/docs/Text-ParserCombinators-ReadPrec.html#t:ReadPrec" title="Text.ParserCombinators.ReadPrec">ReadPrec</a> [<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end] <a href="#v:readListPrec" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:Show" title="Text.Show">Show</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end) <a href="src/Utils.Internal.html#line-101" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Natural:Show:7"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Utils-Internal.html">Utils.Internal</a> <div class="subs methods">Methods<a href="#v:showsPrec">showsPrec</a> :: <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:ShowS" title="Text.Show">ShowS</a> <a href="#v:showsPrec" class="selflink">#</a><a href="#v:show">show</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> <a href="/package/base-4.12.0.0/docs/Data-String.html#t:String" title="Data.String">String</a> <a href="#v:show" class="selflink">#</a><a href="#v:showList">showList</a> :: [<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end] -> <a href="/package/base-4.12.0.0/docs/Text-Show.html#t:ShowS" title="Text.Show">ShowS</a> <a href="#v:showList" class="selflink">#</a></div></details></td></tr><tr><td class="src clearfix"> <a href="/package/deepseq-1.4.4.0/docs/Control-DeepSeq.html#t:NFData" title="Control.DeepSeq">NFData</a> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> start end) <a href="src/Utils.Internal.html#line-101" class="link">Source</a> <a href="#t:Natural" class="selflink">#</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><details id="i:id:Natural:NFData:8"><summary class="hide-when-js-enabled">Instance details</summary>Defined in <a href="Utils-Internal.html">Utils.Internal</a> <div class="subs methods">Methods<a href="#v:rnf">rnf</a> :: <a href="Utils.html#t:Natural" title="Utils">Natural</a> start end -> () <a href="#v:rnf" class="selflink">#</a></div></details></td></tr></table></details></div></div><div class="top"><a id="v:nat" class="def">nat</a> :: forall n m. (<a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> n, <a href="/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat" title="GHC.TypeNats">KnownNat</a> m) => <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> n m <a href="src/Utils.Internal.html#nat" class="link">Source</a> <a href="#v:nat" class="selflink">#</a><div class="doc">Natural constructor function. Throws a runtime error if the <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code>

49+ value is greater than the corresponding <code>m</code> or lower than <code>n</code> in the <code><code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code> n m</code> type.</div></div><a href="#g:1" id="g:1"><h1>Coerce auxiliar functions to help promote <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code> typed functions to</h1></a><div class="top"><a id="v:coerceNat" class="def">coerceNat</a> :: (<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> a a' -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> b b' -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> c c' <a href="src/Utils.Internal.html#coerceNat" class="link">Source</a> <a href="#v:coerceNat" class="selflink">#</a><div class="doc">Auxiliary function that promotes binary <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code> functions to <code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code>

50+ binary functions.</div></div><div class="top"><a id="v:coerceNat2" class="def">coerceNat2</a> :: ((<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>, <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a>) -> (<a href="Utils.html#t:Natural" title="Utils">Natural</a> a a', <a href="Utils.html#t:Natural" title="Utils">Natural</a> b b') -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> c c' -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> d d' <a href="src/Utils.Internal.html#coerceNat2" class="link">Source</a> <a href="#v:coerceNat2" class="selflink">#</a><div class="doc">Auxiliary function that promotes ternary (binary) <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code> functions to <code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code>

51+ functions.</div></div><div class="top"><a id="v:coerceNat3" class="def">coerceNat3</a> :: (<a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> <a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a> -> a) -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> b b' -> <a href="Utils.html#t:Natural" title="Utils">Natural</a> c c' -> a <a href="src/Utils.Internal.html#coerceNat3" class="link">Source</a> <a href="#v:coerceNat3" class="selflink">#</a><div class="doc">Auxiliary function that promotes ternary (binary) <code><a href="/package/base-4.12.0.0/docs/Data-Int.html#t:Int" title="Data.Int">Int</a></code> functions to <code><a href="Utils.html#t:Natural" title="Utils">Natural</a></code>

52+ functions.</div></div></div></div><div id="footer">Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.22.0</div></body></html>

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1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>laop-0.1.0.0: An inductive matrix definition library à la LAoP (Index)</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><link rel="stylesheet" type="text/css" href="quick-jump.css" /><script src="haddock-bundle.min.js" async="async" type="text/javascript"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="/package/laop-0.1.0.0">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul>laop-0.1.0.0: An inductive matrix definition library à la LAoP</div><div id="content"><div id="index">Index<table><tr><td class="src">-|-</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:-45--124--45-" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:-45--124--45-" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">===</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:-61--61--61-" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:-61--61--61-" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">><</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:-62--60-" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:-62--60-" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">abideJS</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:abideJS" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:abideJS" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">abideSJ</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:abideSJ" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:abideSJ" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">bang</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:bang" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:bang" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">bindD</td><td class="module"><a href="Dist.html#v:bindD" title="Dist">Dist</a></td></tr><tr><td class="src">bindM</td><td class="module"><a href="Matrix-Type.html#v:bindM" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="src">choose</td><td class="module"><a href="Dist.html#v:choose" title="Dist">Dist</a></td></tr><tr><td class="src">coerceNat</td><td class="module"><a href="Utils.html#v:coerceNat" title="Utils">Utils</a></td></tr><tr><td class="src">coerceNat2</td><td class="module"><a href="Utils.html#v:coerceNat2" title="Utils">Utils</a></td></tr><tr><td class="src">coerceNat3</td><td class="module"><a href="Utils.html#v:coerceNat3" title="Utils">Utils</a></td></tr><tr><td class="src">col</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:col" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:col" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">columns</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:columns" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:columns" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">comp</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:comp" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:comp" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">cond</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:cond" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:cond" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">constant</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:constant" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:constant" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">Count</td><td class="module"><a href="Matrix-Type.html#t:Count" title="Matrix.Type">Matrix.Type</a>, <a href="Matrix-Nat.html#t:Count" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">D</td><td class="module"><a href="Dist.html#v:D" title="Dist">Dist</a></td></tr><tr><td class="src">Dist</td><td class="module"><a href="Dist.html#t:Dist" title="Dist">Dist</a></td></tr><tr><td class="src">empty</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:empty" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:empty" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">fmapD</td><td class="module"><a href="Dist.html#v:fmapD" title="Dist">Dist</a></td></tr><tr><td class="src">fmapM</td><td class="module"><a href="Matrix-Type.html#v:fmapM" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="src">fromF</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:fromF" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:fromF" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">fromF'</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:fromF-39-" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:fromF-39-" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">FromLists</td><td class="module"><a href="Matrix-Type.html#t:FromLists" title="Matrix.Type">Matrix.Type</a>, <a href="Matrix-Nat.html#t:FromLists" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">fromLists</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:fromLists" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:fromLists" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">FromNat</td><td class="module"><a href="Matrix-Type.html#t:FromNat" title="Matrix.Type">Matrix.Type</a>, <a href="Matrix-Nat.html#t:FromNat" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">i1</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:i1" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:i1" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">i2</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:i2" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:i2" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">identity</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:identity" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:identity" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">junc</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:junc" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:junc" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">khatri</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:khatri" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:khatri" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">kp1</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:kp1" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:kp1" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">kp2</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:kp2" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:kp2" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">linear</td><td class="module"><a href="Dist.html#v:linear" title="Dist">Dist</a></td></tr><tr><td class="src">M</td><td> </td></tr><tr><td class="alt">1 (Data Constructor)</td><td class="module"><a href="Matrix-Type.html#v:M" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Data Constructor)</td><td class="module"><a href="Matrix-Nat.html#v:M" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">Matrix</td><td> </td></tr><tr><td class="alt">1 (Type/Class)</td><td class="module"><a href="Matrix-Type.html#t:Matrix" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Type/Class)</td><td class="module"><a href="Matrix-Nat.html#t:Matrix" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">matrixBuilder</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:matrixBuilder" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:matrixBuilder" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">multD</td><td class="module"><a href="Dist.html#v:multD" title="Dist">Dist</a></td></tr><tr><td class="src">multM</td><td class="module"><a href="Matrix-Type.html#v:multM" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="src">nat</td><td class="module"><a href="Utils.html#v:nat" title="Utils">Utils</a></td></tr><tr><td class="src">Natural</td><td class="module"><a href="Utils.html#t:Natural" title="Utils">Utils</a></td></tr><tr><td class="src">negExp</td><td class="module"><a href="Dist.html#v:negExp" title="Dist">Dist</a></td></tr><tr><td class="src">normal</td><td class="module"><a href="Dist.html#v:normal" title="Dist">Dist</a></td></tr><tr><td class="src">Normalize</td><td class="module"><a href="Matrix-Type.html#t:Normalize" title="Matrix.Type">Matrix.Type</a>, <a href="Matrix-Nat.html#t:Normalize" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">One</td><td class="module"><a href="Matrix-Type.html#t:One" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="src">one</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:one" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:one" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">ones</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:ones" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:ones" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">p1</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:p1" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:p1" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">p2</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:p2" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:p2" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">pretty</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:pretty" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:pretty" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">prettyDist</td><td class="module"><a href="Dist.html#v:prettyDist" title="Dist">Dist</a></td></tr><tr><td class="src">prettyPrint</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:prettyPrint" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:prettyPrint" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">prettyPrintDist</td><td class="module"><a href="Dist.html#v:prettyPrintDist" title="Dist">Dist</a></td></tr><tr><td class="src">Prob</td><td class="module"><a href="Dist.html#t:Prob" title="Dist">Dist</a></td></tr><tr><td class="src">returnD</td><td class="module"><a href="Dist.html#v:returnD" title="Dist">Dist</a></td></tr><tr><td class="src">returnM</td><td class="module"><a href="Matrix-Type.html#v:returnM" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="src">row</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:row" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:row" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">rows</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:rows" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:rows" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">select</td><td class="module"><a href="Matrix-Nat.html#v:select" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">selectD</td><td class="module"><a href="Dist.html#v:selectD" title="Dist">Dist</a></td></tr><tr><td class="src">selectM</td><td class="module"><a href="Matrix-Type.html#v:selectM" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="src">shape</td><td class="module"><a href="Dist.html#v:shape" title="Dist">Dist</a></td></tr><tr><td class="src">split</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:split" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:split" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">toList</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:toList" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:toList" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">toLists</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:toLists" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:toLists" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">toValues</td><td class="module"><a href="Dist.html#v:toValues" title="Dist">Dist</a></td></tr><tr><td class="src">tr</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:tr" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:tr" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">uniform</td><td class="module"><a href="Dist.html#v:uniform" title="Dist">Dist</a></td></tr><tr><td class="src">unitD</td><td class="module"><a href="Dist.html#v:unitD" title="Dist">Dist</a></td></tr><tr><td class="src">unitM</td><td class="module"><a href="Matrix-Type.html#v:unitM" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="src">Zero</td><td class="module"><a href="Matrix-Type.html#t:Zero" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="src">zeros</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:zeros" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:zeros" title="Matrix.Nat">Matrix.Nat</a></td></tr><tr><td class="src">|||</td><td> </td></tr><tr><td class="alt">1 (Function)</td><td class="module"><a href="Matrix-Type.html#v:-124--124--124-" title="Matrix.Type">Matrix.Type</a></td></tr><tr><td class="alt">2 (Function)</td><td class="module"><a href="Matrix-Nat.html#v:-124--124--124-" title="Matrix.Nat">Matrix.Nat</a></td></tr></table></div></div><div id="footer">Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.22.0</div></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/doc-index.jsonnew file+1

@@ -0,0 +1 @@

1+[{"display_html":"data <a href=\"#t:Natural\">Natural</a> (start :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat\" title=\"GHC.TypeNats\">Nat</a>) (end :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat\" title=\"GHC.TypeNats\">Nat</a>)","name":"Natural","module":"Utils","link":"Utils.html#t:Natural"},{"display_html":"<a href=\"#v:nat\">nat</a> :: forall n m. (<a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> n, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> m) => <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a> -> <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> n m","name":"nat","module":"Utils","link":"Utils.html#v:nat"},{"display_html":"<a href=\"#v:coerceNat\">coerceNat</a> :: (<a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a> -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a> -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>) -> <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> a a' -> <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> b b' -> <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> c c'","name":"coerceNat","module":"Utils","link":"Utils.html#v:coerceNat"},{"display_html":"<a href=\"#v:coerceNat2\">coerceNat2</a> :: ((<a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>, <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>) -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a> -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>) -> (<a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> a a', <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> b b') -> <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> c c' -> <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> d d'","name":"coerceNat2","module":"Utils","link":"Utils.html#v:coerceNat2"},{"display_html":"<a href=\"#v:coerceNat3\">coerceNat3</a> :: (<a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a> -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a> -> a) -> <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> b b' -> <a href=\"Utils.html#t:Natural\" title=\"Utils\">Natural</a> c c' -> a","name":"coerceNat3","module":"Utils","link":"Utils.html#v:coerceNat3"},{"display_html":"newtype <a href=\"#t:Matrix\">Matrix</a> e (cols :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a>) (rows :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a>) = <a href=\"#v:M\">M</a> (Matrix e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows))","name":"Matrix M","module":"Matrix.Type","link":"Matrix-Type.html#t:Matrix"},{"display_html":"type <a href=\"#t:Zero\">Zero</a> = <a href=\"/package/base-4.12.0.0/docs/Data-Void.html#t:Void\" title=\"Data.Void\">Void</a>","name":"Zero","module":"Matrix.Type","link":"Matrix-Type.html#t:Zero"},{"display_html":"type <a href=\"#t:One\">One</a> = ()","name":"One","module":"Matrix.Type","link":"Matrix-Type.html#t:One"},{"display_html":"<a href=\"#v:empty\">empty</a> :: <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e <a href=\"Matrix-Type.html#t:Zero\" title=\"Matrix.Type\">Zero</a> <a href=\"Matrix-Type.html#t:Zero\" title=\"Matrix.Type\">Zero</a>","name":"empty","module":"Matrix.Type","link":"Matrix-Type.html#v:empty"},{"display_html":"<a href=\"#v:one\">one</a> :: e -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e <a href=\"Matrix-Type.html#t:One\" title=\"Matrix.Type\">One</a> <a href=\"Matrix-Type.html#t:One\" title=\"Matrix.Type\">One</a>","name":"one","module":"Matrix.Type","link":"Matrix-Type.html#v:one"},{"display_html":"<a href=\"#v:junc\">junc</a> :: <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a rows -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e b rows -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) rows","name":"junc","module":"Matrix.Type","link":"Matrix-Type.html#v:junc"},{"display_html":"<a href=\"#v:split\">split</a> :: <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols a -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols b -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b)","name":"split","module":"Matrix.Type","link":"Matrix-Type.html#v:split"},{"display_html":"type family <a href=\"#t:FromNat\">FromNat</a> (n :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat\" title=\"GHC.TypeNats\">Nat</a>) :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a> where ...","name":"FromNat","module":"Matrix.Type","link":"Matrix-Type.html#t:FromNat"},{"display_html":"type family <a href=\"#t:Count\">Count</a> (d :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a>) :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat\" title=\"GHC.TypeNats\">Nat</a> where ...","name":"Count","module":"Matrix.Type","link":"Matrix-Type.html#t:Count"},{"display_html":"type family <a href=\"#t:Normalize\">Normalize</a> (d :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a>) :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a> where ...","name":"Normalize","module":"Matrix.Type","link":"Matrix-Type.html#t:Normalize"},{"display_html":"class <a href=\"#t:FromLists\">FromLists</a> e cols rows","name":"FromLists","module":"Matrix.Type","link":"Matrix-Type.html#t:FromLists"},{"display_html":"<a href=\"#v:fromLists\">fromLists</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows) => [[e]] -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"fromLists","module":"Matrix.Type","link":"Matrix-Type.html#v:fromLists"},{"display_html":"<a href=\"#v:toLists\">toLists</a> :: <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> [[e]]","name":"toLists","module":"Matrix.Type","link":"Matrix-Type.html#v:toLists"},{"display_html":"<a href=\"#v:toList\">toList</a> :: <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> [e]","name":"toList","module":"Matrix.Type","link":"Matrix-Type.html#v:toList"},{"display_html":"<a href=\"#v:matrixBuilder\">matrixBuilder</a> :: (<a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows))) => ((<a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>, <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>) -> e) -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"matrixBuilder","module":"Matrix.Type","link":"Matrix-Type.html#v:matrixBuilder"},{"display_html":"<a href=\"#v:row\">row</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols) () => [e] -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols <a href=\"Matrix-Type.html#t:One\" title=\"Matrix.Type\">One</a>","name":"row","module":"Matrix.Type","link":"Matrix-Type.html#v:row"},{"display_html":"<a href=\"#v:col\">col</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows) => [e] -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e <a href=\"Matrix-Type.html#t:One\" title=\"Matrix.Type\">One</a> rows","name":"col","module":"Matrix.Type","link":"Matrix-Type.html#v:col"},{"display_html":"<a href=\"#v:zeros\">zeros</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows))) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"zeros","module":"Matrix.Type","link":"Matrix-Type.html#v:zeros"},{"display_html":"<a href=\"#v:ones\">ones</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows))) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"ones","module":"Matrix.Type","link":"Matrix-Type.html#v:ones"},{"display_html":"<a href=\"#v:bang\">bang</a> :: forall e cols. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> e, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols) (), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols))) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols <a href=\"Matrix-Type.html#t:One\" title=\"Matrix.Type\">One</a>","name":"bang","module":"Matrix.Type","link":"Matrix-Type.html#v:bang"},{"display_html":"<a href=\"#v:constant\">constant</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows))) => e -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"constant","module":"Matrix.Type","link":"Matrix-Type.html#v:constant"},{"display_html":"<a href=\"#v:fmapM\">fmapM</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> b, <a href=\"/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq\" title=\"Data.Eq\">Eq</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord\" title=\"Data.Ord\">Ord</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)) => (a -> b) -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e c a -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e c b","name":"fmapM","module":"Matrix.Type","link":"Matrix-Type.html#v:fmapM"},{"display_html":"<a href=\"#v:unitM\">unitM</a> :: <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e () ()","name":"unitM","module":"Matrix.Type","link":"Matrix-Type.html#v:unitM"},{"display_html":"<a href=\"#v:multM\">multM</a> :: (<a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b))), <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b) ~ <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a, <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e c a -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e c b -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e c (a, b)","name":"multM","module":"Matrix.Type","link":"Matrix-Type.html#v:multM"},{"display_html":"<a href=\"#v:selectM\">selectM</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a b -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols b","name":"selectM","module":"Matrix.Type","link":"Matrix-Type.html#v:selectM"},{"display_html":"<a href=\"#v:returnM\">returnM</a> :: forall e a. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> e, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> a)) => a -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e <a href=\"Matrix-Type.html#t:One\" title=\"Matrix.Type\">One</a> a","name":"returnM","module":"Matrix.Type","link":"Matrix-Type.html#v:returnM"},{"display_html":"<a href=\"#v:bindM\">bindM</a> :: <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a b -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e b c -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a c","name":"bindM","module":"Matrix.Type","link":"Matrix-Type.html#v:bindM"},{"display_html":"<a href=\"#v:columns\">columns</a> :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>","name":"columns","module":"Matrix.Type","link":"Matrix-Type.html#v:columns"},{"display_html":"<a href=\"#v:rows\">rows</a> :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>","name":"rows","module":"Matrix.Type","link":"Matrix-Type.html#v:rows"},{"display_html":"<a href=\"#v:tr\">tr</a> :: <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e rows cols","name":"tr","module":"Matrix.Type","link":"Matrix-Type.html#v:tr"},{"display_html":"<a href=\"#v:cond\">cond</a> :: (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) ~ <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a), <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord\" title=\"Data.Ord\">Ord</a> e) => (a -> <a href=\"/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool\" title=\"Data.Bool\">Bool</a>) -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a b -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a b -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a b","name":"cond","module":"Matrix.Type","link":"Matrix-Type.html#v:cond"},{"display_html":"<a href=\"#v:abideJS\">abideJS</a> :: <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"abideJS","module":"Matrix.Type","link":"Matrix-Type.html#v:abideJS"},{"display_html":"<a href=\"#v:abideSJ\">abideSJ</a> :: <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"abideSJ","module":"Matrix.Type","link":"Matrix-Type.html#v:abideSJ"},{"display_html":"<a href=\"#v:-61--61--61-\">(===)</a> :: <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols a -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols b -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b)","name":"===","module":"Matrix.Type","link":"Matrix-Type.html#v:-61--61--61-"},{"display_html":"<a href=\"#v:p1\">p1</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> m n) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> m n) m","name":"p1","module":"Matrix.Type","link":"Matrix-Type.html#v:p1"},{"display_html":"<a href=\"#v:p2\">p2</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> m n) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> m n) n","name":"p2","module":"Matrix.Type","link":"Matrix-Type.html#v:p2"},{"display_html":"<a href=\"#v:-124--124--124-\">(|||)</a> :: <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a rows -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e b rows -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) rows","name":"|||","module":"Matrix.Type","link":"Matrix-Type.html#v:-124--124--124-"},{"display_html":"<a href=\"#v:i1\">i1</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> m n) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e m (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> m n)","name":"i1","module":"Matrix.Type","link":"Matrix-Type.html#v:i1"},{"display_html":"<a href=\"#v:i2\">i2</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> m n) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e n (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> m n)","name":"i2","module":"Matrix.Type","link":"Matrix-Type.html#v:i2"},{"display_html":"<a href=\"#v:-45--124--45-\">(-|-)</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> j)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> j) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> j), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> j) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> j), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> n m) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> k j) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> j)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e n k -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e m j -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> n m) (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> k j)","name":"-|-","module":"Matrix.Type","link":"Matrix-Type.html#v:-45--124--45-"},{"display_html":"<a href=\"#v:-62--60-\">(><)</a> :: forall e m p n q. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> p)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> q)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, n))), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (p, q))), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, n)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, n)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (p, q)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> p), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (p, q)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> q), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, n) ~ <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m, <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> n), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (p, q) ~ <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> p, <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> q)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e m p -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e n q -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e (m, n) (p, q)","name":"><","module":"Matrix.Type","link":"Matrix-Type.html#v:-62--60-"},{"display_html":"<a href=\"#v:kp1\">kp1</a> :: forall e m k. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, k))), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, k)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, k) ~ <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m, <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e (m, k) m","name":"kp1","module":"Matrix.Type","link":"Matrix-Type.html#v:kp1"},{"display_html":"<a href=\"#v:kp2\">kp2</a> :: forall e m k. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, k))), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, k)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (m, k) ~ <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> m, <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> k)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e (m, k) k","name":"kp2","module":"Matrix.Type","link":"Matrix-Type.html#v:kp2"},{"display_html":"<a href=\"#v:khatri\">khatri</a> :: forall e cols a b. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b))), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b) ~ <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a, <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols a -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols b -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols (a, b)","name":"khatri","module":"Matrix.Type","link":"Matrix-Type.html#v:khatri"},{"display_html":"<a href=\"#v:identity\">identity</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a))) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a a","name":"identity","module":"Matrix.Type","link":"Matrix-Type.html#v:identity"},{"display_html":"<a href=\"#v:comp\">comp</a> :: <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cr rows -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols cr -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"comp","module":"Matrix.Type","link":"Matrix-Type.html#v:comp"},{"display_html":"<a href=\"#v:fromF\">fromF</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> b, <a href=\"/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq\" title=\"Data.Eq\">Eq</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord\" title=\"Data.Ord\">Ord</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> rows) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)) => (a -> b) -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows","name":"fromF","module":"Matrix.Type","link":"Matrix-Type.html#v:fromF"},{"display_html":"<a href=\"#v:fromF-39-\">fromF'</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> b, <a href=\"/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq\" title=\"Data.Eq\">Eq</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord\" title=\"Data.Ord\">Ord</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> e (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)) => (a -> b) -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e a b","name":"fromF'","module":"Matrix.Type","link":"Matrix-Type.html#v:fromF-39-"},{"display_html":"<a href=\"#v:pretty\">pretty</a> :: (<a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)), <a href=\"/package/base-4.12.0.0/docs/Text-Show.html#t:Show\" title=\"Text.Show\">Show</a> e) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> <a href=\"/package/base-4.12.0.0/docs/Data-String.html#t:String\" title=\"Data.String\">String</a>","name":"pretty","module":"Matrix.Type","link":"Matrix-Type.html#v:pretty"},{"display_html":"<a href=\"#v:prettyPrint\">prettyPrint</a> :: (<a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> cols)), <a href=\"/package/base-4.12.0.0/docs/Text-Show.html#t:Show\" title=\"Text.Show\">Show</a> e) => <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> e cols rows -> <a href=\"/package/base-4.12.0.0/docs/System-IO.html#t:IO\" title=\"System.IO\">IO</a> ()","name":"prettyPrint","module":"Matrix.Type","link":"Matrix-Type.html#v:prettyPrint"},{"display_html":"newtype <a href=\"#t:Matrix\">Matrix</a> e (cols :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat\" title=\"GHC.TypeNats\">Nat</a>) (rows :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat\" title=\"GHC.TypeNats\">Nat</a>) = <a href=\"#v:M\">M</a> (Matrix e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows))","name":"Matrix M","module":"Matrix.Nat","link":"Matrix-Nat.html#t:Matrix"},{"display_html":"<a href=\"#v:empty\">empty</a> :: <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e 0 0","name":"empty","module":"Matrix.Nat","link":"Matrix-Nat.html#v:empty"},{"display_html":"<a href=\"#v:one\">one</a> :: e -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e 1 1","name":"one","module":"Matrix.Nat","link":"Matrix-Nat.html#v:one"},{"display_html":"<a href=\"#v:junc\">junc</a> :: <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols3 ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols1) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols2) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols1 rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols2 rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols3 rows","name":"junc","module":"Matrix.Nat","link":"Matrix-Nat.html#v:junc"},{"display_html":"<a href=\"#v:split\">split</a> :: <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows3 ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows1) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows2) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows1 -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows2 -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows3","name":"split","module":"Matrix.Nat","link":"Matrix-Nat.html#v:split"},{"display_html":"type family <a href=\"#t:FromNat\">FromNat</a> (n :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat\" title=\"GHC.TypeNats\">Nat</a>) :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a> where ...","name":"FromNat","module":"Matrix.Nat","link":"Matrix-Nat.html#t:FromNat"},{"display_html":"type family <a href=\"#t:Count\">Count</a> (d :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a>) :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:Nat\" title=\"GHC.TypeNats\">Nat</a> where ...","name":"Count","module":"Matrix.Nat","link":"Matrix-Nat.html#t:Count"},{"display_html":"type family <a href=\"#t:Normalize\">Normalize</a> (d :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a>) :: <a href=\"/package/base-4.12.0.0/docs/Data-Kind.html#t:Type\" title=\"Data.Kind\">Type</a> where ...","name":"Normalize","module":"Matrix.Nat","link":"Matrix-Nat.html#t:Normalize"},{"display_html":"class <a href=\"#t:FromLists\">FromLists</a> e cols rows","name":"FromLists","module":"Matrix.Nat","link":"Matrix-Nat.html#t:FromLists"},{"display_html":"<a href=\"#v:fromLists\">fromLists</a> :: <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows) => [[e]] -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"fromLists","module":"Matrix.Nat","link":"Matrix-Nat.html#v:fromLists"},{"display_html":"<a href=\"#v:toLists\">toLists</a> :: <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> [[e]]","name":"toLists","module":"Matrix.Nat","link":"Matrix-Nat.html#v:toLists"},{"display_html":"<a href=\"#v:toList\">toList</a> :: <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> [e]","name":"toList","module":"Matrix.Nat","link":"Matrix-Nat.html#v:toList"},{"display_html":"<a href=\"#v:matrixBuilder\">matrixBuilder</a> :: (<a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows))) => ((<a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>, <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>) -> e) -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"matrixBuilder","module":"Matrix.Nat","link":"Matrix-Nat.html#v:matrixBuilder"},{"display_html":"<a href=\"#v:row\">row</a> :: <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) () => [e] -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols 1","name":"row","module":"Matrix.Nat","link":"Matrix-Nat.html#v:row"},{"display_html":"<a href=\"#v:col\">col</a> :: <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e () (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows) => [e] -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e 1 rows","name":"col","module":"Matrix.Nat","link":"Matrix-Nat.html#v:col"},{"display_html":"<a href=\"#v:zeros\">zeros</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows))) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"zeros","module":"Matrix.Nat","link":"Matrix-Nat.html#v:zeros"},{"display_html":"<a href=\"#v:ones\">ones</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows))) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"ones","module":"Matrix.Nat","link":"Matrix-Nat.html#v:ones"},{"display_html":"<a href=\"#v:bang\">bang</a> :: forall e cols. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> e, <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols))) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols 1","name":"bang","module":"Matrix.Nat","link":"Matrix-Nat.html#v:bang"},{"display_html":"<a href=\"#v:constant\">constant</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows))) => e -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"constant","module":"Matrix.Nat","link":"Matrix-Nat.html#v:constant"},{"display_html":"<a href=\"#v:columns\">columns</a> :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>","name":"columns","module":"Matrix.Nat","link":"Matrix-Nat.html#v:columns"},{"display_html":"<a href=\"#v:rows\">rows</a> :: <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows)) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"/package/base-4.12.0.0/docs/Data-Int.html#t:Int\" title=\"Data.Int\">Int</a>","name":"rows","module":"Matrix.Nat","link":"Matrix-Nat.html#v:rows"},{"display_html":"<a href=\"#v:tr\">tr</a> :: <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e rows cols","name":"tr","module":"Matrix.Nat","link":"Matrix-Nat.html#v:tr"},{"display_html":"<a href=\"#v:select\">select</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows1) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows1), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows1)), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows2 ~ <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows1, <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols1 ~ <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols2, <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows3 ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols3) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows1)) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols1 rows3 -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols3 rows1 -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols2 rows2","name":"select","module":"Matrix.Nat","link":"Matrix-Nat.html#v:select"},{"display_html":"<a href=\"#v:cond\">cond</a> :: (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)) ~ <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e () (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols), <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord\" title=\"Data.Ord\">Ord</a> e) => (a -> <a href=\"/package/base-4.12.0.0/docs/Data-Bool.html#t:Bool\" title=\"Data.Bool\">Bool</a>) -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"cond","module":"Matrix.Nat","link":"Matrix-Nat.html#v:cond"},{"display_html":"<a href=\"#v:abideJS\">abideJS</a> :: <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"abideJS","module":"Matrix.Nat","link":"Matrix-Nat.html#v:abideJS"},{"display_html":"<a href=\"#v:abideSJ\">abideSJ</a> :: <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"abideSJ","module":"Matrix.Nat","link":"Matrix-Nat.html#v:abideSJ"},{"display_html":"<a href=\"#v:-61--61--61-\">(===)</a> :: <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows3 ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows1) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows2) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows1 -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows2 -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows3","name":"===","module":"Matrix.Nat","link":"Matrix-Nat.html#v:-61--61--61-"},{"display_html":"<a href=\"#v:p1\">p1</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> n) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n)) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> n) m","name":"p1","module":"Matrix.Nat","link":"Matrix-Nat.html#v:p1"},{"display_html":"<a href=\"#v:p2\">p2</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> n) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n)) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> n) n","name":"p2","module":"Matrix.Nat","link":"Matrix-Nat.html#v:p2"},{"display_html":"<a href=\"#v:-124--124--124-\">(|||)</a> :: <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols3 ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols1) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols2) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols1 rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols2 rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols3 rows","name":"|||","module":"Matrix.Nat","link":"Matrix-Nat.html#v:-124--124--124-"},{"display_html":"<a href=\"#v:i1\">i1</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (rows <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> n) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n)) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e rows (rows <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> n)","name":"i1","module":"Matrix.Nat","link":"Matrix-Nat.html#v:i1"},{"display_html":"<a href=\"#v:i2\">i2</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> rows) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows)) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e rows (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> rows)","name":"i2","module":"Matrix.Nat","link":"Matrix-Nat.html#v:i2"},{"display_html":"<a href=\"#v:-45--124--45-\">(-|-)</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> j)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> j) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> j), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> j) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> j), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (n <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> m) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (k <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> j) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> j)) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e n k -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e m j -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e (n <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> m) (k <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-43-\" title=\"GHC.TypeNats\">+</a> j)","name":"-|-","module":"Matrix.Nat","link":"Matrix-Nat.html#v:-45--124--45-"},{"display_html":"<a href=\"#v:-62--60-\">(><)</a> :: forall e m p n q. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> p)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> q)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> n))), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (p <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> q))), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> n)) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> n)) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (p <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> q)) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> p), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (p <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> q)) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> q), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> n) ~ <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> <a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> n)), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (p <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> q) ~ <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> p) <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> <a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> q))) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e m p -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e n q -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> n) (p <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> q)","name":"><","module":"Matrix.Nat","link":"Matrix-Nat.html#v:-62--60-"},{"display_html":"<a href=\"#v:kp1\">kp1</a> :: forall e m k. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> k))), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> k)) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> k) ~ <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> <a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k))) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> k) m","name":"kp1","module":"Matrix.Nat","link":"Matrix-Nat.html#v:kp1"},{"display_html":"<a href=\"#v:kp2\">kp2</a> :: forall e m k. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> k)) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> k))), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> k) ~ <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> m) <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> <a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> k))) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e (m <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> k) k","name":"kp2","module":"Matrix.Nat","link":"Matrix-Nat.html#v:kp2"},{"display_html":"<a href=\"#v:khatri\">khatri</a> :: forall e cols a b. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> a)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> b)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (a <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> b))), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (a <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> b)) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> a), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (a <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> b)) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> b), <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (a <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> b) ~ <a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> a) <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> <a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> b))) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols a -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols b -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols (a <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:-42-\" title=\"GHC.TypeNats\">*</a> b)","name":"khatri","module":"Matrix.Nat","link":"Matrix-Nat.html#v:khatri"},{"display_html":"<a href=\"#v:identity\">identity</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols))) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols cols","name":"identity","module":"Matrix.Nat","link":"Matrix-Nat.html#v:identity"},{"display_html":"<a href=\"#v:comp\">comp</a> :: <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cr rows -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols cr -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"comp","module":"Matrix.Nat","link":"Matrix-Nat.html#v:comp"},{"display_html":"<a href=\"#v:fromF\">fromF</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> b, <a href=\"/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq\" title=\"Data.Eq\">Eq</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord\" title=\"Data.Ord\">Ord</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> rows) (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)) => (a -> b) -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows","name":"fromF","module":"Matrix.Nat","link":"Matrix-Nat.html#v:fromF"},{"display_html":"<a href=\"#v:fromF-39-\">fromF'</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> b, <a href=\"/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq\" title=\"Data.Eq\">Eq</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Num\" title=\"Prelude\">Num</a> e, <a href=\"/package/base-4.12.0.0/docs/Data-Ord.html#t:Ord\" title=\"Data.Ord\">Ord</a> e, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:Normalize\" title=\"Matrix.Nat\">Normalize</a> a)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:Normalize\" title=\"Matrix.Nat\">Normalize</a> b)), <a href=\"Matrix-Nat.html#t:FromLists\" title=\"Matrix.Nat\">FromLists</a> e (<a href=\"Matrix-Nat.html#t:Normalize\" title=\"Matrix.Nat\">Normalize</a> b) (<a href=\"Matrix-Nat.html#t:Normalize\" title=\"Matrix.Nat\">Normalize</a> a)) => (a -> b) -> <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> a) (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> b)","name":"fromF'","module":"Matrix.Nat","link":"Matrix-Nat.html#v:fromF-39-"},{"display_html":"<a href=\"#v:pretty\">pretty</a> :: (<a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)), <a href=\"/package/base-4.12.0.0/docs/Text-Show.html#t:Show\" title=\"Text.Show\">Show</a> e) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"/package/base-4.12.0.0/docs/Data-String.html#t:String\" title=\"Data.String\">String</a>","name":"pretty","module":"Matrix.Nat","link":"Matrix-Nat.html#v:pretty"},{"display_html":"<a href=\"#v:prettyPrint\">prettyPrint</a> :: (<a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Nat.html#t:Count\" title=\"Matrix.Nat\">Count</a> (<a href=\"Matrix-Nat.html#t:FromNat\" title=\"Matrix.Nat\">FromNat</a> cols)), <a href=\"/package/base-4.12.0.0/docs/Text-Show.html#t:Show\" title=\"Text.Show\">Show</a> e) => <a href=\"Matrix-Nat.html#t:Matrix\" title=\"Matrix.Nat\">Matrix</a> e cols rows -> <a href=\"/package/base-4.12.0.0/docs/System-IO.html#t:IO\" title=\"System.IO\">IO</a> ()","name":"prettyPrint","module":"Matrix.Nat","link":"Matrix-Nat.html#v:prettyPrint"},{"display_html":"newtype <a href=\"#t:Dist\">Dist</a> a = <a href=\"#v:D\">D</a> (<a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> () a)","name":"Dist D","module":"Dist","link":"Dist.html#t:Dist"},{"display_html":"type <a href=\"#t:Prob\">Prob</a> = <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Double\" title=\"Prelude\">Double</a>","name":"Prob","module":"Dist","link":"Dist.html#t:Prob"},{"display_html":"<a href=\"#v:fmapD\">fmapD</a> :: (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Bounded\" title=\"Prelude\">Bounded</a> b, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> b, <a href=\"/package/base-4.12.0.0/docs/Data-Eq.html#t:Eq\" title=\"Data.Eq\">Eq</a> b, <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)) => (a -> b) -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> b","name":"fmapD","module":"Dist","link":"Dist.html#v:fmapD"},{"display_html":"<a href=\"#v:unitD\">unitD</a> :: <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> ()","name":"unitD","module":"Dist","link":"Dist.html#v:unitD"},{"display_html":"<a href=\"#v:multD\">multD</a> :: (<a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b))), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b)) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b), <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (a, b) ~ <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a, <a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b)) => <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> b -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> (a, b)","name":"multD","module":"Dist","link":"Dist.html#v:multD"},{"display_html":"<a href=\"#v:selectD\">selectD</a> :: (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) ~ <a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b), <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b) (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> b))) => <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> (<a href=\"/package/base-4.12.0.0/docs/Data-Either.html#t:Either\" title=\"Data.Either\">Either</a> a b) -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> a b -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> b","name":"selectD","module":"Dist","link":"Dist.html#v:selectD"},{"display_html":"<a href=\"#v:returnD\">returnD</a> :: forall a. (<a href=\"/package/base-4.12.0.0/docs/Prelude.html#t:Enum\" title=\"Prelude\">Enum</a> a, <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a), <a href=\"/package/base-4.12.0.0/docs/GHC-TypeNats.html#t:KnownNat\" title=\"GHC.TypeNats\">KnownNat</a> (<a href=\"Matrix-Type.html#t:Count\" title=\"Matrix.Type\">Count</a> a)) => a -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a","name":"returnD","module":"Dist","link":"Dist.html#v:returnD"},{"display_html":"<a href=\"#v:bindD\">bindD</a> :: <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a -> <a href=\"Matrix-Type.html#t:Matrix\" title=\"Matrix.Type\">Matrix</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> a b -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> b","name":"bindD","module":"Dist","link":"Dist.html#v:bindD"},{"display_html":"<a href=\"#v:choose\">choose</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) => <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a","name":"choose","module":"Dist","link":"Dist.html#v:choose"},{"display_html":"<a href=\"#v:shape\">shape</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) => (<a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> -> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a>) -> [a] -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a","name":"shape","module":"Dist","link":"Dist.html#v:shape"},{"display_html":"<a href=\"#v:linear\">linear</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) => [a] -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a","name":"linear","module":"Dist","link":"Dist.html#v:linear"},{"display_html":"<a href=\"#v:uniform\">uniform</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) => [a] -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a","name":"uniform","module":"Dist","link":"Dist.html#v:uniform"},{"display_html":"<a href=\"#v:negExp\">negExp</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) => [a] -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a","name":"negExp","module":"Dist","link":"Dist.html#v:negExp"},{"display_html":"<a href=\"#v:normal\">normal</a> :: <a href=\"Matrix-Type.html#t:FromLists\" title=\"Matrix.Type\">FromLists</a> <a href=\"Dist.html#t:Prob\" title=\"Dist\">Prob</a> () (<a href=\"Matrix-Type.html#t:Normalize\" title=\"Matrix.Type\">Normalize</a> a) => [a] -> <a href=\"Dist.html#t:Dist\" title=\"Dist\">Dist</a> a","name":"normal","module":"Dist","link":"Dist.html#v:normal"},{"display_html":"<a href=\"#v:toValues\">toValues</a> :: forall a. 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1+-- Hoogle documentation, generated by Haddock

2+-- See Hoogle, http://www.haskell.org/hoogle/

5+-- | An inductive matrix definition library à la LAoP

6+--

7+-- Please see the README on GitHub at

8+-- <a>https://github.com/bolt12/laop#readme</a>

9+@package laop

10+@version 0.1.0.0

11+

12+

13+-- | LAoP is a library for algebraic (inductive) construction and

14+-- manipulation of matrices in Haskell. See <a>my Msc Thesis</a> for the

15+-- motivation behind the library, the underlying theory, and

16+-- implementation details.

17+--

18+-- This module provides the <a>Natural</a> data type. The semantic

19+-- associated with this data type is that it's meant to be a restricted

20+-- <a>Int</a> value.

21+module Utils

22+

23+-- | Wrapper around <a>Int</a>s that have a restrictive semantic

24+-- associated. A value of type <tt><a>Natural</a> n m</tt> can only be

25+-- instanciated with some <a>Int</a> <tt>i</tt> that's <tt>n <= i

26+-- <= m</tt>.

27+data Natural (start :: Nat) (end :: Nat)

28+

29+-- | Natural constructor function. Throws a runtime error if the <a>Int</a>

30+-- value is greater than the corresponding <tt>m</tt> or lower than

31+-- <tt>n</tt> in the <tt><a>Natural</a> n m</tt> type.

32+nat :: forall n m. (KnownNat n, KnownNat m) => Int -> Natural n m

33+

34+-- | Auxiliary function that promotes binary <a>Int</a> functions to

35+-- <a>Natural</a> binary functions.

36+coerceNat :: (Int -> Int -> Int) -> Natural a a' -> Natural b b' -> Natural c c'

37+

38+-- | Auxiliary function that promotes ternary (binary) <a>Int</a> functions

39+-- to <a>Natural</a> functions.

40+coerceNat2 :: ((Int, Int) -> Int -> Int) -> (Natural a a', Natural b b') -> Natural c c' -> Natural d d'

41+

42+-- | Auxiliary function that promotes ternary (binary) <a>Int</a> functions

43+-- to <a>Natural</a> functions.

44+coerceNat3 :: (Int -> Int -> a) -> Natural b b' -> Natural c c' -> a

45+

46+

47+-- | The LAoP discipline generalises relations and functions treating them

48+-- as Boolean matrices and in turn consider these as arrows.

49+--

50+-- LAoP is a library for algebraic (inductive) construction and

51+-- manipulation of matrices in Haskell. See <a>my Msc Thesis</a> for the

52+-- motivation behind the library, the underlying theory, and

53+-- implementation details.

54+--

55+-- This module offers a newtype wrapper around <a>Matrix</a> that uses

56+-- arbitrary types instead of canonical data types for the matrices

57+-- dimensions.

58+--

59+-- NOTE: If the types in the dimensions are custom they must need

60+-- to implement a <tt>Generic</tt> instance.

61+module Matrix.Type

62+newtype Matrix e (cols :: Type) (rows :: Type)

63+M :: Matrix e (Normalize cols) (Normalize rows) -> Matrix e

64+

65+-- | Zero type alias

66+type Zero = Void

67+

68+-- | One type alias

69+type One = ()

70+

71+-- | Empty matrix constructor

72+empty :: Matrix e Zero Zero

73+

74+-- | Unit matrix constructor

75+one :: e -> Matrix e One One

76+

77+-- | Matrix <tt>Junc</tt> constructor

78+junc :: Normalize (Either a b) ~ Either (Normalize a) (Normalize b) => Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

79+

80+-- | Matrix <tt>Split</tt> constructor

81+split :: Normalize (Either a b) ~ Either (Normalize a) (Normalize b) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

82+

83+-- | Type family that computes of a given type dimension from a given

84+-- natural

85+--

86+-- Thanks to Li-Yao Xia this type family is super fast.

87+type family FromNat (n :: Nat) :: Type

88+

89+-- | Type family that computes the cardinality of a given type dimension.

90+--

91+-- It can also count the cardinality of custom types that implement the

92+-- <a>Generic</a> instance.

93+type family Count (d :: Type) :: Nat

94+

95+-- | Type family that normalizes the representation of a given data

96+-- structure

97+type family Normalize (d :: Type) :: Type

98+

99+-- | Type class for defining the <tt>fromList</tt> conversion function.

100+--

101+-- Given that it is not possible to branch on types at the term level

102+-- type classes are needed bery much like an inductive definition but on

103+-- types.

104+class FromLists e cols rows

105+

106+-- | Build a matrix out of a list of list of elements. Throws a runtime

107+-- error if the dimensions do not match.

108+fromLists :: FromLists e (Normalize cols) (Normalize rows) => [[e]] -> Matrix e cols rows

109+

110+-- | Converts a matrix to a list of lists of elements.

111+toLists :: Matrix e cols rows -> [[e]]

112+

113+-- | Converts a matrix to a list of elements.

114+toList :: Matrix e cols rows -> [e]

115+

116+-- | Matrix builder function. Constructs a matrix provided with a

117+-- construction function.

118+matrixBuilder :: (FromLists e (Normalize cols) (Normalize rows), KnownNat (Count (Normalize cols)), KnownNat (Count (Normalize rows))) => ((Int, Int) -> e) -> Matrix e cols rows

119+

120+-- | Constructs a row vector matrix

121+row :: FromLists e (Normalize cols) () => [e] -> Matrix e cols One

122+

123+-- | Constructs a column vector matrix

124+col :: FromLists e () (Normalize rows) => [e] -> Matrix e One rows

125+

126+-- | The zero matrix. A matrix wholly filled with zeros.

127+zeros :: (Num e, FromLists e (Normalize cols) (Normalize rows), KnownNat (Count (Normalize cols)), KnownNat (Count (Normalize rows))) => Matrix e cols rows

128+

129+-- | The ones matrix. A matrix wholly filled with ones.

130+--

131+-- Also known as T (Top) matrix.

132+ones :: (Num e, FromLists e (Normalize cols) (Normalize rows), KnownNat (Count (Normalize cols)), KnownNat (Count (Normalize rows))) => Matrix e cols rows

133+

134+-- | The T (Top) row vector matrix.

135+bang :: forall e cols. (Num e, Enum e, FromLists e (Normalize cols) (), KnownNat (Count (Normalize cols))) => Matrix e cols One

136+

137+-- | The constant matrix constructor. A matrix wholly filled with a given

138+-- value.

139+constant :: (Num e, FromLists e (Normalize cols) (Normalize rows), KnownNat (Count (Normalize cols)), KnownNat (Count (Normalize rows))) => e -> Matrix e cols rows

140+

141+-- | Functor instance equivalent function

142+fmapM :: (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e, KnownNat (Count (Normalize a)), KnownNat (Count (Normalize b)), FromLists e (Normalize b) (Normalize a)) => (a -> b) -> Matrix e c a -> Matrix e c b

143+

144+-- | Applicative instance equivalent <tt>unit</tt> function,

145+unitM :: Num e => Matrix e () ()

146+

147+-- | Applicative instance equivalent <tt>unit</tt> function,

148+multM :: (KnownNat (Count (Normalize a)), KnownNat (Count (Normalize b)), KnownNat (Count (Normalize (a, b))), Num e, FromLists e (Normalize (a, b)) (Normalize a), FromLists e (Normalize (a, b)) (Normalize b), Normalize (a, b) ~ Normalize (Normalize a, Normalize b)) => Matrix e c a -> Matrix e c b -> Matrix e c (a, b)

149+

150+-- | Selective functors <tt>select</tt> operator equivalent inspired by the

151+-- ArrowMonad solution presented in the paper.

152+selectM :: (Num e, FromLists e (Normalize b) (Normalize b), KnownNat (Count (Normalize b)), Normalize (Either a b) ~ Either (Normalize a) (Normalize b)) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b

153+

154+-- | Monad instance equivalent <a>return</a> function,

155+returnM :: forall e a. (Num e, Enum e, Enum a, FromLists e () (Normalize a), KnownNat (Count a)) => a -> Matrix e One a

156+

157+-- | Monad instance equivalent '(>>=)' function,

158+bindM :: Num e => Matrix e a b -> Matrix e b c -> Matrix e a c

159+

160+-- | Obtain the number of columns.

161+--

162+-- NOTE: The <a>KnownNat</a> constaint is needed in order to obtain the

163+-- dimensions in constant time.

164+--

165+-- TODO: A <a>columns</a> function that does not need the <a>KnownNat</a>

166+-- constraint in exchange for performance.

167+columns :: KnownNat (Count (Normalize cols)) => Matrix e cols rows -> Int

168+

169+-- | Obtain the number of rows.

170+--

171+-- NOTE: The <a>KnownNat</a> constaint is needed in order to obtain the

172+-- dimensions in constant time.

173+--

174+-- TODO: A <a>rows</a> function that does not need the <a>KnownNat</a>

175+-- constraint in exchange for performance.

176+rows :: KnownNat (Count (Normalize rows)) => Matrix e cols rows -> Int

177+

178+-- | Matrix transposition.

179+tr :: Matrix e cols rows -> Matrix e rows cols

180+

181+-- | McCarthy's Conditional expresses probabilistic choice.

182+cond :: (Normalize (Normalize a) ~ Normalize a, KnownNat (Count (Normalize a)), FromLists e () (Normalize a), FromLists e (Normalize a) (), FromLists e (Normalize a) (Normalize a), Bounded a, Enum a, Num e, Ord e) => (a -> Bool) -> Matrix e a b -> Matrix e a b -> Matrix e a b

183+

184+-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.

185+--

186+-- Law:

187+--

188+-- <pre>

189+-- <tt>Junc</tt> (<tt>Split</tt> a c) (<tt>Split</tt> b d) == <tt>Split</tt> (<tt>Junc</tt> a b) (<tt>Junc</tt> c d)

190+-- </pre>

191+abideJS :: Matrix e cols rows -> Matrix e cols rows

192+

193+-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.

194+--

195+-- Law:

196+--

197+-- <pre>

198+-- <tt>Split</tt> (<tt>Junc</tt> a b) (<tt>Junc</tt> c d) == <tt>Junc</tt> (<tt>Split</tt> a c) (<tt>Split</tt> b d)

199+-- </pre>

200+abideSJ :: Matrix e cols rows -> Matrix e cols rows

201+

202+-- | Matrix <tt>Split</tt> constructor

203+(===) :: Normalize (Either a b) ~ Either (Normalize a) (Normalize b) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

204+infixl 2 ===

205+

206+-- | Biproduct first component projection

207+p1 :: (Num e, KnownNat (Count (Normalize n)), KnownNat (Count (Normalize m)), FromLists e (Normalize n) (Normalize m), FromLists e (Normalize m) (Normalize m), Normalize (Either m n) ~ Either (Normalize m) (Normalize n)) => Matrix e (Either m n) m

208+

209+-- | Biproduct second component projection

210+p2 :: (Num e, KnownNat (Count (Normalize n)), KnownNat (Count (Normalize m)), FromLists e (Normalize m) (Normalize n), FromLists e (Normalize n) (Normalize n), Normalize (Either m n) ~ Either (Normalize m) (Normalize n)) => Matrix e (Either m n) n

211+

212+-- | Matrix <tt>Junc</tt> constructor

213+(|||) :: Normalize (Either a b) ~ Either (Normalize a) (Normalize b) => Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

214+infixl 3 |||

215+

216+-- | Biproduct first component injection

217+i1 :: (Num e, KnownNat (Count (Normalize n)), KnownNat (Count (Normalize m)), FromLists e (Normalize n) (Normalize m), FromLists e (Normalize m) (Normalize m), Normalize (Either m n) ~ Either (Normalize m) (Normalize n)) => Matrix e m (Either m n)

218+

219+-- | Biproduct second component injection

220+i2 :: (Num e, KnownNat (Count (Normalize n)), KnownNat (Count (Normalize m)), FromLists e (Normalize m) (Normalize n), FromLists e (Normalize n) (Normalize n), Normalize (Either m n) ~ Either (Normalize m) (Normalize n)) => Matrix e n (Either m n)

221+

222+-- | Matrix coproduct functor also known as matrix direct sum.

223+(-|-) :: (Num e, KnownNat (Count (Normalize j)), KnownNat (Count (Normalize k)), FromLists e (Normalize k) (Normalize k), FromLists e (Normalize j) (Normalize k), FromLists e (Normalize k) (Normalize j), FromLists e (Normalize j) (Normalize j), Normalize (Either n m) ~ Either (Normalize n) (Normalize m), Normalize (Either k j) ~ Either (Normalize k) (Normalize j)) => Matrix e n k -> Matrix e m j -> Matrix e (Either n m) (Either k j)

224+infixl 5 -|-

225+

226+-- | Matrix product functor also known as kronecker product

227+(><) :: forall e m p n q. (Num e, KnownNat (Count (Normalize m)), KnownNat (Count (Normalize n)), KnownNat (Count (Normalize p)), KnownNat (Count (Normalize q)), KnownNat (Count (Normalize (m, n))), KnownNat (Count (Normalize (p, q))), FromLists e (Normalize (m, n)) (Normalize m), FromLists e (Normalize (m, n)) (Normalize n), FromLists e (Normalize (p, q)) (Normalize p), FromLists e (Normalize (p, q)) (Normalize q), Normalize (m, n) ~ Normalize (Normalize m, Normalize n), Normalize (p, q) ~ Normalize (Normalize p, Normalize q)) => Matrix e m p -> Matrix e n q -> Matrix e (m, n) (p, q)

228+infixl 4 ><

229+

230+-- | Khatri Rao product first component projection matrix.

231+kp1 :: forall e m k. (Num e, KnownNat (Count (Normalize m)), KnownNat (Count (Normalize k)), KnownNat (Count (Normalize (m, k))), FromLists e (Normalize (m, k)) (Normalize m), Normalize (m, k) ~ Normalize (Normalize m, Normalize k)) => Matrix e (m, k) m

232+

233+-- | Khatri Rao product second component projection matrix.

234+kp2 :: forall e m k. (Num e, KnownNat (Count (Normalize k)), KnownNat (Count (Normalize m)), KnownNat (Count (Normalize (m, k))), FromLists e (Normalize (m, k)) (Normalize k), Normalize (m, k) ~ Normalize (Normalize m, Normalize k)) => Matrix e (m, k) k

235+

236+-- | Khatri Rao Matrix product also known as matrix pairing.

237+--

238+-- NOTE: That this is not a true categorical product, see for instance:

239+--

240+-- <pre>

241+-- | kp1 <a>comp</a> khatri a b == a

242+-- khatri a b ==> |

243+-- | kp2 <a>comp</a> khatri a b == b

244+-- </pre>

245+--

246+-- Emphasis on the implication symbol.

247+khatri :: forall e cols a b. (Num e, KnownNat (Count (Normalize a)), KnownNat (Count (Normalize b)), KnownNat (Count (Normalize (a, b))), FromLists e (Normalize (a, b)) (Normalize a), FromLists e (Normalize (a, b)) (Normalize b), Normalize (a, b) ~ Normalize (Normalize a, Normalize b)) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a, b)

248+

249+-- | Identity matrix

250+identity :: (Num e, FromLists e (Normalize a) (Normalize a), KnownNat (Count (Normalize a))) => Matrix e a a

251+

252+-- | Matrix composition. Equivalent to matrix-matrix multiplication.

253+--

254+-- This definition takes advantage of divide-and-conquer and fusion laws

255+-- from LAoP.

256+comp :: Num e => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

257+

258+-- | Lifts functions to matrices with arbitrary dimensions.

259+--

260+-- NOTE: Be careful to not ask for a matrix bigger than the cardinality

261+-- of types <tt>a</tt> or <tt>b</tt> allows.

262+fromF :: (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e, KnownNat (Count (Normalize cols)), KnownNat (Count (Normalize rows)), FromLists e (Normalize rows) (Normalize cols)) => (a -> b) -> Matrix e cols rows

263+

264+-- | Lifts functions to matrices with dimensions matching <tt>a</tt> and

265+-- <tt>b</tt> cardinality's.

266+fromF' :: (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e, KnownNat (Count (Normalize a)), KnownNat (Count (Normalize b)), FromLists e (Normalize b) (Normalize a)) => (a -> b) -> Matrix e a b

267+

268+-- | Matrix pretty printer

269+pretty :: (KnownNat (Count (Normalize cols)), Show e) => Matrix e cols rows -> String

270+

271+-- | Matrix pretty printer

272+prettyPrint :: (KnownNat (Count (Normalize cols)), Show e) => Matrix e cols rows -> IO ()

273+instance Control.DeepSeq.NFData e => Control.DeepSeq.NFData (Matrix.Type.Matrix e cols rows)

274+instance GHC.Classes.Ord e => GHC.Classes.Ord (Matrix.Type.Matrix e cols rows)

275+instance GHC.Classes.Eq e => GHC.Classes.Eq (Matrix.Type.Matrix e cols rows)

276+instance GHC.Num.Num e => GHC.Num.Num (Matrix.Type.Matrix e cols rows)

277+instance GHC.Show.Show e => GHC.Show.Show (Matrix.Type.Matrix e cols rows)

278+instance GHC.Num.Num e => Control.Category.Category (Matrix.Type.Matrix e)

279+

280+

281+-- | The LAoP discipline generalises relations and functions treating them

282+-- as Boolean matrices and in turn consider these as arrows.

283+--

284+-- LAoP is a library for algebraic (inductive) construction and

285+-- manipulation of matrices in Haskell. See <a>my Msc Thesis</a> for the

286+-- motivation behind the library, the underlying theory, and

287+-- implementation details.

288+--

289+-- This module offers a newtype wrapper around <a>Matrix</a> that uses

290+-- type level naturals instead of standard data types for the matrices

291+-- dimensions.

292+module Matrix.Nat

293+newtype Matrix e (cols :: Nat) (rows :: Nat)

294+M :: Matrix e (FromNat cols) (FromNat rows) -> Matrix e

295+empty :: Matrix e 0 0

296+one :: e -> Matrix e 1 1

297+junc :: FromNat cols3 ~ Either (FromNat cols1) (FromNat cols2) => Matrix e cols1 rows -> Matrix e cols2 rows -> Matrix e cols3 rows

298+split :: FromNat rows3 ~ Either (FromNat rows1) (FromNat rows2) => Matrix e cols rows1 -> Matrix e cols rows2 -> Matrix e cols rows3

299+

300+-- | Type family that computes of a given type dimension from a given

301+-- natural

302+--

303+-- Thanks to Li-Yao Xia this type family is super fast.

304+type family FromNat (n :: Nat) :: Type

305+

306+-- | Type family that computes the cardinality of a given type dimension.

307+--

308+-- It can also count the cardinality of custom types that implement the

309+-- <a>Generic</a> instance.

310+type family Count (d :: Type) :: Nat

311+

312+-- | Type family that normalizes the representation of a given data

313+-- structure

314+type family Normalize (d :: Type) :: Type

315+

316+-- | Type class for defining the <tt>fromList</tt> conversion function.

317+--

318+-- Given that it is not possible to branch on types at the term level

319+-- type classes are needed bery much like an inductive definition but on

320+-- types.

321+class FromLists e cols rows

322+fromLists :: FromLists e (FromNat cols) (FromNat rows) => [[e]] -> Matrix e cols rows

323+toLists :: Matrix e cols rows -> [[e]]

324+toList :: Matrix e cols rows -> [e]

325+matrixBuilder :: (FromLists e (FromNat cols) (FromNat rows), KnownNat (Count (FromNat cols)), KnownNat (Count (FromNat rows))) => ((Int, Int) -> e) -> Matrix e cols rows

326+row :: FromLists e (FromNat cols) () => [e] -> Matrix e cols 1

327+col :: FromLists e () (FromNat rows) => [e] -> Matrix e 1 rows

328+zeros :: (Num e, FromLists e (FromNat cols) (FromNat rows), KnownNat (Count (FromNat cols)), KnownNat (Count (FromNat rows))) => Matrix e cols rows

329+ones :: (Num e, FromLists e (FromNat cols) (FromNat rows), KnownNat (Count (FromNat cols)), KnownNat (Count (FromNat rows))) => Matrix e cols rows

330+bang :: forall e cols. (Num e, Enum e, FromLists e (FromNat cols) (), KnownNat (Count (FromNat cols))) => Matrix e cols 1

331+constant :: (Num e, FromLists e (FromNat cols) (FromNat rows), KnownNat (Count (FromNat cols)), KnownNat (Count (FromNat rows))) => e -> Matrix e cols rows

332+columns :: KnownNat (Count (FromNat cols)) => Matrix e cols rows -> Int

333+rows :: KnownNat (Count (FromNat rows)) => Matrix e cols rows -> Int

334+tr :: Matrix e cols rows -> Matrix e rows cols

335+select :: (Num e, FromLists e (FromNat rows1) (FromNat rows1), KnownNat (Count (FromNat rows1)), FromNat rows2 ~ FromNat rows1, FromNat cols1 ~ FromNat cols2, FromNat rows3 ~ Either (FromNat cols3) (FromNat rows1)) => Matrix e cols1 rows3 -> Matrix e cols3 rows1 -> Matrix e cols2 rows2

336+cond :: (FromNat (Count (FromNat cols)) ~ FromNat cols, KnownNat (Count (FromNat cols)), FromLists e () (FromNat cols), FromLists e (FromNat cols) (), FromLists e (FromNat cols) (FromNat cols), Bounded a, Enum a, Num e, Ord e) => (a -> Bool) -> Matrix e cols rows -> Matrix e cols rows -> Matrix e cols rows

337+abideJS :: Matrix e cols rows -> Matrix e cols rows

338+abideSJ :: Matrix e cols rows -> Matrix e cols rows

339+(===) :: FromNat rows3 ~ Either (FromNat rows1) (FromNat rows2) => Matrix e cols rows1 -> Matrix e cols rows2 -> Matrix e cols rows3

340+infixl 2 ===

341+p1 :: (Num e, KnownNat (Count (FromNat n)), KnownNat (Count (FromNat m)), FromLists e (FromNat n) (FromNat m), FromLists e (FromNat m) (FromNat m), FromNat (m + n) ~ Either (FromNat m) (FromNat n)) => Matrix e (m + n) m

342+p2 :: (Num e, KnownNat (Count (FromNat n)), KnownNat (Count (FromNat m)), FromLists e (FromNat m) (FromNat n), FromLists e (FromNat n) (FromNat n), FromNat (m + n) ~ Either (FromNat m) (FromNat n)) => Matrix e (m + n) n

343+(|||) :: FromNat cols3 ~ Either (FromNat cols1) (FromNat cols2) => Matrix e cols1 rows -> Matrix e cols2 rows -> Matrix e cols3 rows

344+infixl 3 |||

345+i1 :: (Num e, KnownNat (Count (FromNat n)), KnownNat (Count (FromNat rows)), FromLists e (FromNat n) (FromNat rows), FromLists e (FromNat rows) (FromNat rows), FromNat (rows + n) ~ Either (FromNat rows) (FromNat n)) => Matrix e rows (rows + n)

346+i2 :: (Num e, KnownNat (Count (FromNat rows)), KnownNat (Count (FromNat m)), FromLists e (FromNat m) (FromNat rows), FromLists e (FromNat rows) (FromNat rows), FromNat (m + rows) ~ Either (FromNat m) (FromNat rows)) => Matrix e rows (m + rows)

347+(-|-) :: (Num e, KnownNat (Count (FromNat j)), KnownNat (Count (FromNat k)), FromLists e (FromNat k) (FromNat k), FromLists e (FromNat j) (FromNat k), FromLists e (FromNat k) (FromNat j), FromLists e (FromNat j) (FromNat j), FromNat (n + m) ~ Either (FromNat n) (FromNat m), FromNat (k + j) ~ Either (FromNat k) (FromNat j)) => Matrix e n k -> Matrix e m j -> Matrix e (n + m) (k + j)

348+infixl 5 -|-

349+(><) :: forall e m p n q. (Num e, KnownNat (Count (FromNat m)), KnownNat (Count (FromNat n)), KnownNat (Count (FromNat p)), KnownNat (Count (FromNat q)), KnownNat (Count (FromNat (m * n))), KnownNat (Count (FromNat (p * q))), FromLists e (FromNat (m * n)) (FromNat m), FromLists e (FromNat (m * n)) (FromNat n), FromLists e (FromNat (p * q)) (FromNat p), FromLists e (FromNat (p * q)) (FromNat q), FromNat (m * n) ~ FromNat (Count (FromNat m) * Count (FromNat n)), FromNat (p * q) ~ FromNat (Count (FromNat p) * Count (FromNat q))) => Matrix e m p -> Matrix e n q -> Matrix e (m * n) (p * q)

350+infixl 4 ><

351+kp1 :: forall e m k. (Num e, KnownNat (Count (FromNat m)), KnownNat (Count (FromNat k)), KnownNat (Count (FromNat (m * k))), FromLists e (FromNat (m * k)) (FromNat m), FromNat (m * k) ~ FromNat (Count (FromNat m) * Count (FromNat k))) => Matrix e (m * k) m

352+kp2 :: forall e m k. (Num e, KnownNat (Count (FromNat k)), FromLists e (FromNat (m * k)) (FromNat k), KnownNat (Count (FromNat m)), KnownNat (Count (FromNat (m * k))), FromNat (m * k) ~ FromNat (Count (FromNat m) * Count (FromNat k))) => Matrix e (m * k) k

353+khatri :: forall e cols a b. (Num e, KnownNat (Count (FromNat a)), KnownNat (Count (FromNat b)), KnownNat (Count (FromNat (a * b))), FromLists e (FromNat (a * b)) (FromNat a), FromLists e (FromNat (a * b)) (FromNat b), FromNat (a * b) ~ FromNat (Count (FromNat a) * Count (FromNat b))) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a * b)

354+identity :: (Num e, FromLists e (FromNat cols) (FromNat cols), KnownNat (Count (FromNat cols))) => Matrix e cols cols

355+comp :: Num e => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

356+fromF :: (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e, KnownNat (Count (FromNat cols)), KnownNat (Count (FromNat rows)), FromLists e (FromNat rows) (FromNat cols)) => (a -> b) -> Matrix e cols rows

357+fromF' :: (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e, KnownNat (Count (Normalize a)), KnownNat (Count (Normalize b)), FromLists e (Normalize b) (Normalize a)) => (a -> b) -> Matrix e (Count a) (Count b)

358+pretty :: (KnownNat (Count (FromNat cols)), Show e) => Matrix e cols rows -> String

359+prettyPrint :: (KnownNat (Count (FromNat cols)), Show e) => Matrix e cols rows -> IO ()

360+instance Control.DeepSeq.NFData e => Control.DeepSeq.NFData (Matrix.Nat.Matrix e cols rows)

361+instance GHC.Classes.Ord e => GHC.Classes.Ord (Matrix.Nat.Matrix e cols rows)

362+instance GHC.Classes.Eq e => GHC.Classes.Eq (Matrix.Nat.Matrix e cols rows)

363+instance GHC.Num.Num e => GHC.Num.Num (Matrix.Nat.Matrix e cols rows)

364+instance GHC.Show.Show e => GHC.Show.Show (Matrix.Nat.Matrix e cols rows)

365+instance GHC.Num.Num e => Control.Category.Category (Matrix.Nat.Matrix e)

366+

367+

368+-- | LAoP is a library for algebraic (inductive) construction and

369+-- manipulation of matrices in Haskell. See <a>my Msc Thesis</a> for the

370+-- motivation behind the library, the underlying theory, and

371+-- implementation details.

372+--

373+-- This module exports a type synonym <a>Dist</a> that represents a

374+-- stochastic distribution matrix and several distribution construction

375+-- functions.

376+module Dist

377+

378+-- | Type synonym for column vector matrices. This represents a probability

379+-- distribution.

380+newtype Dist a

381+D :: Matrix Prob () a -> Dist a

382+

383+-- | Type synonym for probability value

384+type Prob = Double

385+

386+-- | Functor instance

387+fmapD :: (Bounded a, Bounded b, Enum a, Enum b, Eq b, KnownNat (Count (Normalize a)), KnownNat (Count (Normalize b)), FromLists Prob (Normalize b) (Normalize a)) => (a -> b) -> Dist a -> Dist b

388+

389+-- | Applicative/Monoidal instance <tt>unit</tt> function

390+unitD :: Dist ()

391+

392+-- | Applicative/Monoidal instance <tt>mult</tt> function

393+multD :: (KnownNat (Count (Normalize a)), KnownNat (Count (Normalize b)), KnownNat (Count (Normalize (a, b))), FromLists Prob (Normalize (a, b)) (Normalize a), FromLists Prob (Normalize (a, b)) (Normalize b), Normalize (a, b) ~ Normalize (Normalize a, Normalize b)) => Dist a -> Dist b -> Dist (a, b)

394+

395+-- | Selective instance function

396+selectD :: (Normalize (Either a b) ~ Either (Normalize a) (Normalize b), FromLists Prob (Normalize b) (Normalize b), KnownNat (Count (Normalize b))) => Dist (Either a b) -> Matrix Prob a b -> Dist b

397+

398+-- | Monad instance <a>return</a> function

399+returnD :: forall a. (Enum a, FromLists Prob () (Normalize a), KnownNat (Count a)) => a -> Dist a

400+

401+-- | Monad instance '(>>=)' function

402+bindD :: Dist a -> Matrix Prob a b -> Dist b

403+

404+-- | Constructs a Bernoulli distribution

405+choose :: FromLists Prob () (Normalize a) => Prob -> Dist a

406+

407+-- | Creates a distribution given a shape function

408+shape :: FromLists Prob () (Normalize a) => (Prob -> Prob) -> [a] -> Dist a

409+

410+-- | Constructs a Linear distribution

411+linear :: FromLists Prob () (Normalize a) => [a] -> Dist a

412+

413+-- | Constructs an Uniform distribution

414+uniform :: FromLists Prob () (Normalize a) => [a] -> Dist a

415+

416+-- | Constructs an Negative Exponential distribution

417+negExp :: FromLists Prob () (Normalize a) => [a] -> Dist a

418+

419+-- | Constructs an Normal distribution

420+normal :: FromLists Prob () (Normalize a) => [a] -> Dist a

421+

422+-- | Transforms a <a>Dist</a> into a list of pairs.

423+toValues :: forall a. (Enum a, KnownNat (Count a), FromLists Prob () (Normalize a)) => Dist a -> [(a, Prob)]

424+

425+-- | Pretty a distribution

426+prettyDist :: forall a. (Show a, Enum a, KnownNat (Count a), FromLists Prob () (Normalize a)) => Dist a -> String

427+

428+-- | Pretty Print a distribution

429+prettyPrintDist :: forall a. (Show a, Enum a, KnownNat (Count a), FromLists Prob () (Normalize a)) => Dist a -> IO ()

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445+

446+.doc table {

447+ border-collapse: collapse;

448+ border-spacing: 0px;

449+}

450+

451+.doc th,

452+.doc td {

453+ padding: 5px;

454+ border: 1px solid #ddd;

455+}

456+

457+.doc th {

458+ background-color: #f0f0f0;

459+}

460+

461+.clearfix:after {

462+ clear: both;

463+ content: " ";

464+ display: block;

465+ height: 0;

466+ visibility: hidden;

467+}

468+

469+.subs ul {

470+ list-style: none;

471+ display: table;

472+ margin: 0;

473+}

474+

475+.subs ul li {

476+ display: table-row;

477+}

478+

479+.subs ul li dfn {

480+ display: table-cell;

481+ font-style: normal;

482+ font-weight: bold;

483+ margin: 1px 0;

484+ white-space: nowrap;

485+}

486+

487+.subs ul li > .doc {

488+ display: table-cell;

489+ padding-left: 0.5em;

490+ margin-bottom: 0.5em;

491+}

492+

493+.subs ul li > .doc p {

494+ margin: 0;

495+}

496+

497+/* Render short-style data instances */

498+.inst ul {

499+ height: 100%;

500+ padding: 0.5em;

501+ margin: 0;

502+}

503+

504+.inst, .inst li {

505+ list-style: none;

506+ margin-left: 1em;

507+}

508+

509+/* Workaround for bug in Firefox (issue #384) */

510+.inst-left {

511+ float: left;

512+}

513+

514+.top p.src {

515+ border-top: 1px solid #ccc;

516+}

517+

518+.subs, .doc {

519+ /* use this selector for one level of indent */

520+ padding-left: 2em;

521+}

522+

523+.warning {

524+ color: red;

525+}

526+

527+.arguments {

528+ margin-top: -0.4em;

529+}

530+.arguments .caption {

531+ display: none;

532+}

533+

534+.fields { padding-left: 1em; }

535+

536+.fields .caption { display: none; }

537+

538+.fields p { margin: 0 0; }

539+

540+/* this seems bulky to me

541+.methods, .constructors {

542+ background: #f8f8f8;

543+ border: 1px solid #eee;

544+}

545+*/

546+

547+/* @end */

548+

549+/* @group Auxillary Pages */

550+

551+

552+.extension-list {

553+ list-style-type: none;

554+ margin-left: 0;

555+}

556+

557+#mini {

558+ margin: 0 auto;

559+ padding: 0 1em 1em;

560+}

561+

562+#mini > * {

563+ font-size: 93%; /* 12pt */

564+}

565+

566+#mini #module-list .caption,

567+#mini #module-header .caption {

568+ font-size: 125%; /* 15pt */

569+}

570+

571+#mini #interface h1,

572+#mini #interface h2,

573+#mini #interface h3,

574+#mini #interface h4 {

575+ font-size: 109%; /* 13pt */

576+ margin: 1em 0 0;

577+}

578+

579+#mini #interface .top,

580+#mini #interface .src {

581+ margin: 0;

582+}

583+

584+#mini #module-list ul {

585+ list-style: none;

586+ margin: 0;

587+}

588+

589+#alphabet ul {

590+ list-style: none;

591+ padding: 0;

592+ margin: 0.5em 0 0;

593+ text-align: center;

594+}

595+

596+#alphabet li {

597+ display: inline;

598+ margin: 0 0.25em;

599+}

600+

601+#alphabet a {

602+ font-weight: bold;

603+}

604+

605+#index .caption,

606+#module-list .caption { font-size: 131%; /* 17pt */ }

607+

608+#index table {

609+ margin-left: 2em;

610+}

611+

612+#index .src {

613+ font-weight: bold;

614+}

615+#index .alt {

616+ font-size: 77%; /* 10pt */

617+ font-style: italic;

618+ padding-left: 2em;

619+}

620+

621+#index td + td {

622+ padding-left: 1em;

623+}

624+

625+#module-list ul {

626+ list-style: none;

627+ margin: 0 0 0 2em;

628+}

629+

630+#module-list li {

631+ clear: right;

632+}

633+

634+#module-list span.collapser,

635+#module-list span.expander {

636+ background-position: 0 0.3em;

637+}

638+

639+#module-list .package {

640+ float: right;

641+}

642+

643+:target {

644+ background-color: #ffff00;

645+}

646+

647+/* @end */

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1+/* @group Search box layout */

3+#search {

4+ position: fixed;

5+ top: 3.2em;

6+ bottom: 0;

7+ left: calc(50% - 22em);

8+ width: 44em;

9+ z-index: 1000;

10+ pointer-events: none;

11+ overflow-y: auto;

12+}

13+

14+#search.hidden {

15+ display: none;

16+}

17+

18+#search-form, #search-results {

19+ box-shadow: 2px 2px 6px rgb(199, 204, 208);

20+ pointer-events: all;

21+}

22+

23+#search-form input {

24+ font-size: 1.25em; line-height: 2.3em; height: 2.4em;

25+ display: block;

26+ box-sizing: border-box;

27+ width: 100%;

28+ margin: 0;

29+ padding: 0 0.75em;

30+ border: 0.05em solid rgb(151, 179, 202);

31+}

32+

33+#search input:focus {

34+ outline: none;

35+}

36+

37+#search p.error {

38+ color: rgb(107, 24, 24);

39+ font-weight: bold;

40+}

41+

42+#search-results {

43+ box-sizing: border-box;

44+ border: 0.05em solid #b2d5fb;

45+ background: #e8f3ff;

46+}

47+

48+#search-form input + #search-results {

49+ border-top: none;

50+ top: 3em;

51+ max-height: calc(100% - 3em);

52+}

53+

54+/* @end */

55+

56+/* @group search results */

57+

58+#search-results > ul {

59+ margin: 0;

60+ list-style: none;

61+}

62+

63+#search-results > ul > li,

64+#search-results > p,

65+#search-results > table {

66+ padding: 0.5em 1em;

67+ margin: 0;

68+}

69+

70+#search-results > ul > li {

71+ border-bottom: 1px solid #b2d5fb;

72+}

73+

74+#search-results > ul > li > ul {

75+ list-style: none;

76+}

77+

78+.search-module h4 {

79+ margin: 0;

80+}

81+

82+.search-module > ul {

83+ margin: 0.5em 0 0.5em 2em;

84+}

85+

86+.search-module > ul > li > a[href] {

87+ display: block;

88+ color: inherit;

89+ padding: 0.25em 0.5em;

90+}

91+

92+.search-module > ul > li > a[href].active-link {

93+ background: #faf9dc;

94+}

95+

96+.search-module a[href]:hover {

97+ text-decoration: none;

98+}

99+

100+.search-result a a {

101+ pointer-events: none;

102+}

103+

104+.search-result ul.subs {

105+ display: inline-block;

106+ margin: 0; padding: 0;

107+}

108+

109+.search-result ul.subs li {

110+ display: none;

111+}

112+

113+.search-result ul.subs::after {

114+ display: inline-block;

115+ content: "...";

116+ color: rgb(78,98,114);

117+ margin: 0 0.25em;

118+}

119+

120+.more-results {

121+ color: rgb(99, 141, 173);

122+ position: relative;

123+}

124+

125+.more-results::before {

126+ content: "+";

127+ display: inline-block;

128+ color: #b2d5fb;

129+ font-weight: bold;

130+ font-size: 1.25em; line-height: inherit;

131+ position: absolute;

132+ left: -1em;

133+}

134+

135+/* @end */

136+

137+/* @group Keyboard shortcuts table */

138+

139+.keyboard-shortcuts {

140+ line-height: 1.6em;

141+}

142+

143+.keyboard-shortcuts th {

144+ color: rgb(78,98,114);

145+}

146+

147+.keyboard-shortcuts td:first-child,

148+.keyboard-shortcuts th:first-child {

149+ text-align: right;

150+ padding-right: 0.6em;

151+}

152+

153+.key {

154+ display: inline-block;

155+ font-size: 0.9em;

156+ min-width: 0.8em; line-height: 1.2em;

157+ text-align: center;

158+ background: #b2d5fb;

159+ border: 1px solid #74a3d6;

160+ padding: 0 0.2em;

161+ margin: 0 0.1em;

162+}

163+

164+/* @end */

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2+//# sourceMappingURL=quick-jump.min.js.map

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/src/Dist.Internal.htmlnew file+174

@@ -0,0 +1,174 @@

1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="style.css" /><script type="text/javascript" src="highlight.js"></script></head><body><pre>{-# LANGUAGE GADTs #-}

2+<a name="line-2"></a>{-# LANGUAGE AllowAmbiguousTypes #-}

3+<a name="line-3"></a>{-# LANGUAGE TypeApplications #-}

4+<a name="line-4"></a>{-# LANGUAGE KindSignatures #-}

5+<a name="line-5"></a>{-# LANGUAGE ScopedTypeVariables #-}

6+<a name="line-6"></a>{-# LANGUAGE FlexibleContexts #-}

7+<a name="line-7"></a>{-# LANGUAGE DataKinds #-}

8+<a name="line-8"></a>{-# LANGUAGE RankNTypes #-}

9+<a name="line-9"></a>

10+<a name="line-10"></a>module Dist.Internal

11+<a name="line-11"></a> (

12+<a name="line-12"></a> <a href="Dist.Internal.html#Dist">Dist</a>(..),

13+<a name="line-13"></a> <a href="Dist.Internal.html#Prob">Prob</a>,

14+<a name="line-14"></a>

15+<a name="line-15"></a> <a href="Dist.Internal.html#fmapD">fmapD</a>,

16+<a name="line-16"></a> <a href="Dist.Internal.html#unitD">unitD</a>,

17+<a name="line-17"></a> <a href="Dist.Internal.html#multD">multD</a>,

18+<a name="line-18"></a> <a href="Dist.Internal.html#selectD">selectD</a>,

19+<a name="line-19"></a> <a href="Dist.Internal.html#returnD">returnD</a>,

20+<a name="line-20"></a> <a href="Dist.Internal.html#bindD">bindD</a>,

21+<a name="line-21"></a> (<a href="Dist.Internal.html#%3F%3F">??</a>),

22+<a name="line-22"></a>

23+<a name="line-23"></a> <a href="Dist.Internal.html#choose">choose</a>,

24+<a name="line-24"></a> <a href="Dist.Internal.html#shape">shape</a>,

25+<a name="line-25"></a> <a href="Dist.Internal.html#linear">linear</a>,

26+<a name="line-26"></a> <a href="Dist.Internal.html#uniform">uniform</a>,

27+<a name="line-27"></a> <a href="Dist.Internal.html#negExp">negExp</a>,

28+<a name="line-28"></a> <a href="Dist.Internal.html#normal">normal</a>,

29+<a name="line-29"></a> <a href="Dist.Internal.html#toValues">toValues</a>,

30+<a name="line-30"></a> <a href="Dist.Internal.html#prettyDist">prettyDist</a>,

31+<a name="line-31"></a> <a href="Dist.Internal.html#prettyPrintDist">prettyPrintDist</a>

32+<a name="line-32"></a> )

33+<a name="line-33"></a> where

34+<a name="line-34"></a>

35+<a name="line-35"></a>import <a href="Matrix.Type.html">Matrix.Type</a>

36+<a name="line-36"></a>import <a href="Utils.html">Utils</a>

37+<a name="line-37"></a>import GHC.TypeLits

38+<a name="line-38"></a>import Data.Proxy

39+<a name="line-39"></a>import Data.List (sortBy)

40+<a name="line-40"></a>

41+<a name="line-41"></a>-- | Type synonym for probability value

42+<a name="line-42"></a>type <a name="Prob"><a href="Dist.Internal.html#Prob">Prob</a></a> = Double

43+<a name="line-43"></a>

44+<a name="line-44"></a>-- | Type synonym for column vector matrices. This represents a probability

45+<a name="line-45"></a>-- distribution.

46+<a name="line-46"></a>newtype <a name="Dist"><a href="Dist.Internal.html#Dist">Dist</a></a> <a name="local-6989586621679068539"><a href="#local-6989586621679068539">a</a></a> = <a name="D"><a href="Dist.Internal.html#D">D</a></a> (<a href="Matrix.Type.html#Matrix">Matrix</a> <a href="Dist.Internal.html#Prob">Prob</a> () <a href="#local-6989586621679068539">a</a>)

47+<a name="line-47"></a>

48+<a name="line-48"></a>-- | Functor instance

49+<a name="line-49"></a>fmapD ::

50+<a name="line-50"></a> ( Bounded <a href="#local-6989586621679068558">a</a>,

51+<a name="line-51"></a> Bounded <a href="#local-6989586621679068559">b</a>,

52+<a name="line-52"></a> Enum <a href="#local-6989586621679068558">a</a>,

53+<a name="line-53"></a> Enum <a href="#local-6989586621679068559">b</a>,

54+<a name="line-54"></a> Eq <a href="#local-6989586621679068559">b</a>,

55+<a name="line-55"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068558">a</a>)),

56+<a name="line-56"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068559">b</a>)),

57+<a name="line-57"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068559">b</a>) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068558">a</a>)

58+<a name="line-58"></a> )

59+<a name="line-59"></a> =>

60+<a name="line-60"></a> (<a href="#local-6989586621679068558">a</a> -> <a href="#local-6989586621679068559">b</a>) -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068558">a</a> -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068559">b</a>

61+<a name="line-61"></a><a name="fmapD"><a href="Dist.Internal.html#fmapD">fmapD</a></a> <a name="local-6989586621679068560"><a href="#local-6989586621679068560">f</a></a> (<a href="Dist.Internal.html#D">D</a> <a name="local-6989586621679068561"><a href="#local-6989586621679068561">m</a></a>) = <a href="Dist.Internal.html#D">D</a> (<a href="Matrix.Type.html#fromF%27">fromF'</a> <a href="#local-6989586621679068560">f</a> `<a href="Matrix.Type.html#comp">comp</a>` <a href="#local-6989586621679068561">m</a>)

62+<a name="line-62"></a>

63+<a name="line-63"></a>-- | Applicative/Monoidal instance 'unit' function

64+<a name="line-64"></a>unitD :: <a href="Dist.Internal.html#Dist">Dist</a> ()

65+<a name="line-65"></a><a name="unitD"><a href="Dist.Internal.html#unitD">unitD</a></a> = <a href="Dist.Internal.html#D">D</a> (<a href="Matrix.Type.html#one">one</a> 1)

66+<a name="line-66"></a>

67+<a name="line-67"></a>-- | Applicative/Monoidal instance 'mult' function

68+<a name="line-68"></a>multD ::

69+<a name="line-69"></a> ( KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068556">a</a>)),

70+<a name="line-70"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068557">b</a>)),

71+<a name="line-71"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679068556">a</a>, <a href="#local-6989586621679068557">b</a>))),

72+<a name="line-72"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679068556">a</a>, <a href="#local-6989586621679068557">b</a>)) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068556">a</a>),

73+<a name="line-73"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679068556">a</a>, <a href="#local-6989586621679068557">b</a>)) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068557">b</a>),

74+<a name="line-74"></a> Normalize (<a href="#local-6989586621679068556">a</a>, <a href="#local-6989586621679068557">b</a>) ~ <a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068556">a</a>, <a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068557">b</a>)

75+<a name="line-75"></a> ) => <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068556">a</a> -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068557">b</a> -> <a href="Dist.Internal.html#Dist">Dist</a> (<a href="#local-6989586621679068556">a</a>, <a href="#local-6989586621679068557">b</a>)

76+<a name="line-76"></a><a name="multD"><a href="Dist.Internal.html#multD">multD</a></a> (<a href="Dist.Internal.html#D">D</a> <a name="local-6989586621679068562"><a href="#local-6989586621679068562">a</a></a>) (<a href="Dist.Internal.html#D">D</a> <a name="local-6989586621679068563"><a href="#local-6989586621679068563">b</a></a>) = <a href="Dist.Internal.html#D">D</a> (<a href="Matrix.Type.html#khatri">khatri</a> <a href="#local-6989586621679068562">a</a> <a href="#local-6989586621679068563">b</a>)

77+<a name="line-77"></a>

78+<a name="line-78"></a>-- | Selective instance function

79+<a name="line-79"></a>selectD ::

80+<a name="line-80"></a> ( Normalize (Either <a href="#local-6989586621679068554">a</a> <a href="#local-6989586621679068555">b</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068554">a</a>) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068555">b</a>),

81+<a name="line-81"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068555">b</a>) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068555">b</a>),

82+<a name="line-82"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068555">b</a>))

83+<a name="line-83"></a> ) => <a href="Dist.Internal.html#Dist">Dist</a> (Either <a href="#local-6989586621679068554">a</a> <a href="#local-6989586621679068555">b</a>) -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="Dist.Internal.html#Prob">Prob</a> <a href="#local-6989586621679068554">a</a> <a href="#local-6989586621679068555">b</a> -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068555">b</a>

84+<a name="line-84"></a><a name="selectD"><a href="Dist.Internal.html#selectD">selectD</a></a> (<a href="Dist.Internal.html#D">D</a> <a name="local-6989586621679068564"><a href="#local-6989586621679068564">d</a></a>) <a name="local-6989586621679068565"><a href="#local-6989586621679068565">m</a></a> = <a href="Dist.Internal.html#D">D</a> (<a href="Matrix.Type.html#junc">junc</a> <a href="#local-6989586621679068565">m</a> <a href="Matrix.Type.html#identity">identity</a> `<a href="Matrix.Type.html#comp">comp</a>` <a href="#local-6989586621679068564">d</a>)

85+<a name="line-85"></a>

86+<a name="line-86"></a>

87+<a name="line-87"></a>-- | Monad instance 'return' function

88+<a name="line-88"></a>returnD :: forall <a name="local-6989586621679068553"><a href="#local-6989586621679068553">a</a></a> . (Enum <a href="#local-6989586621679068553">a</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068553">a</a>), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679068553">a</a>)) => <a href="#local-6989586621679068553">a</a> -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068553">a</a>

89+<a name="line-89"></a><a name="returnD"><a href="Dist.Internal.html#returnD">returnD</a></a> <a name="local-6989586621679068566"><a href="#local-6989586621679068566">a</a></a> = <a href="Dist.Internal.html#D">D</a> (<a href="Matrix.Type.html#col">col</a> <a href="#local-6989586621679068569">l</a>)

90+<a name="line-90"></a> where

91+<a name="line-91"></a> <a name="local-6989586621679068567"><a href="#local-6989586621679068567">i</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679068553">a</a>))

92+<a name="line-92"></a> <a name="local-6989586621679068568"><a href="#local-6989586621679068568">x</a></a> = fromEnum <a href="#local-6989586621679068566">a</a>

93+<a name="line-93"></a> <a name="local-6989586621679068569"><a href="#local-6989586621679068569">l</a></a> = take <a href="#local-6989586621679068568">x</a> [0,0..] ++ [1] ++ take (<a href="#local-6989586621679068567">i</a> - <a href="#local-6989586621679068568">x</a> - 1) [0,0..]

94+<a name="line-94"></a>

95+<a name="line-95"></a>-- | Monad instance '(>>=)' function

96+<a name="line-96"></a>bindD :: <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068551">a</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="Dist.Internal.html#Prob">Prob</a> <a href="#local-6989586621679068551">a</a> <a href="#local-6989586621679068552">b</a> -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068552">b</a>

97+<a name="line-97"></a><a name="bindD"><a href="Dist.Internal.html#bindD">bindD</a></a> (<a href="Dist.Internal.html#D">D</a> <a name="local-6989586621679068570"><a href="#local-6989586621679068570">d</a></a>) <a name="local-6989586621679068571"><a href="#local-6989586621679068571">m</a></a> = <a href="Dist.Internal.html#D">D</a> (<a href="#local-6989586621679068571">m</a> `<a href="Matrix.Type.html#comp">comp</a>` <a href="#local-6989586621679068570">d</a>)

98+<a name="line-98"></a>

99+<a name="line-99"></a>-- | Extract probabilities given an Event.

100+<a name="line-100"></a>(??) ::

101+<a name="line-101"></a> ( Enum <a href="#local-6989586621679068550">a</a>,

102+<a name="line-102"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679068550">a</a>),

103+<a name="line-103"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068550">a</a>)

104+<a name="line-104"></a> ) => (<a href="#local-6989586621679068550">a</a> -> Bool) -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068550">a</a> -> <a href="Dist.Internal.html#Prob">Prob</a>

105+<a name="line-105"></a>(<a name="%3F%3F"><a href="Dist.Internal.html#%3F%3F">??</a></a>) <a name="local-6989586621679068572"><a href="#local-6989586621679068572">p</a></a> <a name="local-6989586621679068573"><a href="#local-6989586621679068573">d</a></a> =

106+<a name="line-106"></a> let <a name="local-6989586621679068574"><a href="#local-6989586621679068574">l</a></a> = <a href="Dist.Internal.html#toValues">toValues</a> <a href="#local-6989586621679068573">d</a>

107+<a name="line-107"></a> <a name="local-6989586621679068575"><a href="#local-6989586621679068575">x</a></a> = filter (<a href="#local-6989586621679068572">p</a> . fst) <a href="#local-6989586621679068574">l</a>

108+<a name="line-108"></a> in sum . map snd $ <a href="#local-6989586621679068575">x</a>

109+<a name="line-109"></a>

110+<a name="line-110"></a>-- Distribution Construction

111+<a name="line-111"></a>

112+<a name="line-112"></a>-- | Constructs a Bernoulli distribution

113+<a name="line-113"></a>choose :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068549">a</a>)) => <a href="Dist.Internal.html#Prob">Prob</a> -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068549">a</a>

114+<a name="line-114"></a><a name="choose"><a href="Dist.Internal.html#choose">choose</a></a> <a name="local-6989586621679068576"><a href="#local-6989586621679068576">prob</a></a> = <a href="Dist.Internal.html#D">D</a> (<a href="Matrix.Type.html#col">col</a> [<a href="#local-6989586621679068576">prob</a>, 1 - <a href="#local-6989586621679068576">prob</a>])

115+<a name="line-115"></a>

116+<a name="line-116"></a>-- | Creates a distribution given a shape function

117+<a name="line-117"></a>shape :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068548">a</a>)) => (<a href="Dist.Internal.html#Prob">Prob</a> -> <a href="Dist.Internal.html#Prob">Prob</a>) -> [<a href="#local-6989586621679068548">a</a>] -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068548">a</a>

118+<a name="line-118"></a><a name="shape"><a href="Dist.Internal.html#shape">shape</a></a> _ [] = error "Probability.shape: empty list"

119+<a name="line-119"></a>shape <a name="local-6989586621679068577"><a href="#local-6989586621679068577">f</a></a> <a name="local-6989586621679068578"><a href="#local-6989586621679068578">xs</a></a> =

120+<a name="line-120"></a> let <a name="local-6989586621679068579"><a href="#local-6989586621679068579">incr</a></a> = 1 / fromIntegral (length <a href="#local-6989586621679068578">xs</a> - 1)

121+<a name="line-121"></a> <a name="local-6989586621679068580"><a href="#local-6989586621679068580">ps</a></a> = map <a href="#local-6989586621679068577">f</a> (iterate (+<a href="#local-6989586621679068579">incr</a>) 0)

122+<a name="line-122"></a> in <a href="Dist.Internal.html#fromFreqs">fromFreqs</a> (zip <a href="#local-6989586621679068578">xs</a> <a href="#local-6989586621679068580">ps</a>)

123+<a name="line-123"></a>

124+<a name="line-124"></a>-- | Constructs a Linear distribution

125+<a name="line-125"></a>linear :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068547">a</a>)) => [<a href="#local-6989586621679068547">a</a>] -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068547">a</a>

126+<a name="line-126"></a><a name="linear"><a href="Dist.Internal.html#linear">linear</a></a> = <a href="Dist.Internal.html#shape">shape</a> id

127+<a name="line-127"></a>

128+<a name="line-128"></a>-- | Constructs an Uniform distribution

129+<a name="line-129"></a>uniform :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068546">a</a>)) => [<a href="#local-6989586621679068546">a</a>] -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068546">a</a>

130+<a name="line-130"></a><a name="uniform"><a href="Dist.Internal.html#uniform">uniform</a></a> = <a href="Dist.Internal.html#shape">shape</a> (const 1)

131+<a name="line-131"></a>

132+<a name="line-132"></a>-- | Constructs an Negative Exponential distribution

133+<a name="line-133"></a>negExp :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068545">a</a>)) => [<a href="#local-6989586621679068545">a</a>] -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068545">a</a>

134+<a name="line-134"></a><a name="negExp"><a href="Dist.Internal.html#negExp">negExp</a></a> = <a href="Dist.Internal.html#shape">shape</a> (\<a name="local-6989586621679068581"><a href="#local-6989586621679068581">x</a></a> -> exp (-<a href="#local-6989586621679068581">x</a>))

135+<a name="line-135"></a>

136+<a name="line-136"></a>-- | Constructs an Normal distribution

137+<a name="line-137"></a>normal :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068544">a</a>)) => [<a href="#local-6989586621679068544">a</a>] -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068544">a</a>

138+<a name="line-138"></a><a name="normal"><a href="Dist.Internal.html#normal">normal</a></a> = <a href="Dist.Internal.html#shape">shape</a> (<a href="Dist.Internal.html#normalCurve">normalCurve</a> 0.5 0.5)

139+<a name="line-139"></a>

140+<a name="line-140"></a>-- | Transforms a 'Dist' into a list of pairs.

141+<a name="line-141"></a>toValues :: forall <a name="local-6989586621679068543"><a href="#local-6989586621679068543">a</a></a> . (Enum <a href="#local-6989586621679068543">a</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679068543">a</a>), <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068543">a</a>)) => <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068543">a</a> -> [(<a href="#local-6989586621679068543">a</a>, <a href="Dist.Internal.html#Prob">Prob</a>)]

142+<a name="line-142"></a><a name="toValues"><a href="Dist.Internal.html#toValues">toValues</a></a> (<a href="Dist.Internal.html#D">D</a> <a name="local-6989586621679068582"><a href="#local-6989586621679068582">d</a></a>) =

143+<a name="line-143"></a> let <a name="local-6989586621679068583"><a href="#local-6989586621679068583">rows</a></a> = fromInteger (natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679068543">a</a>)))

144+<a name="line-144"></a> <a name="local-6989586621679068584"><a href="#local-6989586621679068584">probs</a></a> = <a href="Matrix.Type.html#toList">toList</a> <a href="#local-6989586621679068582">d</a>

145+<a name="line-145"></a> <a name="local-6989586621679068585"><a href="#local-6989586621679068585">res</a></a> = zip (map toEnum [0..<a href="#local-6989586621679068583">rows</a>]) <a href="#local-6989586621679068584">probs</a>

146+<a name="line-146"></a> in <a href="#local-6989586621679068585">res</a>

147+<a name="line-147"></a>

148+<a name="line-148"></a>-- | Pretty a distribution

149+<a name="line-149"></a>prettyDist :: forall <a name="local-6989586621679068542"><a href="#local-6989586621679068542">a</a></a>. (Show <a href="#local-6989586621679068542">a</a>, Enum <a href="#local-6989586621679068542">a</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679068542">a</a>), <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068542">a</a>)) => <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068542">a</a> -> String

150+<a name="line-150"></a><a name="prettyDist"><a href="Dist.Internal.html#prettyDist">prettyDist</a></a> <a name="local-6989586621679068586"><a href="#local-6989586621679068586">d</a></a> =

151+<a name="line-151"></a> let <a name="local-6989586621679068592"><a href="#local-6989586621679068592">values</a></a> = sortBy (\(<a name="local-6989586621679068594"><a href="#local-6989586621679068594">a</a></a>, <a name="local-6989586621679068595"><a href="#local-6989586621679068595">p1</a></a>) (<a name="local-6989586621679068596"><a href="#local-6989586621679068596">b</a></a>, <a name="local-6989586621679068597"><a href="#local-6989586621679068597">p2</a></a>) -> compare <a href="#local-6989586621679068597">p2</a> <a href="#local-6989586621679068595">p1</a>) (<a href="Dist.Internal.html#toValues">toValues</a> @<a href="#local-6989586621679068542">a</a> <a href="#local-6989586621679068586">d</a>)

152+<a name="line-152"></a> <a name="local-6989586621679068593"><a href="#local-6989586621679068593">w</a></a> = maximum (map (length . show . fst) <a href="#local-6989586621679068592">values</a>)

153+<a name="line-153"></a> in concatMap

154+<a name="line-154"></a> (\(<a name="local-6989586621679068598"><a href="#local-6989586621679068598">x</a></a>,<a name="local-6989586621679068599"><a href="#local-6989586621679068599">p</a></a>) -> <a href="#local-6989586621679068588">showR</a> <a href="#local-6989586621679068593">w</a> <a href="#local-6989586621679068598">x</a> ++ ' ': <a href="#local-6989586621679068587">showProb</a> <a href="#local-6989586621679068599">p</a> ++ "\n")

155+<a name="line-155"></a> <a href="#local-6989586621679068592">values</a>

156+<a name="line-156"></a> where

157+<a name="line-157"></a> <a name="local-6989586621679068587"><a href="#local-6989586621679068587">showProb</a></a> <a name="local-6989586621679068589"><a href="#local-6989586621679068589">p</a></a> = show (<a href="#local-6989586621679068589">p</a> * 100) ++ "%"

158+<a name="line-158"></a> <a name="local-6989586621679068588"><a href="#local-6989586621679068588">showR</a></a> <a name="local-6989586621679068590"><a href="#local-6989586621679068590">n</a></a> <a name="local-6989586621679068591"><a href="#local-6989586621679068591">x</a></a> = show <a href="#local-6989586621679068591">x</a> ++ " "

159+<a name="line-159"></a>

160+<a name="line-160"></a>-- | Pretty Print a distribution

161+<a name="line-161"></a>prettyPrintDist :: forall <a name="local-6989586621679068541"><a href="#local-6989586621679068541">a</a></a> . (Show <a href="#local-6989586621679068541">a</a>, Enum <a href="#local-6989586621679068541">a</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679068541">a</a>), <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068541">a</a>)) => <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068541">a</a> -> IO ()

162+<a name="line-162"></a><a name="prettyPrintDist"><a href="Dist.Internal.html#prettyPrintDist">prettyPrintDist</a></a> = putStrLn . <a href="Dist.Internal.html#prettyDist">prettyDist</a> @<a href="#local-6989586621679068541">a</a>

163+<a name="line-163"></a>

164+<a name="line-164"></a>-- Auxiliary functions

165+<a name="line-165"></a>

166+<a name="line-166"></a>fromFreqs :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="Dist.Internal.html#Prob">Prob</a> () (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679068540">a</a>)) => [(<a href="#local-6989586621679068540">a</a>,<a href="Dist.Internal.html#Prob">Prob</a>)] -> <a href="Dist.Internal.html#Dist">Dist</a> <a href="#local-6989586621679068540">a</a>

167+<a name="line-167"></a><a name="fromFreqs"><a href="Dist.Internal.html#fromFreqs">fromFreqs</a></a> <a name="local-6989586621679068600"><a href="#local-6989586621679068600">xs</a></a> = <a href="Dist.Internal.html#D">D</a> (<a href="Matrix.Type.html#col">col</a> (map (\(<a name="local-6989586621679068602"><a href="#local-6989586621679068602">x</a></a>,<a name="local-6989586621679068603"><a href="#local-6989586621679068603">p</a></a>) -> <a href="#local-6989586621679068603">p</a>/<a href="#local-6989586621679068601">q</a>) <a href="#local-6989586621679068600">xs</a>))

168+<a name="line-168"></a> where <a name="local-6989586621679068601"><a href="#local-6989586621679068601">q</a></a> = sum $ map snd <a href="#local-6989586621679068600">xs</a>

169+<a name="line-169"></a>

170+<a name="line-170"></a>normalCurve :: <a href="Dist.Internal.html#Prob">Prob</a> -> <a href="Dist.Internal.html#Prob">Prob</a> -> <a href="Dist.Internal.html#Prob">Prob</a> -> <a href="Dist.Internal.html#Prob">Prob</a>

171+<a name="line-171"></a><a name="normalCurve"><a href="Dist.Internal.html#normalCurve">normalCurve</a></a> <a name="local-6989586621679068604"><a href="#local-6989586621679068604">mean</a></a> <a name="local-6989586621679068605"><a href="#local-6989586621679068605">dev</a></a> <a name="local-6989586621679068606"><a href="#local-6989586621679068606">x</a></a> =

172+<a name="line-172"></a> let <a name="local-6989586621679068607"><a href="#local-6989586621679068607">u</a></a> = (<a href="#local-6989586621679068606">x</a> - <a href="#local-6989586621679068604">mean</a>) / <a href="#local-6989586621679068605">dev</a>

173+<a name="line-173"></a> in exp (-1/2 * <a href="#local-6989586621679068607">u</a>^(2::Int)) / sqrt (2 * pi)

174+<a name="line-174"></a></pre></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/src/Dist.htmlnew file+70

@@ -0,0 +1,70 @@

1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="style.css" /><script type="text/javascript" src="highlight.js"></script></head><body><pre>-----------------------------------------------------------------------------

2+<a name="line-2"></a>-- |

3+<a name="line-3"></a>-- Module : Dist

4+<a name="line-4"></a>-- Copyright : (c) Armando Santos 2019-2020

5+<a name="line-5"></a>-- Maintainer : armandoifsantos@gmail.com

6+<a name="line-6"></a>-- Stability : experimental

7+<a name="line-7"></a>--

8+<a name="line-8"></a>-- __LAoP__ is a library for algebraic (inductive) construction and manipulation of matrices

9+<a name="line-9"></a>-- in Haskell. See <https://github.com/bolt12/master-thesis my Msc Thesis> for the

10+<a name="line-10"></a>-- motivation behind the library, the underlying theory, and implementation details.

11+<a name="line-11"></a>--

12+<a name="line-12"></a>-- This module exports a type synonym 'Dist'

13+<a name="line-13"></a>-- that represents a stochastic distribution

14+<a name="line-14"></a>-- matrix and several distribution construction

15+<a name="line-15"></a>-- functions.

16+<a name="line-16"></a>--

17+<a name="line-17"></a>-----------------------------------------------------------------------------

18+<a name="line-18"></a>

19+<a name="line-19"></a>module Dist

20+<a name="line-20"></a> ( -- | If the sum of the rows of a column matrix

21+<a name="line-21"></a> -- is equal to 1 then this stochastic matrix

22+<a name="line-22"></a> -- can be seen as a probability distribution.

23+<a name="line-23"></a> --

24+<a name="line-24"></a> --

25+<a name="line-25"></a> -- This module is still experimental but it's

26+<a name="line-26"></a> -- already possible to model probabilistic programming

27+<a name="line-27"></a> -- problems with it. Import 'Matrix.Nat' or 'Matrix.Type'

28+<a name="line-28"></a> -- to access LAoP matrix combinators and then all you have

29+<a name="line-29"></a> -- to do is to define your sample space, either by creating a new data

30+<a name="line-30"></a> -- type or by abstracting it out via 'Natural'.

31+<a name="line-31"></a> --

32+<a name="line-32"></a> -- Write manipulation functions and promote them to matrices via

33+<a name="line-33"></a> -- 'fromF' or 'fromF'' and you're good to go!

34+<a name="line-34"></a>

35+<a name="line-35"></a> -- * 'Dist' and 'Prob' type synonyms

36+<a name="line-36"></a> <a href="Dist.Internal.html#Dist">Dist</a> (..),

37+<a name="line-37"></a> <a href="Dist.Internal.html#Prob">Prob</a>,

38+<a name="line-38"></a>

39+<a name="line-39"></a> -- * Functor instance equivalent functions

40+<a name="line-40"></a> <a href="Dist.Internal.html#fmapD">fmapD</a>,

41+<a name="line-41"></a>

42+<a name="line-42"></a> -- * Applicative equivalent functions

43+<a name="line-43"></a> <a href="Dist.Internal.html#unitD">unitD</a>,

44+<a name="line-44"></a> <a href="Dist.Internal.html#multD">multD</a>,

45+<a name="line-45"></a>

46+<a name="line-46"></a> -- * Selective equivalent functions

47+<a name="line-47"></a> <a href="Dist.Internal.html#selectD">selectD</a>,

48+<a name="line-48"></a>

49+<a name="line-49"></a> -- * Monad equivalent functions

50+<a name="line-50"></a> <a href="Dist.Internal.html#returnD">returnD</a>,

51+<a name="line-51"></a> <a href="Dist.Internal.html#bindD">bindD</a>,

52+<a name="line-52"></a>

53+<a name="line-53"></a> -- * Distribution construction functions

54+<a name="line-54"></a> <a href="Dist.Internal.html#choose">choose</a>,

55+<a name="line-55"></a> <a href="Dist.Internal.html#shape">shape</a>,

56+<a name="line-56"></a> <a href="Dist.Internal.html#linear">linear</a>,

57+<a name="line-57"></a> <a href="Dist.Internal.html#uniform">uniform</a>,

58+<a name="line-58"></a> <a href="Dist.Internal.html#negExp">negExp</a>,

59+<a name="line-59"></a> <a href="Dist.Internal.html#normal">normal</a>,

60+<a name="line-60"></a>

61+<a name="line-61"></a> -- * Converto to list of pairs

62+<a name="line-62"></a> <a href="Dist.Internal.html#toValues">toValues</a>,

63+<a name="line-63"></a> -- * Pretty print distribution

64+<a name="line-64"></a> <a href="Dist.Internal.html#prettyDist">prettyDist</a>,

65+<a name="line-65"></a> <a href="Dist.Internal.html#prettyPrintDist">prettyPrintDist</a>

66+<a name="line-66"></a> )

67+<a name="line-67"></a>where

68+<a name="line-68"></a>

69+<a name="line-69"></a>import <a href="Dist.Internal.html">Dist.Internal</a>

70+<a name="line-70"></a></pre></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/src/Matrix.Internal.htmlnew file+903

@@ -0,0 +1,903 @@

1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="style.css" /><script type="text/javascript" src="highlight.js"></script></head><body><pre>{-# LANGUAGE AllowAmbiguousTypes #-}

2+<a name="line-2"></a>{-# LANGUAGE DataKinds #-}

3+<a name="line-3"></a>{-# LANGUAGE FlexibleContexts #-}

4+<a name="line-4"></a>{-# LANGUAGE FlexibleInstances #-}

5+<a name="line-5"></a>{-# LANGUAGE GADTs #-}

6+<a name="line-6"></a>{-# LANGUAGE InstanceSigs #-}

7+<a name="line-7"></a>{-# LANGUAGE MultiParamTypeClasses #-}

8+<a name="line-8"></a>{-# LANGUAGE NoStarIsType #-}

9+<a name="line-9"></a>{-# LANGUAGE ScopedTypeVariables #-}

10+<a name="line-10"></a>{-# LANGUAGE StandaloneDeriving #-}

11+<a name="line-11"></a>{-# LANGUAGE TypeApplications #-}

12+<a name="line-12"></a>{-# LANGUAGE TypeFamilies #-}

13+<a name="line-13"></a>{-# LANGUAGE TypeOperators #-}

14+<a name="line-14"></a>{-# LANGUAGE UndecidableInstances #-}

15+<a name="line-15"></a>

16+<a name="line-16"></a>-----------------------------------------------------------------------------

17+<a name="line-17"></a>-- |

18+<a name="line-18"></a>-- Module : Matrix.Internal

19+<a name="line-19"></a>-- Copyright : (c) Armando Santos 2019-2020

20+<a name="line-20"></a>-- Maintainer : armandoifsantos@gmail.com

21+<a name="line-21"></a>-- Stability : experimental

22+<a name="line-22"></a>--

23+<a name="line-23"></a>-- The LAoP discipline generalises relations and functions treating them as

24+<a name="line-24"></a>-- Boolean matrices and in turn consider these as arrows.

25+<a name="line-25"></a>--

26+<a name="line-26"></a>-- __LAoP__ is a library for algebraic (inductive) construction and manipulation of matrices

27+<a name="line-27"></a>-- in Haskell. See <https://github.com/bolt12/master-thesis my Msc Thesis> for the

28+<a name="line-28"></a>-- motivation behind the library, the underlying theory, and implementation details.

29+<a name="line-29"></a>--

30+<a name="line-30"></a>-- This module offers many of the combinators mentioned in the work of

31+<a name="line-31"></a>-- Macedo (2012) and Oliveira (2012).

32+<a name="line-32"></a>--

33+<a name="line-33"></a>-- This is an Internal module and it is no supposed to be imported.

34+<a name="line-34"></a>--

35+<a name="line-35"></a>-----------------------------------------------------------------------------

36+<a name="line-36"></a>

37+<a name="line-37"></a>module Matrix.Internal

38+<a name="line-38"></a> ( -- | This definition makes use of the fact that 'Void' is

39+<a name="line-39"></a> -- isomorphic to 0 and '()' to 1 and captures matrix

40+<a name="line-40"></a> -- dimensions as stacks of 'Either's.

41+<a name="line-41"></a> --

42+<a name="line-42"></a> -- There exists two type families that make it easier to write

43+<a name="line-43"></a> -- matrix dimensions: 'FromNat' and 'Count'. This approach

44+<a name="line-44"></a> -- leads to a very straightforward implementation

45+<a name="line-45"></a> -- of LAoP combinators.

46+<a name="line-46"></a>

47+<a name="line-47"></a> -- * Type safe matrix representation

48+<a name="line-48"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> (..),

49+<a name="line-49"></a>

50+<a name="line-50"></a> -- * Primitives

51+<a name="line-51"></a> <a href="Matrix.Internal.html#empty">empty</a>,

52+<a name="line-52"></a> <a href="Matrix.Internal.html#one">one</a>,

53+<a name="line-53"></a> <a href="Matrix.Internal.html#junc">junc</a>,

54+<a name="line-54"></a> <a href="Matrix.Internal.html#split">split</a>,

55+<a name="line-55"></a>

56+<a name="line-56"></a> -- * Auxiliary type families

57+<a name="line-57"></a> <a href="Matrix.Internal.html#FromNat">FromNat</a>,

58+<a name="line-58"></a> <a href="Matrix.Internal.html#Count">Count</a>,

59+<a name="line-59"></a> <a href="Matrix.Internal.html#Normalize">Normalize</a>,

60+<a name="line-60"></a>

61+<a name="line-61"></a> -- * Matrix construction and conversion

62+<a name="line-62"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a>,

63+<a name="line-63"></a> <a href="Matrix.Internal.html#fromLists">fromLists</a>,

64+<a name="line-64"></a> <a href="Matrix.Internal.html#toLists">toLists</a>,

65+<a name="line-65"></a> <a href="Matrix.Internal.html#toList">toList</a>,

66+<a name="line-66"></a> <a href="Matrix.Internal.html#matrixBuilder">matrixBuilder</a>,

67+<a name="line-67"></a> <a href="Matrix.Internal.html#row">row</a>,

68+<a name="line-68"></a> <a href="Matrix.Internal.html#col">col</a>,

69+<a name="line-69"></a> <a href="Matrix.Internal.html#zeros">zeros</a>,

70+<a name="line-70"></a> <a href="Matrix.Internal.html#ones">ones</a>,

71+<a name="line-71"></a> <a href="Matrix.Internal.html#bang">bang</a>,

72+<a name="line-72"></a> <a href="Matrix.Internal.html#constant">constant</a>,

73+<a name="line-73"></a>

74+<a name="line-74"></a> -- * Misc

75+<a name="line-75"></a> -- ** Get dimensions

76+<a name="line-76"></a> <a href="Matrix.Internal.html#columns">columns</a>,

77+<a name="line-77"></a> <a href="Matrix.Internal.html#rows">rows</a>,

78+<a name="line-78"></a>

79+<a name="line-79"></a> -- ** Matrix Transposition

80+<a name="line-80"></a> <a href="Matrix.Internal.html#tr">tr</a>,

81+<a name="line-81"></a>

82+<a name="line-82"></a> -- ** Selective operator

83+<a name="line-83"></a> <a href="Matrix.Internal.html#select">select</a>,

84+<a name="line-84"></a>

85+<a name="line-85"></a> -- ** McCarthy's Conditional

86+<a name="line-86"></a> <a href="Matrix.Internal.html#cond">cond</a>,

87+<a name="line-87"></a>

88+<a name="line-88"></a> -- ** Matrix "abiding"

89+<a name="line-89"></a> <a href="Matrix.Internal.html#abideJS">abideJS</a>,

90+<a name="line-90"></a> <a href="Matrix.Internal.html#abideSJ">abideSJ</a>,

91+<a name="line-91"></a>

92+<a name="line-92"></a> -- * Biproduct approach

93+<a name="line-93"></a> -- ** Split

94+<a name="line-94"></a> (<a href="Matrix.Internal.html#%3D%3D%3D">===</a>),

95+<a name="line-95"></a> -- *** Projections

96+<a name="line-96"></a> <a href="Matrix.Internal.html#p1">p1</a>,

97+<a name="line-97"></a> <a href="Matrix.Internal.html#p2">p2</a>,

98+<a name="line-98"></a> -- ** Junc

99+<a name="line-99"></a> (<a href="Matrix.Internal.html#%7C%7C%7C">|||</a>),

100+<a name="line-100"></a> -- *** Injections

101+<a name="line-101"></a> <a href="Matrix.Internal.html#i1">i1</a>,

102+<a name="line-102"></a> <a href="Matrix.Internal.html#i2">i2</a>,

103+<a name="line-103"></a> -- ** Bifunctors

104+<a name="line-104"></a> (<a href="Matrix.Internal.html#-%7C-">-|-</a>),

105+<a name="line-105"></a> (<a href="Matrix.Internal.html#%3E%3C">><</a>),

106+<a name="line-106"></a>

107+<a name="line-107"></a> -- ** Applicative matrix combinators

108+<a name="line-108"></a>

109+<a name="line-109"></a> -- | Note that given the restrictions imposed it is not possible to

110+<a name="line-110"></a> -- implement the standard type classes present in standard Haskell.

111+<a name="line-111"></a> -- *** Matrix pairing projections

112+<a name="line-112"></a> <a href="Matrix.Internal.html#kp1">kp1</a>,

113+<a name="line-113"></a> <a href="Matrix.Internal.html#kp2">kp2</a>,

114+<a name="line-114"></a>

115+<a name="line-115"></a> -- *** Matrix pairing

116+<a name="line-116"></a> <a href="Matrix.Internal.html#khatri">khatri</a>,

117+<a name="line-117"></a>

118+<a name="line-118"></a> -- * Matrix composition and lifting

119+<a name="line-119"></a>

120+<a name="line-120"></a> -- ** Arrow matrix combinators

121+<a name="line-121"></a>

122+<a name="line-122"></a> -- | Note that given the restrictions imposed it is not possible to

123+<a name="line-123"></a> -- implement the standard type classes present in standard Haskell.

124+<a name="line-124"></a> <a href="Matrix.Internal.html#identity">identity</a>,

125+<a name="line-125"></a> <a href="Matrix.Internal.html#comp">comp</a>,

126+<a name="line-126"></a> <a href="Matrix.Internal.html#fromF">fromF</a>,

127+<a name="line-127"></a> <a href="Matrix.Internal.html#fromF%27">fromF'</a>,

128+<a name="line-128"></a>

129+<a name="line-129"></a> -- * Matrix printing

130+<a name="line-130"></a> <a href="Matrix.Internal.html#pretty">pretty</a>,

131+<a name="line-131"></a> <a href="Matrix.Internal.html#prettyPrint">prettyPrint</a>,

132+<a name="line-132"></a>

133+<a name="line-133"></a> -- * Other

134+<a name="line-134"></a> <a href="Matrix.Internal.html#toBool">toBool</a>,

135+<a name="line-135"></a> <a href="Matrix.Internal.html#fromBool">fromBool</a>,

136+<a name="line-136"></a> <a href="Matrix.Internal.html#compRel">compRel</a>,

137+<a name="line-137"></a> <a href="Matrix.Internal.html#fromFRel">fromFRel</a>,

138+<a name="line-138"></a> <a href="Matrix.Internal.html#fromFRel%27">fromFRel'</a>,

139+<a name="line-139"></a> <a href="Matrix.Internal.html#orM">orM</a>,

140+<a name="line-140"></a> <a href="Matrix.Internal.html#andM">andM</a>,

141+<a name="line-141"></a> <a href="Matrix.Internal.html#subM">subM</a>

142+<a name="line-142"></a> )

143+<a name="line-143"></a> where

144+<a name="line-144"></a>

145+<a name="line-145"></a>import <a href="Utils.html">Utils</a>

146+<a name="line-146"></a>import Data.Bool

147+<a name="line-147"></a>import Data.Kind

148+<a name="line-148"></a>import Data.List

149+<a name="line-149"></a>import Data.Proxy

150+<a name="line-150"></a>import Data.Void

151+<a name="line-151"></a>import GHC.TypeLits

152+<a name="line-152"></a>import Data.Type.Equality

153+<a name="line-153"></a>import GHC.Generics

154+<a name="line-154"></a>import Control.DeepSeq

155+<a name="line-155"></a>import Control.Category

156+<a name="line-156"></a>import Prelude hiding ((.))

157+<a name="line-157"></a>

158+<a name="line-158"></a>-- | LAoP (Linear Algebra of Programming) Inductive Matrix definition.

159+<a name="line-159"></a>data <a name="Matrix"><a href="Matrix.Internal.html#Matrix">Matrix</a></a> <a name="local-6989586621679038240"><a href="#local-6989586621679038240">e</a></a> <a name="local-6989586621679038241"><a href="#local-6989586621679038241">cols</a></a> <a name="local-6989586621679038242"><a href="#local-6989586621679038242">rows</a></a> where

160+<a name="line-160"></a> <a name="Empty"><a href="Matrix.Internal.html#Empty">Empty</a></a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038243">e</a> Void Void

161+<a name="line-161"></a> <a name="One"><a href="Matrix.Internal.html#One">One</a></a> :: <a href="#local-6989586621679038244">e</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038244">e</a> () ()

162+<a name="line-162"></a> <a name="Junc"><a href="Matrix.Internal.html#Junc">Junc</a></a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038245">e</a> <a href="#local-6989586621679038246">a</a> <a href="#local-6989586621679038247">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038245">e</a> <a href="#local-6989586621679038248">b</a> <a href="#local-6989586621679038247">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038245">e</a> (Either <a href="#local-6989586621679038246">a</a> <a href="#local-6989586621679038248">b</a>) <a href="#local-6989586621679038247">rows</a>

163+<a name="line-163"></a> <a name="Split"><a href="Matrix.Internal.html#Split">Split</a></a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038249">e</a> <a href="#local-6989586621679038250">cols</a> <a href="#local-6989586621679038251">a</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038249">e</a> <a href="#local-6989586621679038250">cols</a> <a href="#local-6989586621679038252">b</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038249">e</a> <a href="#local-6989586621679038250">cols</a> (Either <a href="#local-6989586621679038251">a</a> <a href="#local-6989586621679038252">b</a>)

164+<a name="line-164"></a>

165+<a name="line-165"></a>deriving instance (Show <a href="#local-6989586621679039296">e</a>) => Show (<a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679039296">e</a> <a href="#local-6989586621679039297">cols</a> <a href="#local-6989586621679039298">rows</a>)

166+<a name="line-166"></a>

167+<a name="line-167"></a>-- | Type family that computes the cardinality of a given type dimension.

168+<a name="line-168"></a>--

169+<a name="line-169"></a>-- It can also count the cardinality of custom types that implement the

170+<a name="line-170"></a>-- 'Generic' instance.

171+<a name="line-171"></a>type family <a name="Count"><a href="Matrix.Internal.html#Count">Count</a></a> (<a name="local-6989586621679038215"><a href="#local-6989586621679038215">d</a></a> :: Type) :: Nat where

172+<a name="line-172"></a> Count (<a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679038216">n</a> <a href="#local-6989586621679038217">m</a>) = (m - <a href="#local-6989586621679038216">n</a>) + 1

173+<a name="line-173"></a> Count (Either <a href="#local-6989586621679038218">a</a> <a href="#local-6989586621679038219">b</a>) = (+) (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038218">a</a>) (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038219">b</a>)

174+<a name="line-174"></a> Count (<a href="#local-6989586621679038220">a</a>, <a href="#local-6989586621679038221">b</a>) = (*) (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038220">a</a>) (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038221">b</a>)

175+<a name="line-175"></a> Count (<a href="#local-6989586621679038222">a</a> -> <a href="#local-6989586621679038223">b</a>) = (^) (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038223">b</a>) (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038222">a</a>)

176+<a name="line-176"></a> -- Generics

177+<a name="line-177"></a> Count (M1 _ _ <a href="#local-6989586621679038224">f</a> <a href="#local-6989586621679038225">p</a>) = <a href="Matrix.Internal.html#Count">Count</a> (<a href="#local-6989586621679038224">f</a> <a href="#local-6989586621679038225">p</a>)

178+<a name="line-178"></a> Count (K1 _ _ _) = 1

179+<a name="line-179"></a> Count (V1 _) = 0

180+<a name="line-180"></a> Count (U1 _) = 1

181+<a name="line-181"></a> Count ((:*:) <a href="#local-6989586621679038233">a</a> <a href="#local-6989586621679038234">b</a> <a href="#local-6989586621679038235">p</a>) = Count (<a href="#local-6989586621679038233">a</a> <a href="#local-6989586621679038235">p</a>) * <a href="Matrix.Internal.html#Count">Count</a> (<a href="#local-6989586621679038234">b</a> <a href="#local-6989586621679038235">p</a>)

182+<a name="line-182"></a> Count ((:+:) <a href="#local-6989586621679038236">a</a> <a href="#local-6989586621679038237">b</a> <a href="#local-6989586621679038238">p</a>) = Count (<a href="#local-6989586621679038236">a</a> <a href="#local-6989586621679038238">p</a>) + <a href="Matrix.Internal.html#Count">Count</a> (<a href="#local-6989586621679038237">b</a> <a href="#local-6989586621679038238">p</a>)

183+<a name="line-183"></a> Count <a href="#local-6989586621679038239">d</a> = <a href="Matrix.Internal.html#Count">Count</a> (Rep <a href="#local-6989586621679038239">d</a> R)

184+<a name="line-184"></a>

185+<a name="line-185"></a>-- | Type family that computes of a given type dimension from a given natural

186+<a name="line-186"></a>--

187+<a name="line-187"></a>-- Thanks to Li-Yao Xia this type family is super fast.

188+<a name="line-188"></a>type family <a name="FromNat"><a href="Matrix.Internal.html#FromNat">FromNat</a></a> (<a name="local-6989586621679038213"><a href="#local-6989586621679038213">n</a></a> :: Nat) :: Type where

189+<a name="line-189"></a> FromNat 0 = Void

190+<a name="line-190"></a> FromNat 1 = ()

191+<a name="line-191"></a> FromNat <a href="#local-6989586621679038214">n</a> = <a href="Matrix.Internal.html#FromNat%27">FromNat'</a> (Mod <a href="#local-6989586621679038214">n</a> 2 == 0) (<a href="Matrix.Internal.html#FromNat">FromNat</a> (Div <a href="#local-6989586621679038214">n</a> 2))

192+<a name="line-192"></a>

193+<a name="line-193"></a>type family <a name="FromNat%27"><a href="Matrix.Internal.html#FromNat%27">FromNat'</a></a> (<a name="local-6989586621679038066"><a href="#local-6989586621679038066">b</a></a> :: Bool) (<a name="local-6989586621679038067"><a href="#local-6989586621679038067">m</a></a> :: Type) :: Type where

194+<a name="line-194"></a> FromNat' 'True <a href="#local-6989586621679038068">m</a> = Either <a href="#local-6989586621679038068">m</a> <a href="#local-6989586621679038068">m</a>

195+<a name="line-195"></a> FromNat' 'False <a href="#local-6989586621679038212">m</a> = Either () (Either <a href="#local-6989586621679038212">m</a> <a href="#local-6989586621679038212">m</a>)

196+<a name="line-196"></a>

197+<a name="line-197"></a>-- | Type family that normalizes the representation of a given data

198+<a name="line-198"></a>-- structure

199+<a name="line-199"></a>type family <a name="Normalize"><a href="Matrix.Internal.html#Normalize">Normalize</a></a> (<a name="local-6989586621679038064"><a href="#local-6989586621679038064">d</a></a> :: Type) :: Type where

200+<a name="line-200"></a> Normalize <a href="#local-6989586621679038065">d</a> = <a href="Matrix.Internal.html#FromNat">FromNat</a> (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038065">d</a>)

201+<a name="line-201"></a>

202+<a name="line-202"></a>-- | It isn't possible to implement the 'id' function so it's

203+<a name="line-203"></a>-- implementation is 'undefined'. However 'comp' can be and this partial

204+<a name="line-204"></a>-- class implementation exists just to make the code more readable.

205+<a name="line-205"></a>--

206+<a name="line-206"></a>-- Please use 'identity' instead.

207+<a name="line-207"></a>instance (Num <a href="#local-6989586621679038572">e</a>) => Category (<a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038572">e</a>) where

208+<a name="line-208"></a> <a name="local-8214565720323789508">id</a> = undefined

209+<a name="line-209"></a> (<a name="local-8214565720323789507">.</a>) = <a href="Matrix.Internal.html#comp">comp</a>

210+<a name="line-210"></a>

211+<a name="line-211"></a>instance NFData <a href="#local-6989586621679038564">e</a> => NFData (<a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038564">e</a> <a href="#local-6989586621679038565">cols</a> <a href="#local-6989586621679038566">rows</a>) where

212+<a name="line-212"></a> <a name="local-8214565720323790686">rnf</a> <a href="Matrix.Internal.html#Empty">Empty</a> = ()

213+<a name="line-213"></a> rnf (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038567"><a href="#local-6989586621679038567">e</a></a>) = rnf <a href="#local-6989586621679038567">e</a>

214+<a name="line-214"></a> rnf (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038568"><a href="#local-6989586621679038568">a</a></a> <a name="local-6989586621679038569"><a href="#local-6989586621679038569">b</a></a>) = rnf <a href="#local-6989586621679038568">a</a> `seq` rnf <a href="#local-6989586621679038569">b</a>

215+<a name="line-215"></a> rnf (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038570"><a href="#local-6989586621679038570">a</a></a> <a name="local-6989586621679038571"><a href="#local-6989586621679038571">b</a></a>) = rnf <a href="#local-6989586621679038570">a</a> `seq` rnf <a href="#local-6989586621679038571">b</a>

216+<a name="line-216"></a>

217+<a name="line-217"></a>instance Eq <a href="#local-6989586621679038547">e</a> => Eq (<a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038547">e</a> <a href="#local-6989586621679038548">cols</a> <a href="#local-6989586621679038549">rows</a>) where

218+<a name="line-218"></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a name="local-3458764513820541095">==</a> <a href="Matrix.Internal.html#Empty">Empty</a> = True

219+<a name="line-219"></a> (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038550"><a href="#local-6989586621679038550">a</a></a>) == (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038551"><a href="#local-6989586621679038551">b</a></a>) = <a href="#local-6989586621679038550">a</a> == <a href="#local-6989586621679038551">b</a>

220+<a name="line-220"></a> (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038552"><a href="#local-6989586621679038552">a</a></a> <a name="local-6989586621679038553"><a href="#local-6989586621679038553">b</a></a>) == (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038554"><a href="#local-6989586621679038554">c</a></a> <a name="local-6989586621679038555"><a href="#local-6989586621679038555">d</a></a>) = <a href="#local-6989586621679038552">a</a> == <a href="#local-6989586621679038554">c</a> && <a href="#local-6989586621679038553">b</a> == <a href="#local-6989586621679038555">d</a>

221+<a name="line-221"></a> (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038556"><a href="#local-6989586621679038556">a</a></a> <a name="local-6989586621679038557"><a href="#local-6989586621679038557">b</a></a>) == (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038558"><a href="#local-6989586621679038558">c</a></a> <a name="local-6989586621679038559"><a href="#local-6989586621679038559">d</a></a>) = <a href="#local-6989586621679038556">a</a> == <a href="#local-6989586621679038558">c</a> && <a href="#local-6989586621679038557">b</a> == <a href="#local-6989586621679038559">d</a>

222+<a name="line-222"></a> <a name="local-6989586621679038560"><a href="#local-6989586621679038560">x</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) == <a name="local-6989586621679038561"><a href="#local-6989586621679038561">y</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) = <a href="#local-6989586621679038560">x</a> == <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038561">y</a>

223+<a name="line-223"></a> <a name="local-6989586621679038562"><a href="#local-6989586621679038562">x</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) == <a name="local-6989586621679038563"><a href="#local-6989586621679038563">y</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) = <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038562">x</a> == <a href="#local-6989586621679038563">y</a>

224+<a name="line-224"></a>

225+<a name="line-225"></a>instance Num <a href="#local-6989586621679038492">e</a> => Num (<a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038492">e</a> <a href="#local-6989586621679038493">cols</a> <a href="#local-6989586621679038494">rows</a>) where

226+<a name="line-226"></a>

227+<a name="line-227"></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a name="local-8214565720323790403">+</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

228+<a name="line-228"></a> (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038495"><a href="#local-6989586621679038495">a</a></a>) + (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038496"><a href="#local-6989586621679038496">b</a></a>) = <a href="Matrix.Internal.html#One">One</a> (<a href="#local-6989586621679038495">a</a> + <a href="#local-6989586621679038496">b</a>)

229+<a name="line-229"></a> (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038497"><a href="#local-6989586621679038497">a</a></a> <a name="local-6989586621679038498"><a href="#local-6989586621679038498">b</a></a>) + (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038499"><a href="#local-6989586621679038499">c</a></a> <a name="local-6989586621679038500"><a href="#local-6989586621679038500">d</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="#local-6989586621679038497">a</a> + <a href="#local-6989586621679038499">c</a>) (<a href="#local-6989586621679038498">b</a> + <a href="#local-6989586621679038500">d</a>)

230+<a name="line-230"></a> (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038501"><a href="#local-6989586621679038501">a</a></a> <a name="local-6989586621679038502"><a href="#local-6989586621679038502">b</a></a>) + (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038503"><a href="#local-6989586621679038503">c</a></a> <a name="local-6989586621679038504"><a href="#local-6989586621679038504">d</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="#local-6989586621679038501">a</a> + <a href="#local-6989586621679038503">c</a>) (<a href="#local-6989586621679038502">b</a> + <a href="#local-6989586621679038504">d</a>)

231+<a name="line-231"></a> <a name="local-6989586621679038505"><a href="#local-6989586621679038505">x</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) + <a name="local-6989586621679038506"><a href="#local-6989586621679038506">y</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) = <a href="#local-6989586621679038505">x</a> + <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038506">y</a>

232+<a name="line-232"></a> <a name="local-6989586621679038507"><a href="#local-6989586621679038507">x</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) + <a name="local-6989586621679038508"><a href="#local-6989586621679038508">y</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) = <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038507">x</a> + <a href="#local-6989586621679038508">y</a>

233+<a name="line-233"></a>

234+<a name="line-234"></a> <a href="Matrix.Internal.html#Empty">Empty</a> - <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

235+<a name="line-235"></a> (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038509"><a href="#local-6989586621679038509">a</a></a>) - (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038510"><a href="#local-6989586621679038510">b</a></a>) = <a href="Matrix.Internal.html#One">One</a> (<a href="#local-6989586621679038509">a</a> - <a href="#local-6989586621679038510">b</a>)

236+<a name="line-236"></a> (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038511"><a href="#local-6989586621679038511">a</a></a> <a name="local-6989586621679038512"><a href="#local-6989586621679038512">b</a></a>) - (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038513"><a href="#local-6989586621679038513">c</a></a> <a name="local-6989586621679038514"><a href="#local-6989586621679038514">d</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="#local-6989586621679038511">a</a> - <a href="#local-6989586621679038513">c</a>) (<a href="#local-6989586621679038512">b</a> - <a href="#local-6989586621679038514">d</a>)

237+<a name="line-237"></a> (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038515"><a href="#local-6989586621679038515">a</a></a> <a name="local-6989586621679038516"><a href="#local-6989586621679038516">b</a></a>) - (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038517"><a href="#local-6989586621679038517">c</a></a> <a name="local-6989586621679038518"><a href="#local-6989586621679038518">d</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="#local-6989586621679038515">a</a> - <a href="#local-6989586621679038517">c</a>) (<a href="#local-6989586621679038516">b</a> - <a href="#local-6989586621679038518">d</a>)

238+<a name="line-238"></a> <a name="local-6989586621679038519"><a href="#local-6989586621679038519">x</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) - <a name="local-6989586621679038520"><a href="#local-6989586621679038520">y</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) = <a href="#local-6989586621679038519">x</a> - <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038520">y</a>

239+<a name="line-239"></a> <a name="local-6989586621679038521"><a href="#local-6989586621679038521">x</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) - <a name="local-6989586621679038522"><a href="#local-6989586621679038522">y</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) = <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038521">x</a> - <a href="#local-6989586621679038522">y</a>

240+<a name="line-240"></a>

241+<a name="line-241"></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a name="local-8214565720323790402">*</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

242+<a name="line-242"></a> (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038523"><a href="#local-6989586621679038523">a</a></a>) * (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038524"><a href="#local-6989586621679038524">b</a></a>) = <a href="Matrix.Internal.html#One">One</a> (<a href="#local-6989586621679038523">a</a> * <a href="#local-6989586621679038524">b</a>)

243+<a name="line-243"></a> (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038525"><a href="#local-6989586621679038525">a</a></a> <a name="local-6989586621679038526"><a href="#local-6989586621679038526">b</a></a>) * (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038527"><a href="#local-6989586621679038527">c</a></a> <a name="local-6989586621679038528"><a href="#local-6989586621679038528">d</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="#local-6989586621679038525">a</a> * <a href="#local-6989586621679038527">c</a>) (<a href="#local-6989586621679038526">b</a> * <a href="#local-6989586621679038528">d</a>)

244+<a name="line-244"></a> (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038529"><a href="#local-6989586621679038529">a</a></a> <a name="local-6989586621679038530"><a href="#local-6989586621679038530">b</a></a>) * (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038531"><a href="#local-6989586621679038531">c</a></a> <a name="local-6989586621679038532"><a href="#local-6989586621679038532">d</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="#local-6989586621679038529">a</a> * <a href="#local-6989586621679038531">c</a>) (<a href="#local-6989586621679038530">b</a> * <a href="#local-6989586621679038532">d</a>)

245+<a name="line-245"></a> <a name="local-6989586621679038533"><a href="#local-6989586621679038533">x</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) * <a name="local-6989586621679038534"><a href="#local-6989586621679038534">y</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) = <a href="#local-6989586621679038533">x</a> * <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038534">y</a>

246+<a name="line-246"></a> <a name="local-6989586621679038535"><a href="#local-6989586621679038535">x</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) * <a name="local-6989586621679038536"><a href="#local-6989586621679038536">y</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) = <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038535">x</a> * <a href="#local-6989586621679038536">y</a>

247+<a name="line-247"></a>

248+<a name="line-248"></a> <a name="local-8214565720323790401">abs</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

249+<a name="line-249"></a> abs (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038537"><a href="#local-6989586621679038537">a</a></a>) = <a href="Matrix.Internal.html#One">One</a> (abs <a href="#local-6989586621679038537">a</a>)

250+<a name="line-250"></a> abs (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038538"><a href="#local-6989586621679038538">a</a></a> <a name="local-6989586621679038539"><a href="#local-6989586621679038539">b</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (abs <a href="#local-6989586621679038538">a</a>) (abs <a href="#local-6989586621679038539">b</a>)

251+<a name="line-251"></a> abs (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038540"><a href="#local-6989586621679038540">a</a></a> <a name="local-6989586621679038541"><a href="#local-6989586621679038541">b</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (abs <a href="#local-6989586621679038540">a</a>) (abs <a href="#local-6989586621679038541">b</a>)

252+<a name="line-252"></a>

253+<a name="line-253"></a> <a name="local-8214565720323790400">signum</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

254+<a name="line-254"></a> signum (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038542"><a href="#local-6989586621679038542">a</a></a>) = <a href="Matrix.Internal.html#One">One</a> (signum <a href="#local-6989586621679038542">a</a>)

255+<a name="line-255"></a> signum (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038543"><a href="#local-6989586621679038543">a</a></a> <a name="local-6989586621679038544"><a href="#local-6989586621679038544">b</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (signum <a href="#local-6989586621679038543">a</a>) (signum <a href="#local-6989586621679038544">b</a>)

256+<a name="line-256"></a> signum (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038545"><a href="#local-6989586621679038545">a</a></a> <a name="local-6989586621679038546"><a href="#local-6989586621679038546">b</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (signum <a href="#local-6989586621679038545">a</a>) (signum <a href="#local-6989586621679038546">b</a>)

257+<a name="line-257"></a>

258+<a name="line-258"></a>instance Ord <a href="#local-6989586621679038475">e</a> => Ord (<a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038475">e</a> <a href="#local-6989586621679038476">cols</a> <a href="#local-6989586621679038477">rows</a>) where

259+<a name="line-259"></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a name="local-8214565720323790495"><=</a> <a href="Matrix.Internal.html#Empty">Empty</a> = True

260+<a name="line-260"></a> (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038478"><a href="#local-6989586621679038478">a</a></a>) <= (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038479"><a href="#local-6989586621679038479">b</a></a>) = <a href="#local-6989586621679038478">a</a> <= <a href="#local-6989586621679038479">b</a>

261+<a name="line-261"></a> (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038480"><a href="#local-6989586621679038480">a</a></a> <a name="local-6989586621679038481"><a href="#local-6989586621679038481">b</a></a>) <= (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038482"><a href="#local-6989586621679038482">c</a></a> <a name="local-6989586621679038483"><a href="#local-6989586621679038483">d</a></a>) = (<a href="#local-6989586621679038480">a</a> <= <a href="#local-6989586621679038482">c</a>) && (<a href="#local-6989586621679038481">b</a> <= <a href="#local-6989586621679038483">d</a>)

262+<a name="line-262"></a> (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038484"><a href="#local-6989586621679038484">a</a></a> <a name="local-6989586621679038485"><a href="#local-6989586621679038485">b</a></a>) <= (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038486"><a href="#local-6989586621679038486">c</a></a> <a name="local-6989586621679038487"><a href="#local-6989586621679038487">d</a></a>) = (<a href="#local-6989586621679038484">a</a> <= <a href="#local-6989586621679038486">c</a>) && (<a href="#local-6989586621679038485">b</a> <= <a href="#local-6989586621679038487">d</a>)

263+<a name="line-263"></a> <a name="local-6989586621679038488"><a href="#local-6989586621679038488">x</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) <= <a name="local-6989586621679038489"><a href="#local-6989586621679038489">y</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) = <a href="#local-6989586621679038488">x</a> <= <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038489">y</a>

264+<a name="line-264"></a> <a name="local-6989586621679038490"><a href="#local-6989586621679038490">x</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) <= <a name="local-6989586621679038491"><a href="#local-6989586621679038491">y</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) = <a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038490">x</a> <= <a href="#local-6989586621679038491">y</a>

265+<a name="line-265"></a>

266+<a name="line-266"></a>-- Primitives

267+<a name="line-267"></a>

268+<a name="line-268"></a>-- | Empty matrix constructor

269+<a name="line-269"></a>empty :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038712">e</a> Void Void

270+<a name="line-270"></a><a name="empty"><a href="Matrix.Internal.html#empty">empty</a></a> = <a href="Matrix.Internal.html#Empty">Empty</a>

271+<a name="line-271"></a>

272+<a name="line-272"></a>-- | Unit matrix constructor

273+<a name="line-273"></a>one :: <a href="#local-6989586621679038711">e</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038711">e</a> () ()

274+<a name="line-274"></a><a name="one"><a href="Matrix.Internal.html#one">one</a></a> = <a href="Matrix.Internal.html#One">One</a>

275+<a name="line-275"></a>

276+<a name="line-276"></a>-- | Matrix 'Junc' constructor

277+<a name="line-277"></a>junc :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038707">e</a> <a href="#local-6989586621679038708">a</a> <a href="#local-6989586621679038709">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038707">e</a> <a href="#local-6989586621679038710">b</a> <a href="#local-6989586621679038709">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038707">e</a> (Either <a href="#local-6989586621679038708">a</a> <a href="#local-6989586621679038710">b</a>) <a href="#local-6989586621679038709">rows</a>

278+<a name="line-278"></a><a name="junc"><a href="Matrix.Internal.html#junc">junc</a></a> = <a href="Matrix.Internal.html#Junc">Junc</a>

279+<a name="line-279"></a>

280+<a name="line-280"></a>infixl 3 <a href="Matrix.Internal.html#%7C%7C%7C">|||</a>

281+<a name="line-281"></a>

282+<a name="line-282"></a>-- | Matrix 'Junc' constructor

283+<a name="line-283"></a>(|||) :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038703">e</a> <a href="#local-6989586621679038704">a</a> <a href="#local-6989586621679038705">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038703">e</a> <a href="#local-6989586621679038706">b</a> <a href="#local-6989586621679038705">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038703">e</a> (Either <a href="#local-6989586621679038704">a</a> <a href="#local-6989586621679038706">b</a>) <a href="#local-6989586621679038705">rows</a>

284+<a name="line-284"></a>(<a name="%7C%7C%7C"><a href="Matrix.Internal.html#%7C%7C%7C">|||</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a>

285+<a name="line-285"></a>

286+<a name="line-286"></a>-- | Matrix 'Split' constructor

287+<a name="line-287"></a>split :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038699">e</a> <a href="#local-6989586621679038700">cols</a> <a href="#local-6989586621679038701">a</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038699">e</a> <a href="#local-6989586621679038700">cols</a> <a href="#local-6989586621679038702">b</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038699">e</a> <a href="#local-6989586621679038700">cols</a> (Either <a href="#local-6989586621679038701">a</a> <a href="#local-6989586621679038702">b</a>)

288+<a name="line-288"></a><a name="split"><a href="Matrix.Internal.html#split">split</a></a> = <a href="Matrix.Internal.html#Split">Split</a>

289+<a name="line-289"></a>

290+<a name="line-290"></a>infixl 2 <a href="Matrix.Internal.html#%3D%3D%3D">===</a>

291+<a name="line-291"></a>

292+<a name="line-292"></a>-- | Matrix 'Split' constructor

293+<a name="line-293"></a>(===) :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038695">e</a> <a href="#local-6989586621679038696">cols</a> <a href="#local-6989586621679038697">a</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038695">e</a> <a href="#local-6989586621679038696">cols</a> <a href="#local-6989586621679038698">b</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038695">e</a> <a href="#local-6989586621679038696">cols</a> (Either <a href="#local-6989586621679038697">a</a> <a href="#local-6989586621679038698">b</a>)

294+<a name="line-294"></a>(<a name="%3D%3D%3D"><a href="Matrix.Internal.html#%3D%3D%3D">===</a></a>) = <a href="Matrix.Internal.html#Split">Split</a>

295+<a name="line-295"></a>

296+<a name="line-296"></a>-- Construction

297+<a name="line-297"></a>

298+<a name="line-298"></a>-- | Type class for defining the 'fromList' conversion function.

299+<a name="line-299"></a>--

300+<a name="line-300"></a>-- Given that it is not possible to branch on types at the term level type

301+<a name="line-301"></a>-- classes are needed bery much like an inductive definition but on types.

302+<a name="line-302"></a>class <a name="FromLists"><a href="Matrix.Internal.html#FromLists">FromLists</a></a> <a name="local-6989586621679038061"><a href="#local-6989586621679038061">e</a></a> <a name="local-6989586621679038062"><a href="#local-6989586621679038062">cols</a></a> <a name="local-6989586621679038063"><a href="#local-6989586621679038063">rows</a></a> where

303+<a name="line-303"></a> -- | Build a matrix out of a list of list of elements. Throws a runtime

304+<a name="line-304"></a> -- error if the dimensions do not match.

305+<a name="line-305"></a> <a name="fromLists"><a href="Matrix.Internal.html#fromLists">fromLists</a></a> :: [[<a href="#local-6989586621679038061">e</a>]] -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038061">e</a> <a href="#local-6989586621679038062">cols</a> <a href="#local-6989586621679038063">rows</a>

306+<a name="line-306"></a>

307+<a name="line-307"></a>instance <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038474">e</a> Void Void where

308+<a name="line-308"></a> <a name="local-8214565720323812914"><a href="Matrix.Internal.html#fromLists">fromLists</a></a> [] = <a href="Matrix.Internal.html#Empty">Empty</a>

309+<a name="line-309"></a> fromLists _ = error "Wrong dimensions"

310+<a name="line-310"></a>

311+<a name="line-311"></a>instance {-# OVERLAPPING #-} <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038472">e</a> () () where

312+<a name="line-312"></a> <a name="local-8214565720323812914"><a href="Matrix.Internal.html#fromLists">fromLists</a></a> [[<a name="local-6989586621679038473"><a href="#local-6989586621679038473">e</a></a>]] = <a href="Matrix.Internal.html#One">One</a> <a href="#local-6989586621679038473">e</a>

313+<a name="line-313"></a> fromLists _ = error "Wrong dimensions"

314+<a name="line-314"></a>

315+<a name="line-315"></a>instance {-# OVERLAPPING #-} (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038468">e</a> <a href="#local-6989586621679038469">cols</a> ()) => <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038468">e</a> (Either () <a href="#local-6989586621679038469">cols</a>) () where

316+<a name="line-316"></a> <a name="local-8214565720323812914"><a href="Matrix.Internal.html#fromLists">fromLists</a></a> [<a name="local-6989586621679038470"><a href="#local-6989586621679038470">h</a></a> : <a name="local-6989586621679038471"><a href="#local-6989586621679038471">t</a></a>] = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#One">One</a> <a href="#local-6989586621679038470">h</a>) (<a href="Matrix.Internal.html#fromLists">fromLists</a> [<a href="#local-6989586621679038471">t</a>])

317+<a name="line-317"></a> fromLists _ = error "Wrong dimensions"

318+<a name="line-318"></a>

319+<a name="line-319"></a>instance {-# OVERLAPPABLE #-} (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038463">e</a> <a href="#local-6989586621679038464">a</a> (), <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038463">e</a> <a href="#local-6989586621679038465">b</a> (), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038464">a</a>)) => <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038463">e</a> (Either <a href="#local-6989586621679038464">a</a> <a href="#local-6989586621679038465">b</a>) () where

320+<a name="line-320"></a> <a name="local-8214565720323812914"><a href="Matrix.Internal.html#fromLists">fromLists</a></a> [<a name="local-6989586621679038466"><a href="#local-6989586621679038466">l</a></a>] =

321+<a name="line-321"></a> let <a name="local-6989586621679038467"><a href="#local-6989586621679038467">rowsA</a></a> = fromInteger (natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038464">a</a>)))

322+<a name="line-322"></a> in <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#fromLists">fromLists</a> [take <a href="#local-6989586621679038467">rowsA</a> <a href="#local-6989586621679038466">l</a>]) (<a href="Matrix.Internal.html#fromLists">fromLists</a> [drop <a href="#local-6989586621679038467">rowsA</a> <a href="#local-6989586621679038466">l</a>])

323+<a name="line-323"></a> fromLists _ = error "Wrong dimensions"

324+<a name="line-324"></a>

325+<a name="line-325"></a>instance {-# OVERLAPPING #-} (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038459">e</a> () <a href="#local-6989586621679038460">rows</a>) => <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038459">e</a> () (Either () <a href="#local-6989586621679038460">rows</a>) where

326+<a name="line-326"></a> <a name="local-8214565720323812914"><a href="Matrix.Internal.html#fromLists">fromLists</a></a> ([<a name="local-6989586621679038461"><a href="#local-6989586621679038461">h</a></a>] : <a name="local-6989586621679038462"><a href="#local-6989586621679038462">t</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#One">One</a> <a href="#local-6989586621679038461">h</a>) (<a href="Matrix.Internal.html#fromLists">fromLists</a> <a href="#local-6989586621679038462">t</a>)

327+<a name="line-327"></a> fromLists _ = error "Wrong dimensions"

328+<a name="line-328"></a>

329+<a name="line-329"></a>instance {-# OVERLAPPABLE #-} (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038454">e</a> () <a href="#local-6989586621679038455">a</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038454">e</a> () <a href="#local-6989586621679038456">b</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038455">a</a>)) => <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038454">e</a> () (Either <a href="#local-6989586621679038455">a</a> <a href="#local-6989586621679038456">b</a>) where

330+<a name="line-330"></a> <a name="local-8214565720323812914"><a href="Matrix.Internal.html#fromLists">fromLists</a></a> <a name="local-6989586621679038457"><a href="#local-6989586621679038457">l</a></a>@([_] : _) =

331+<a name="line-331"></a> let <a name="local-6989586621679038458"><a href="#local-6989586621679038458">rowsA</a></a> = fromInteger (natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038455">a</a>)))

332+<a name="line-332"></a> in <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#fromLists">fromLists</a> (take <a href="#local-6989586621679038458">rowsA</a> <a href="#local-6989586621679038457">l</a>)) (<a href="Matrix.Internal.html#fromLists">fromLists</a> (drop <a href="#local-6989586621679038458">rowsA</a> <a href="#local-6989586621679038457">l</a>))

333+<a name="line-333"></a> fromLists _ = error "Wrong dimensions"

334+<a name="line-334"></a>

335+<a name="line-335"></a>instance {-# OVERLAPPABLE #-} (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038253">e</a> (Either <a href="#local-6989586621679038254">a</a> <a href="#local-6989586621679038255">b</a>) <a href="#local-6989586621679038256">c</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038253">e</a> (Either <a href="#local-6989586621679038254">a</a> <a href="#local-6989586621679038255">b</a>) <a href="#local-6989586621679038257">d</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038256">c</a>)) => <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038253">e</a> (Either <a href="#local-6989586621679038254">a</a> <a href="#local-6989586621679038255">b</a>) (Either <a href="#local-6989586621679038256">c</a> <a href="#local-6989586621679038257">d</a>) where

336+<a name="line-336"></a> <a name="local-8214565720323812914"><a href="Matrix.Internal.html#fromLists">fromLists</a></a> <a name="local-6989586621679038258"><a href="#local-6989586621679038258">l</a></a>@(<a name="local-6989586621679038259"><a href="#local-6989586621679038259">h</a></a> : <a name="local-6989586621679038260"><a href="#local-6989586621679038260">t</a></a>) =

337+<a name="line-337"></a> let <a name="local-6989586621679038261"><a href="#local-6989586621679038261">lh</a></a> = length <a href="#local-6989586621679038259">h</a>

338+<a name="line-338"></a> <a name="local-6989586621679038262"><a href="#local-6989586621679038262">rowsC</a></a> = fromInteger (natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038256">c</a>)))

339+<a name="line-339"></a> <a name="local-6989586621679038263"><a href="#local-6989586621679038263">condition</a></a> = all (== <a href="#local-6989586621679038261">lh</a>) (map length <a href="#local-6989586621679038260">t</a>)

340+<a name="line-340"></a> in if <a href="#local-6989586621679038261">lh</a> > 0 && <a href="#local-6989586621679038263">condition</a>

341+<a name="line-341"></a> then <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#fromLists">fromLists</a> (take <a href="#local-6989586621679038262">rowsC</a> <a href="#local-6989586621679038258">l</a>)) (<a href="Matrix.Internal.html#fromLists">fromLists</a> (drop <a href="#local-6989586621679038262">rowsC</a> <a href="#local-6989586621679038258">l</a>))

342+<a name="line-342"></a> else error "Not all rows have the same length"

343+<a name="line-343"></a>

344+<a name="line-344"></a>-- | Matrix builder function. Constructs a matrix provided with

345+<a name="line-345"></a>-- a construction function.

346+<a name="line-346"></a>matrixBuilder ::

347+<a name="line-347"></a> forall <a name="local-6989586621679038692"><a href="#local-6989586621679038692">e</a></a> <a name="local-6989586621679038693"><a href="#local-6989586621679038693">cols</a></a> <a name="local-6989586621679038694"><a href="#local-6989586621679038694">rows</a></a>.

348+<a name="line-348"></a> ( <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038692">e</a> <a href="#local-6989586621679038693">cols</a> <a href="#local-6989586621679038694">rows</a>,

349+<a name="line-349"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038693">cols</a>),

350+<a name="line-350"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038694">rows</a>)

351+<a name="line-351"></a> ) =>

352+<a name="line-352"></a> ((Int, Int) -> <a href="#local-6989586621679038692">e</a>) ->

353+<a name="line-353"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038692">e</a> <a href="#local-6989586621679038693">cols</a> <a href="#local-6989586621679038694">rows</a>

354+<a name="line-354"></a><a name="matrixBuilder"><a href="Matrix.Internal.html#matrixBuilder">matrixBuilder</a></a> <a name="local-6989586621679038713"><a href="#local-6989586621679038713">f</a></a> =

355+<a name="line-355"></a> let <a name="local-6989586621679038714"><a href="#local-6989586621679038714">c</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038693">cols</a>))

356+<a name="line-356"></a> <a name="local-6989586621679038715"><a href="#local-6989586621679038715">r</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038694">rows</a>))

357+<a name="line-357"></a> <a name="local-6989586621679038716"><a href="#local-6989586621679038716">positions</a></a> = [(<a href="#local-6989586621679038717">a</a>, <a href="#local-6989586621679038718">b</a>) | <a name="local-6989586621679038717"><a href="#local-6989586621679038717">a</a></a> <- [0 .. (<a href="#local-6989586621679038715">r</a> - 1)], <a name="local-6989586621679038718"><a href="#local-6989586621679038718">b</a></a> <- [0 .. (<a href="#local-6989586621679038714">c</a> - 1)]]

358+<a name="line-358"></a> in <a href="Matrix.Internal.html#fromLists">fromLists</a> . map (map <a href="#local-6989586621679038713">f</a>) . groupBy (\(<a name="local-6989586621679038874"><a href="#local-6989586621679038874">x</a></a>, _) (<a name="local-6989586621679038875"><a href="#local-6989586621679038875">w</a></a>, _) -> <a href="#local-6989586621679038874">x</a> == <a href="#local-6989586621679038875">w</a>) $ <a href="#local-6989586621679038716">positions</a>

359+<a name="line-359"></a>

360+<a name="line-360"></a>-- | Constructs a column vector matrix

361+<a name="line-361"></a>col :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038690">e</a> () <a href="#local-6989586621679038691">rows</a>) => [<a href="#local-6989586621679038690">e</a>] -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038690">e</a> () <a href="#local-6989586621679038691">rows</a>

362+<a name="line-362"></a><a name="col"><a href="Matrix.Internal.html#col">col</a></a> = <a href="Matrix.Internal.html#fromLists">fromLists</a> . map (: [])

363+<a name="line-363"></a>

364+<a name="line-364"></a>-- | Constructs a row vector matrix

365+<a name="line-365"></a>row :: (<a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038688">e</a> <a href="#local-6989586621679038689">cols</a> ()) => [<a href="#local-6989586621679038688">e</a>] -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038688">e</a> <a href="#local-6989586621679038689">cols</a> ()

366+<a name="line-366"></a><a name="row"><a href="Matrix.Internal.html#row">row</a></a> = <a href="Matrix.Internal.html#fromLists">fromLists</a> . (: [])

367+<a name="line-367"></a>

368+<a name="line-368"></a>-- | Lifts functions to matrices with arbitrary dimensions.

369+<a name="line-369"></a>--

370+<a name="line-370"></a>-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of

371+<a name="line-371"></a>-- types @a@ or @b@ allows.

372+<a name="line-372"></a>fromF ::

373+<a name="line-373"></a> forall <a name="local-6989586621679038683"><a href="#local-6989586621679038683">a</a></a> <a name="local-6989586621679038684"><a href="#local-6989586621679038684">b</a></a> <a name="local-6989586621679038685"><a href="#local-6989586621679038685">cols</a></a> <a name="local-6989586621679038686"><a href="#local-6989586621679038686">rows</a></a> <a name="local-6989586621679038687"><a href="#local-6989586621679038687">e</a></a>.

374+<a name="line-374"></a> ( Bounded <a href="#local-6989586621679038683">a</a>,

375+<a name="line-375"></a> Bounded <a href="#local-6989586621679038684">b</a>,

376+<a name="line-376"></a> Enum <a href="#local-6989586621679038683">a</a>,

377+<a name="line-377"></a> Enum <a href="#local-6989586621679038684">b</a>,

378+<a name="line-378"></a> Eq <a href="#local-6989586621679038684">b</a>,

379+<a name="line-379"></a> Num <a href="#local-6989586621679038687">e</a>,

380+<a name="line-380"></a> Ord <a href="#local-6989586621679038687">e</a>,

381+<a name="line-381"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038685">cols</a>),

382+<a name="line-382"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038686">rows</a>),

383+<a name="line-383"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038687">e</a> <a href="#local-6989586621679038686">rows</a> <a href="#local-6989586621679038685">cols</a>

384+<a name="line-384"></a> ) =>

385+<a name="line-385"></a> (<a href="#local-6989586621679038683">a</a> -> <a href="#local-6989586621679038684">b</a>) ->

386+<a name="line-386"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038687">e</a> <a href="#local-6989586621679038685">cols</a> <a href="#local-6989586621679038686">rows</a>

387+<a name="line-387"></a><a name="fromF"><a href="Matrix.Internal.html#fromF">fromF</a></a> <a name="local-6989586621679038876"><a href="#local-6989586621679038876">f</a></a> =

388+<a name="line-388"></a> let <a name="local-6989586621679038880"><a href="#local-6989586621679038880">minA</a></a> = minBound @<a href="#local-6989586621679038683">a</a>

389+<a name="line-389"></a> <a name="local-6989586621679038881"><a href="#local-6989586621679038881">maxA</a></a> = maxBound @<a href="#local-6989586621679038683">a</a>

390+<a name="line-390"></a> <a name="local-6989586621679038882"><a href="#local-6989586621679038882">minB</a></a> = minBound @<a href="#local-6989586621679038684">b</a>

391+<a name="line-391"></a> <a name="local-6989586621679038883"><a href="#local-6989586621679038883">maxB</a></a> = maxBound @<a href="#local-6989586621679038684">b</a>

392+<a name="line-392"></a> <a name="local-6989586621679038884"><a href="#local-6989586621679038884">ccols</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038685">cols</a>))

393+<a name="line-393"></a> <a name="local-6989586621679038885"><a href="#local-6989586621679038885">rrows</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038686">rows</a>))

394+<a name="line-394"></a> <a name="local-6989586621679038886"><a href="#local-6989586621679038886">elementsA</a></a> = take <a href="#local-6989586621679038884">ccols</a> [<a href="#local-6989586621679038880">minA</a> .. <a href="#local-6989586621679038881">maxA</a>]

395+<a name="line-395"></a> <a name="local-6989586621679038887"><a href="#local-6989586621679038887">elementsB</a></a> = take <a href="#local-6989586621679038885">rrows</a> [<a href="#local-6989586621679038882">minB</a> .. <a href="#local-6989586621679038883">maxB</a>]

396+<a name="line-396"></a> <a name="local-6989586621679038888"><a href="#local-6989586621679038888">combinations</a></a> = (,) <$> <a href="#local-6989586621679038886">elementsA</a> <*> <a href="#local-6989586621679038887">elementsB</a>

397+<a name="line-397"></a> <a name="local-6989586621679038889"><a href="#local-6989586621679038889">combAp</a></a> = map snd . sort . map (\(<a name="local-6989586621679038920"><a href="#local-6989586621679038920">a</a></a>, <a name="local-6989586621679038921"><a href="#local-6989586621679038921">b</a></a>) -> if <a href="#local-6989586621679038876">f</a> <a href="#local-6989586621679038920">a</a> == <a href="#local-6989586621679038921">b</a>

398+<a name="line-398"></a> then ((fromEnum <a href="#local-6989586621679038920">a</a>, fromEnum <a href="#local-6989586621679038921">b</a>), 1)

399+<a name="line-399"></a> else ((fromEnum <a href="#local-6989586621679038920">a</a>, fromEnum <a href="#local-6989586621679038921">b</a>), 0)) $ <a href="#local-6989586621679038888">combinations</a>

400+<a name="line-400"></a> <a name="local-6989586621679038890"><a href="#local-6989586621679038890">mList</a></a> = <a href="#local-6989586621679038877">buildList</a> <a href="#local-6989586621679038889">combAp</a> <a href="#local-6989586621679038885">rrows</a>

401+<a name="line-401"></a> in <a href="Matrix.Internal.html#tr">tr</a> $ <a href="Matrix.Internal.html#fromLists">fromLists</a> <a href="#local-6989586621679038890">mList</a>

402+<a name="line-402"></a> where

403+<a name="line-403"></a> <a name="local-6989586621679038877"><a href="#local-6989586621679038877">buildList</a></a> [] _ = []

404+<a name="line-404"></a> buildList <a name="local-6989586621679038878"><a href="#local-6989586621679038878">l</a></a> <a name="local-6989586621679038879"><a href="#local-6989586621679038879">r</a></a> = take <a href="#local-6989586621679038879">r</a> <a href="#local-6989586621679038878">l</a> : <a href="#local-6989586621679038877">buildList</a> (drop <a href="#local-6989586621679038879">r</a> <a href="#local-6989586621679038878">l</a>) <a href="#local-6989586621679038879">r</a>

405+<a name="line-405"></a>

406+<a name="line-406"></a>-- | Lifts functions to matrices with dimensions matching @a@ and @b@

407+<a name="line-407"></a>-- cardinality's.

408+<a name="line-408"></a>fromF' ::

409+<a name="line-409"></a> forall <a name="local-6989586621679038680"><a href="#local-6989586621679038680">a</a></a> <a name="local-6989586621679038681"><a href="#local-6989586621679038681">b</a></a> <a name="local-6989586621679038682"><a href="#local-6989586621679038682">e</a></a>.

410+<a name="line-410"></a> ( Bounded <a href="#local-6989586621679038680">a</a>,

411+<a name="line-411"></a> Bounded <a href="#local-6989586621679038681">b</a>,

412+<a name="line-412"></a> Enum <a href="#local-6989586621679038680">a</a>,

413+<a name="line-413"></a> Enum <a href="#local-6989586621679038681">b</a>,

414+<a name="line-414"></a> Eq <a href="#local-6989586621679038681">b</a>,

415+<a name="line-415"></a> Num <a href="#local-6989586621679038682">e</a>,

416+<a name="line-416"></a> Ord <a href="#local-6989586621679038682">e</a>,

417+<a name="line-417"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038680">a</a>)),

418+<a name="line-418"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038681">b</a>)),

419+<a name="line-419"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038682">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038681">b</a>) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038680">a</a>)

420+<a name="line-420"></a> ) =>

421+<a name="line-421"></a> (<a href="#local-6989586621679038680">a</a> -> <a href="#local-6989586621679038681">b</a>) ->

422+<a name="line-422"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038682">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038680">a</a>) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038681">b</a>)

423+<a name="line-423"></a><a name="fromF%27"><a href="Matrix.Internal.html#fromF%27">fromF'</a></a> <a name="local-6989586621679038922"><a href="#local-6989586621679038922">f</a></a> =

424+<a name="line-424"></a> let <a name="local-6989586621679038926"><a href="#local-6989586621679038926">minA</a></a> = minBound @<a href="#local-6989586621679038680">a</a>

425+<a name="line-425"></a> <a name="local-6989586621679038927"><a href="#local-6989586621679038927">maxA</a></a> = maxBound @<a href="#local-6989586621679038680">a</a>

426+<a name="line-426"></a> <a name="local-6989586621679038928"><a href="#local-6989586621679038928">minB</a></a> = minBound @<a href="#local-6989586621679038681">b</a>

427+<a name="line-427"></a> <a name="local-6989586621679038929"><a href="#local-6989586621679038929">maxB</a></a> = maxBound @<a href="#local-6989586621679038681">b</a>

428+<a name="line-428"></a> <a name="local-6989586621679038930"><a href="#local-6989586621679038930">ccols</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038680">a</a>)))

429+<a name="line-429"></a> <a name="local-6989586621679038931"><a href="#local-6989586621679038931">rrows</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038681">b</a>)))

430+<a name="line-430"></a> <a name="local-6989586621679038932"><a href="#local-6989586621679038932">elementsA</a></a> = take <a href="#local-6989586621679038930">ccols</a> [<a href="#local-6989586621679038926">minA</a> .. <a href="#local-6989586621679038927">maxA</a>]

431+<a name="line-431"></a> <a name="local-6989586621679038933"><a href="#local-6989586621679038933">elementsB</a></a> = take <a href="#local-6989586621679038931">rrows</a> [<a href="#local-6989586621679038928">minB</a> .. <a href="#local-6989586621679038929">maxB</a>]

432+<a name="line-432"></a> <a name="local-6989586621679038934"><a href="#local-6989586621679038934">combinations</a></a> = (,) <$> <a href="#local-6989586621679038932">elementsA</a> <*> <a href="#local-6989586621679038933">elementsB</a>

433+<a name="line-433"></a> <a name="local-6989586621679038935"><a href="#local-6989586621679038935">combAp</a></a> = map snd . sort . map (\(<a name="local-6989586621679038937"><a href="#local-6989586621679038937">a</a></a>, <a name="local-6989586621679038938"><a href="#local-6989586621679038938">b</a></a>) -> if <a href="#local-6989586621679038922">f</a> <a href="#local-6989586621679038937">a</a> == <a href="#local-6989586621679038938">b</a>

434+<a name="line-434"></a> then ((fromEnum <a href="#local-6989586621679038937">a</a>, fromEnum <a href="#local-6989586621679038938">b</a>), 1)

435+<a name="line-435"></a> else ((fromEnum <a href="#local-6989586621679038937">a</a>, fromEnum <a href="#local-6989586621679038938">b</a>), 0)) $ <a href="#local-6989586621679038934">combinations</a>

436+<a name="line-436"></a> <a name="local-6989586621679038936"><a href="#local-6989586621679038936">mList</a></a> = <a href="#local-6989586621679038923">buildList</a> <a href="#local-6989586621679038935">combAp</a> <a href="#local-6989586621679038931">rrows</a>

437+<a name="line-437"></a> in <a href="Matrix.Internal.html#tr">tr</a> $ <a href="Matrix.Internal.html#fromLists">fromLists</a> <a href="#local-6989586621679038936">mList</a>

438+<a name="line-438"></a> where

439+<a name="line-439"></a> <a name="local-6989586621679038923"><a href="#local-6989586621679038923">buildList</a></a> [] _ = []

440+<a name="line-440"></a> buildList <a name="local-6989586621679038924"><a href="#local-6989586621679038924">l</a></a> <a name="local-6989586621679038925"><a href="#local-6989586621679038925">r</a></a> = take <a href="#local-6989586621679038925">r</a> <a href="#local-6989586621679038924">l</a> : <a href="#local-6989586621679038923">buildList</a> (drop <a href="#local-6989586621679038925">r</a> <a href="#local-6989586621679038924">l</a>) <a href="#local-6989586621679038925">r</a>

441+<a name="line-441"></a>

442+<a name="line-442"></a>-- Conversion

443+<a name="line-443"></a>

444+<a name="line-444"></a>-- | Converts a matrix to a list of lists of elements.

445+<a name="line-445"></a>toLists :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038677">e</a> <a href="#local-6989586621679038678">cols</a> <a href="#local-6989586621679038679">rows</a> -> [[<a href="#local-6989586621679038677">e</a>]]

446+<a name="line-446"></a><a name="toLists"><a href="Matrix.Internal.html#toLists">toLists</a></a> <a href="Matrix.Internal.html#Empty">Empty</a> = []

447+<a name="line-447"></a>toLists (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038939"><a href="#local-6989586621679038939">e</a></a>) = [[<a href="#local-6989586621679038939">e</a>]]

448+<a name="line-448"></a>toLists (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038940"><a href="#local-6989586621679038940">l</a></a> <a name="local-6989586621679038941"><a href="#local-6989586621679038941">r</a></a>) = <a href="Matrix.Internal.html#toLists">toLists</a> <a href="#local-6989586621679038940">l</a> ++ <a href="Matrix.Internal.html#toLists">toLists</a> <a href="#local-6989586621679038941">r</a>

449+<a name="line-449"></a>toLists (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038942"><a href="#local-6989586621679038942">l</a></a> <a name="local-6989586621679038943"><a href="#local-6989586621679038943">r</a></a>) = zipWith (++) (<a href="Matrix.Internal.html#toLists">toLists</a> <a href="#local-6989586621679038942">l</a>) (<a href="Matrix.Internal.html#toLists">toLists</a> <a href="#local-6989586621679038943">r</a>)

450+<a name="line-450"></a>

451+<a name="line-451"></a>-- | Converts a matrix to a list of elements.

452+<a name="line-452"></a>toList :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038674">e</a> <a href="#local-6989586621679038675">cols</a> <a href="#local-6989586621679038676">rows</a> -> [<a href="#local-6989586621679038674">e</a>]

453+<a name="line-453"></a><a name="toList"><a href="Matrix.Internal.html#toList">toList</a></a> = concat . <a href="Matrix.Internal.html#toLists">toLists</a>

454+<a name="line-454"></a>

455+<a name="line-455"></a>-- Zeros Matrix

456+<a name="line-456"></a>

457+<a name="line-457"></a>-- | The zero matrix. A matrix wholly filled with zeros.

458+<a name="line-458"></a>zeros :: (Num <a href="#local-6989586621679038671">e</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038671">e</a> <a href="#local-6989586621679038672">cols</a> <a href="#local-6989586621679038673">rows</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038672">cols</a>), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038673">rows</a>)) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038671">e</a> <a href="#local-6989586621679038672">cols</a> <a href="#local-6989586621679038673">rows</a>

459+<a name="line-459"></a><a name="zeros"><a href="Matrix.Internal.html#zeros">zeros</a></a> = <a href="Matrix.Internal.html#matrixBuilder">matrixBuilder</a> (const 0)

460+<a name="line-460"></a>

461+<a name="line-461"></a>-- Ones Matrix

462+<a name="line-462"></a>

463+<a name="line-463"></a>-- | The ones matrix. A matrix wholly filled with ones.

464+<a name="line-464"></a>--

465+<a name="line-465"></a>-- Also known as T (Top) matrix.

466+<a name="line-466"></a>ones :: (Num <a href="#local-6989586621679038668">e</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038668">e</a> <a href="#local-6989586621679038669">cols</a> <a href="#local-6989586621679038670">rows</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038669">cols</a>), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038670">rows</a>)) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038668">e</a> <a href="#local-6989586621679038669">cols</a> <a href="#local-6989586621679038670">rows</a>

467+<a name="line-467"></a><a name="ones"><a href="Matrix.Internal.html#ones">ones</a></a> = <a href="Matrix.Internal.html#matrixBuilder">matrixBuilder</a> (const 1)

468+<a name="line-468"></a>

469+<a name="line-469"></a>-- Const Matrix

470+<a name="line-470"></a>

471+<a name="line-471"></a>-- | The constant matrix constructor. A matrix wholly filled with a given

472+<a name="line-472"></a>-- value.

473+<a name="line-473"></a>constant :: (Num <a href="#local-6989586621679038665">e</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038665">e</a> <a href="#local-6989586621679038666">cols</a> <a href="#local-6989586621679038667">rows</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038666">cols</a>), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038667">rows</a>)) => <a href="#local-6989586621679038665">e</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038665">e</a> <a href="#local-6989586621679038666">cols</a> <a href="#local-6989586621679038667">rows</a>

474+<a name="line-474"></a><a name="constant"><a href="Matrix.Internal.html#constant">constant</a></a> <a name="local-6989586621679038944"><a href="#local-6989586621679038944">e</a></a> = <a href="Matrix.Internal.html#matrixBuilder">matrixBuilder</a> (const <a href="#local-6989586621679038944">e</a>)

475+<a name="line-475"></a>

476+<a name="line-476"></a>-- Bang Matrix

477+<a name="line-477"></a>

478+<a name="line-478"></a>-- | The T (Top) row vector matrix.

479+<a name="line-479"></a>bang :: forall <a name="local-6989586621679038663"><a href="#local-6989586621679038663">e</a></a> <a name="local-6989586621679038664"><a href="#local-6989586621679038664">cols</a></a>. (Num <a href="#local-6989586621679038663">e</a>, Enum <a href="#local-6989586621679038663">e</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038663">e</a> <a href="#local-6989586621679038664">cols</a> (), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038664">cols</a>)) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038663">e</a> <a href="#local-6989586621679038664">cols</a> ()

480+<a name="line-480"></a><a name="bang"><a href="Matrix.Internal.html#bang">bang</a></a> =

481+<a name="line-481"></a> let <a name="local-6989586621679038945"><a href="#local-6989586621679038945">c</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038664">cols</a>))

482+<a name="line-482"></a> in <a href="Matrix.Internal.html#fromLists">fromLists</a> [take <a href="#local-6989586621679038945">c</a> [1, 1 ..]]

483+<a name="line-483"></a>

484+<a name="line-484"></a>-- Identity Matrix

485+<a name="line-485"></a>

486+<a name="line-486"></a>-- | Identity matrix.

487+<a name="line-487"></a>identity :: (Num <a href="#local-6989586621679038661">e</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038661">e</a> <a href="#local-6989586621679038662">cols</a> <a href="#local-6989586621679038662">cols</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038662">cols</a>)) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038661">e</a> <a href="#local-6989586621679038662">cols</a> <a href="#local-6989586621679038662">cols</a>

488+<a name="line-488"></a><a name="identity"><a href="Matrix.Internal.html#identity">identity</a></a> = <a href="Matrix.Internal.html#matrixBuilder">matrixBuilder</a> (bool 0 1 . uncurry (==))

489+<a name="line-489"></a>

490+<a name="line-490"></a>-- Matrix composition (MMM)

491+<a name="line-491"></a>

492+<a name="line-492"></a>-- | Matrix composition. Equivalent to matrix-matrix multiplication.

493+<a name="line-493"></a>--

494+<a name="line-494"></a>-- This definition takes advantage of divide-and-conquer and fusion laws

495+<a name="line-495"></a>-- from LAoP.

496+<a name="line-496"></a>comp :: (Num <a href="#local-6989586621679038657">e</a>) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038657">e</a> <a href="#local-6989586621679038658">cr</a> <a href="#local-6989586621679038659">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038657">e</a> <a href="#local-6989586621679038660">cols</a> <a href="#local-6989586621679038658">cr</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038657">e</a> <a href="#local-6989586621679038660">cols</a> <a href="#local-6989586621679038659">rows</a>

497+<a name="line-497"></a><a name="comp"><a href="Matrix.Internal.html#comp">comp</a></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

498+<a name="line-498"></a>comp (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038946"><a href="#local-6989586621679038946">a</a></a>) (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038947"><a href="#local-6989586621679038947">b</a></a>) = <a href="Matrix.Internal.html#One">One</a> (<a href="#local-6989586621679038946">a</a> * <a href="#local-6989586621679038947">b</a>)

499+<a name="line-499"></a>comp (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038948"><a href="#local-6989586621679038948">a</a></a> <a name="local-6989586621679038949"><a href="#local-6989586621679038949">b</a></a>) (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038950"><a href="#local-6989586621679038950">c</a></a> <a name="local-6989586621679038951"><a href="#local-6989586621679038951">d</a></a>) = <a href="Matrix.Internal.html#comp">comp</a> <a href="#local-6989586621679038948">a</a> <a href="#local-6989586621679038950">c</a> + <a href="Matrix.Internal.html#comp">comp</a> <a href="#local-6989586621679038949">b</a> <a href="#local-6989586621679038951">d</a> -- Divide-and-conquer law

500+<a name="line-500"></a>comp (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038952"><a href="#local-6989586621679038952">a</a></a> <a name="local-6989586621679038953"><a href="#local-6989586621679038953">b</a></a>) <a name="local-6989586621679038954"><a href="#local-6989586621679038954">c</a></a> = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#comp">comp</a> <a href="#local-6989586621679038952">a</a> <a href="#local-6989586621679038954">c</a>) (<a href="Matrix.Internal.html#comp">comp</a> <a href="#local-6989586621679038953">b</a> <a href="#local-6989586621679038954">c</a>) -- Split fusion law

501+<a name="line-501"></a>comp <a name="local-6989586621679038955"><a href="#local-6989586621679038955">c</a></a> (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038956"><a href="#local-6989586621679038956">a</a></a> <a name="local-6989586621679038957"><a href="#local-6989586621679038957">b</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#comp">comp</a> <a href="#local-6989586621679038955">c</a> <a href="#local-6989586621679038956">a</a>) (<a href="Matrix.Internal.html#comp">comp</a> <a href="#local-6989586621679038955">c</a> <a href="#local-6989586621679038957">b</a>) -- Junc fusion law

502+<a name="line-502"></a>

503+<a name="line-503"></a>-- Projections

504+<a name="line-504"></a>

505+<a name="line-505"></a>-- | Biproduct first component projection

506+<a name="line-506"></a>p1 :: forall <a name="local-6989586621679038654"><a href="#local-6989586621679038654">e</a></a> <a name="local-6989586621679038655"><a href="#local-6989586621679038655">m</a></a> <a name="local-6989586621679038656"><a href="#local-6989586621679038656">n</a></a>. (Num <a href="#local-6989586621679038654">e</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038656">n</a>), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038655">m</a>), <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038654">e</a> <a href="#local-6989586621679038656">n</a> <a href="#local-6989586621679038655">m</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038654">e</a> <a href="#local-6989586621679038655">m</a> <a href="#local-6989586621679038655">m</a>) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038654">e</a> (Either <a href="#local-6989586621679038655">m</a> <a href="#local-6989586621679038656">n</a>) <a href="#local-6989586621679038655">m</a>

507+<a name="line-507"></a><a name="p1"><a href="Matrix.Internal.html#p1">p1</a></a> =

508+<a name="line-508"></a> let <a name="local-6989586621679038958"><a href="#local-6989586621679038958">iden</a></a> = <a href="Matrix.Internal.html#identity">identity</a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038654">e</a> <a href="#local-6989586621679038655">m</a> <a href="#local-6989586621679038655">m</a>

509+<a name="line-509"></a> <a name="local-6989586621679038959"><a href="#local-6989586621679038959">zero</a></a> = <a href="Matrix.Internal.html#zeros">zeros</a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038654">e</a> <a href="#local-6989586621679038656">n</a> <a href="#local-6989586621679038655">m</a>

510+<a name="line-510"></a> in <a href="Matrix.Internal.html#junc">junc</a> <a href="#local-6989586621679038958">iden</a> <a href="#local-6989586621679038959">zero</a>

511+<a name="line-511"></a>

512+<a name="line-512"></a>-- | Biproduct second component projection

513+<a name="line-513"></a>p2 :: forall <a name="local-6989586621679038651"><a href="#local-6989586621679038651">e</a></a> <a name="local-6989586621679038652"><a href="#local-6989586621679038652">m</a></a> <a name="local-6989586621679038653"><a href="#local-6989586621679038653">n</a></a>. (Num <a href="#local-6989586621679038651">e</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038653">n</a>), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038652">m</a>), <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038651">e</a> <a href="#local-6989586621679038652">m</a> <a href="#local-6989586621679038653">n</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038651">e</a> <a href="#local-6989586621679038653">n</a> <a href="#local-6989586621679038653">n</a>) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038651">e</a> (Either <a href="#local-6989586621679038652">m</a> <a href="#local-6989586621679038653">n</a>) <a href="#local-6989586621679038653">n</a>

514+<a name="line-514"></a><a name="p2"><a href="Matrix.Internal.html#p2">p2</a></a> =

515+<a name="line-515"></a> let <a name="local-6989586621679038960"><a href="#local-6989586621679038960">iden</a></a> = <a href="Matrix.Internal.html#identity">identity</a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038651">e</a> <a href="#local-6989586621679038653">n</a> <a href="#local-6989586621679038653">n</a>

516+<a name="line-516"></a> <a name="local-6989586621679038961"><a href="#local-6989586621679038961">zero</a></a> = <a href="Matrix.Internal.html#zeros">zeros</a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038651">e</a> <a href="#local-6989586621679038652">m</a> <a href="#local-6989586621679038653">n</a>

517+<a name="line-517"></a> in <a href="Matrix.Internal.html#junc">junc</a> <a href="#local-6989586621679038961">zero</a> <a href="#local-6989586621679038960">iden</a>

518+<a name="line-518"></a>

519+<a name="line-519"></a>-- Injections

520+<a name="line-520"></a>

521+<a name="line-521"></a>-- | Biproduct first component injection

522+<a name="line-522"></a>i1 :: (Num <a href="#local-6989586621679038648">e</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038649">n</a>), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038650">m</a>), <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038648">e</a> <a href="#local-6989586621679038649">n</a> <a href="#local-6989586621679038650">m</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038648">e</a> <a href="#local-6989586621679038650">m</a> <a href="#local-6989586621679038650">m</a>) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038648">e</a> <a href="#local-6989586621679038650">m</a> (Either <a href="#local-6989586621679038650">m</a> <a href="#local-6989586621679038649">n</a>)

523+<a name="line-523"></a><a name="i1"><a href="Matrix.Internal.html#i1">i1</a></a> = <a href="Matrix.Internal.html#tr">tr</a> <a href="Matrix.Internal.html#p1">p1</a>

524+<a name="line-524"></a>

525+<a name="line-525"></a>-- | Biproduct second component injection

526+<a name="line-526"></a>i2 :: (Num <a href="#local-6989586621679038645">e</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038646">n</a>), KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038647">m</a>), <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038645">e</a> <a href="#local-6989586621679038647">m</a> <a href="#local-6989586621679038646">n</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038645">e</a> <a href="#local-6989586621679038646">n</a> <a href="#local-6989586621679038646">n</a>) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038645">e</a> <a href="#local-6989586621679038646">n</a> (Either <a href="#local-6989586621679038647">m</a> <a href="#local-6989586621679038646">n</a>)

527+<a name="line-527"></a><a name="i2"><a href="Matrix.Internal.html#i2">i2</a></a> = <a href="Matrix.Internal.html#tr">tr</a> <a href="Matrix.Internal.html#p2">p2</a>

528+<a name="line-528"></a>

529+<a name="line-529"></a>-- Dimensions

530+<a name="line-530"></a>

531+<a name="line-531"></a>-- | Obtain the number of rows.

532+<a name="line-532"></a>--

533+<a name="line-533"></a>-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

534+<a name="line-534"></a>-- dimensions in constant time.

535+<a name="line-535"></a>--

536+<a name="line-536"></a>-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in

537+<a name="line-537"></a>-- exchange for performance.

538+<a name="line-538"></a>rows :: forall <a name="local-6989586621679038642"><a href="#local-6989586621679038642">e</a></a> <a name="local-6989586621679038643"><a href="#local-6989586621679038643">cols</a></a> <a name="local-6989586621679038644"><a href="#local-6989586621679038644">rows</a></a>. (KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038644">rows</a>)) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038642">e</a> <a href="#local-6989586621679038643">cols</a> <a href="#local-6989586621679038644">rows</a> -> Int

539+<a name="line-539"></a><a name="rows"><a href="Matrix.Internal.html#rows">rows</a></a> _ = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038644">rows</a>))

540+<a name="line-540"></a>

541+<a name="line-541"></a>-- | Obtain the number of columns.

542+<a name="line-542"></a>--

543+<a name="line-543"></a>-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

544+<a name="line-544"></a>-- dimensions in constant time.

545+<a name="line-545"></a>--

546+<a name="line-546"></a>-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in

547+<a name="line-547"></a>-- exchange for performance.

548+<a name="line-548"></a>columns :: forall <a name="local-6989586621679038639"><a href="#local-6989586621679038639">e</a></a> <a name="local-6989586621679038640"><a href="#local-6989586621679038640">cols</a></a> <a name="local-6989586621679038641"><a href="#local-6989586621679038641">rows</a></a>. (KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038640">cols</a>)) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038639">e</a> <a href="#local-6989586621679038640">cols</a> <a href="#local-6989586621679038641">rows</a> -> Int

549+<a name="line-549"></a><a name="columns"><a href="Matrix.Internal.html#columns">columns</a></a> _ = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038640">cols</a>))

550+<a name="line-550"></a>

551+<a name="line-551"></a>-- Coproduct Bifunctor

552+<a name="line-552"></a>

553+<a name="line-553"></a>infixl 5 <a href="Matrix.Internal.html#-%7C-">-|-</a>

554+<a name="line-554"></a>

555+<a name="line-555"></a>-- | Matrix coproduct functor also known as matrix direct sum.

556+<a name="line-556"></a>(-|-) ::

557+<a name="line-557"></a> forall <a name="local-6989586621679038634"><a href="#local-6989586621679038634">e</a></a> <a name="local-6989586621679038635"><a href="#local-6989586621679038635">n</a></a> <a name="local-6989586621679038636"><a href="#local-6989586621679038636">k</a></a> <a name="local-6989586621679038637"><a href="#local-6989586621679038637">m</a></a> <a name="local-6989586621679038638"><a href="#local-6989586621679038638">j</a></a>.

558+<a name="line-558"></a> ( Num <a href="#local-6989586621679038634">e</a>,

559+<a name="line-559"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038638">j</a>),

560+<a name="line-560"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038636">k</a>),

561+<a name="line-561"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038634">e</a> <a href="#local-6989586621679038636">k</a> <a href="#local-6989586621679038636">k</a>,

562+<a name="line-562"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038634">e</a> <a href="#local-6989586621679038638">j</a> <a href="#local-6989586621679038636">k</a>,

563+<a name="line-563"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038634">e</a> <a href="#local-6989586621679038636">k</a> <a href="#local-6989586621679038638">j</a>,

564+<a name="line-564"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038634">e</a> <a href="#local-6989586621679038638">j</a> <a href="#local-6989586621679038638">j</a>

565+<a name="line-565"></a> ) =>

566+<a name="line-566"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038634">e</a> <a href="#local-6989586621679038635">n</a> <a href="#local-6989586621679038636">k</a> ->

567+<a name="line-567"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038634">e</a> <a href="#local-6989586621679038637">m</a> <a href="#local-6989586621679038638">j</a> ->

568+<a name="line-568"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038634">e</a> (Either <a href="#local-6989586621679038635">n</a> <a href="#local-6989586621679038637">m</a>) (Either <a href="#local-6989586621679038636">k</a> <a href="#local-6989586621679038638">j</a>)

569+<a name="line-569"></a>(<a name="-%7C-"><a href="Matrix.Internal.html#-%7C-">-|-</a></a>) <a name="local-6989586621679038962"><a href="#local-6989586621679038962">a</a></a> <a name="local-6989586621679038963"><a href="#local-6989586621679038963">b</a></a> = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#i1">i1</a> . <a href="#local-6989586621679038962">a</a>) (<a href="Matrix.Internal.html#i2">i2</a> . <a href="#local-6989586621679038963">b</a>)

570+<a name="line-570"></a>

571+<a name="line-571"></a>-- Khatri Rao Product and projections

572+<a name="line-572"></a>

573+<a name="line-573"></a>-- | Khatri Rao product first component projection matrix.

574+<a name="line-574"></a>kp1 ::

575+<a name="line-575"></a> forall <a name="local-6989586621679038631"><a href="#local-6989586621679038631">e</a></a> <a name="local-6989586621679038632"><a href="#local-6989586621679038632">m</a></a> <a name="local-6989586621679038633"><a href="#local-6989586621679038633">k</a></a> .

576+<a name="line-576"></a> ( Num <a href="#local-6989586621679038631">e</a>,

577+<a name="line-577"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038633">k</a>),

578+<a name="line-578"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038631">e</a> (<a href="Matrix.Internal.html#FromNat">FromNat</a> (Count <a href="#local-6989586621679038632">m</a> * <a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038633">k</a>)) <a href="#local-6989586621679038632">m</a>,

579+<a name="line-579"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038632">m</a>),

580+<a name="line-580"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038632">m</a>, <a href="#local-6989586621679038633">k</a>)))

581+<a name="line-581"></a> ) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038631">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038632">m</a>, <a href="#local-6989586621679038633">k</a>)) <a href="#local-6989586621679038632">m</a>

582+<a name="line-582"></a><a name="kp1"><a href="Matrix.Internal.html#kp1">kp1</a></a> = <a href="Matrix.Internal.html#matrixBuilder">matrixBuilder</a> <a href="#local-6989586621679038965">f</a>

583+<a name="line-583"></a> where

584+<a name="line-584"></a> <a name="local-6989586621679038964"><a href="#local-6989586621679038964">offset</a></a> = fromInteger (natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038633">k</a>)))

585+<a name="line-585"></a> <a name="local-6989586621679038965"><a href="#local-6989586621679038965">f</a></a> (<a name="local-6989586621679038966"><a href="#local-6989586621679038966">x</a></a>, <a name="local-6989586621679038967"><a href="#local-6989586621679038967">y</a></a>)

586+<a name="line-586"></a> | <a href="#local-6989586621679038967">y</a> >= (<a href="#local-6989586621679038966">x</a> * <a href="#local-6989586621679038964">offset</a>) && <a href="#local-6989586621679038967">y</a> <= (<a href="#local-6989586621679038966">x</a> * <a href="#local-6989586621679038964">offset</a> + <a href="#local-6989586621679038964">offset</a> - 1) = 1

587+<a name="line-587"></a> | otherwise = 0

588+<a name="line-588"></a>

589+<a name="line-589"></a>-- | Khatri Rao product second component projection matrix.

590+<a name="line-590"></a>kp2 ::

591+<a name="line-591"></a> forall <a name="local-6989586621679038628"><a href="#local-6989586621679038628">e</a></a> <a name="local-6989586621679038629"><a href="#local-6989586621679038629">m</a></a> <a name="local-6989586621679038630"><a href="#local-6989586621679038630">k</a></a> .

592+<a name="line-592"></a> ( Num <a href="#local-6989586621679038628">e</a>,

593+<a name="line-593"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038630">k</a>),

594+<a name="line-594"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038628">e</a> (<a href="Matrix.Internal.html#FromNat">FromNat</a> (Count <a href="#local-6989586621679038629">m</a> * <a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038630">k</a>)) <a href="#local-6989586621679038630">k</a>,

595+<a name="line-595"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038629">m</a>),

596+<a name="line-596"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038629">m</a>, <a href="#local-6989586621679038630">k</a>)))

597+<a name="line-597"></a> ) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038628">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038629">m</a>, <a href="#local-6989586621679038630">k</a>)) <a href="#local-6989586621679038630">k</a>

598+<a name="line-598"></a><a name="kp2"><a href="Matrix.Internal.html#kp2">kp2</a></a> = <a href="Matrix.Internal.html#matrixBuilder">matrixBuilder</a> <a href="#local-6989586621679038969">f</a>

599+<a name="line-599"></a> where

600+<a name="line-600"></a> <a name="local-6989586621679038968"><a href="#local-6989586621679038968">offset</a></a> = fromInteger (natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038630">k</a>)))

601+<a name="line-601"></a> <a name="local-6989586621679038969"><a href="#local-6989586621679038969">f</a></a> (<a name="local-6989586621679038970"><a href="#local-6989586621679038970">x</a></a>, <a name="local-6989586621679038971"><a href="#local-6989586621679038971">y</a></a>)

602+<a name="line-602"></a> | <a href="#local-6989586621679038970">x</a> == <a href="#local-6989586621679038971">y</a> || mod (<a href="#local-6989586621679038971">y</a> - <a href="#local-6989586621679038970">x</a>) <a href="#local-6989586621679038968">offset</a> == 0 = 1

603+<a name="line-603"></a> | otherwise = 0

604+<a name="line-604"></a>

605+<a name="line-605"></a>-- | Khatri Rao Matrix product also known as matrix pairing.

606+<a name="line-606"></a>--

607+<a name="line-607"></a>-- NOTE: That this is not a true categorical product, see for instance:

608+<a name="line-608"></a>--

609+<a name="line-609"></a>-- @

610+<a name="line-610"></a>-- | kp1 . khatri a b == a

611+<a name="line-611"></a>-- khatri a b ==> |

612+<a name="line-612"></a>-- | kp2 . khatri a b == b

613+<a name="line-613"></a>-- @

614+<a name="line-614"></a>--

615+<a name="line-615"></a>-- __Emphasis__ on the implication symbol.

616+<a name="line-616"></a>khatri ::

617+<a name="line-617"></a> forall <a name="local-6989586621679038624"><a href="#local-6989586621679038624">e</a></a> <a name="local-6989586621679038625"><a href="#local-6989586621679038625">cols</a></a> <a name="local-6989586621679038626"><a href="#local-6989586621679038626">a</a></a> <a name="local-6989586621679038627"><a href="#local-6989586621679038627">b</a></a>.

618+<a name="line-618"></a> ( Num <a href="#local-6989586621679038624">e</a>,

619+<a name="line-619"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038626">a</a>),

620+<a name="line-620"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038627">b</a>),

621+<a name="line-621"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038626">a</a>, <a href="#local-6989586621679038627">b</a>))),

622+<a name="line-622"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038624">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038626">a</a>, <a href="#local-6989586621679038627">b</a>)) <a href="#local-6989586621679038626">a</a>,

623+<a name="line-623"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038624">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038626">a</a>, <a href="#local-6989586621679038627">b</a>)) <a href="#local-6989586621679038627">b</a>

624+<a name="line-624"></a> ) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038624">e</a> <a href="#local-6989586621679038625">cols</a> <a href="#local-6989586621679038626">a</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038624">e</a> <a href="#local-6989586621679038625">cols</a> <a href="#local-6989586621679038627">b</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038624">e</a> <a href="#local-6989586621679038625">cols</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038626">a</a>, <a href="#local-6989586621679038627">b</a>))

625+<a name="line-625"></a><a name="khatri"><a href="Matrix.Internal.html#khatri">khatri</a></a> <a name="local-6989586621679038972"><a href="#local-6989586621679038972">a</a></a> <a name="local-6989586621679038973"><a href="#local-6989586621679038973">b</a></a> =

626+<a name="line-626"></a> let <a name="local-6989586621679038974"><a href="#local-6989586621679038974">kp1'</a></a> = <a href="Matrix.Internal.html#kp1">kp1</a> @<a href="#local-6989586621679038624">e</a> @<a href="#local-6989586621679038626">a</a> @<a href="#local-6989586621679038627">b</a>

627+<a name="line-627"></a> <a name="local-6989586621679038975"><a href="#local-6989586621679038975">kp2'</a></a> = <a href="Matrix.Internal.html#kp2">kp2</a> @<a href="#local-6989586621679038624">e</a> @<a href="#local-6989586621679038626">a</a> @<a href="#local-6989586621679038627">b</a>

628+<a name="line-628"></a> in (<a href="Matrix.Internal.html#tr">tr</a> <a href="#local-6989586621679038974">kp1'</a>) . <a href="#local-6989586621679038972">a</a> * (<a href="Matrix.Internal.html#tr">tr</a> <a href="#local-6989586621679038975">kp2'</a>) . <a href="#local-6989586621679038973">b</a>

629+<a name="line-629"></a>

630+<a name="line-630"></a>-- Product Bifunctor (Kronecker)

631+<a name="line-631"></a>

632+<a name="line-632"></a>infixl 4 <a href="Matrix.Internal.html#%3E%3C">><</a>

633+<a name="line-633"></a>

634+<a name="line-634"></a>-- | Matrix product functor also known as kronecker product

635+<a name="line-635"></a>(><) ::

636+<a name="line-636"></a> forall <a name="local-6989586621679038619"><a href="#local-6989586621679038619">e</a></a> <a name="local-6989586621679038620"><a href="#local-6989586621679038620">m</a></a> <a name="local-6989586621679038621"><a href="#local-6989586621679038621">p</a></a> <a name="local-6989586621679038622"><a href="#local-6989586621679038622">n</a></a> <a name="local-6989586621679038623"><a href="#local-6989586621679038623">q</a></a>.

637+<a name="line-637"></a> ( Num <a href="#local-6989586621679038619">e</a>,

638+<a name="line-638"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038620">m</a>),

639+<a name="line-639"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038622">n</a>),

640+<a name="line-640"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038621">p</a>),

641+<a name="line-641"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038623">q</a>),

642+<a name="line-642"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038620">m</a>, <a href="#local-6989586621679038622">n</a>))),

643+<a name="line-643"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038619">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038620">m</a>, <a href="#local-6989586621679038622">n</a>)) <a href="#local-6989586621679038620">m</a>,

644+<a name="line-644"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038619">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038620">m</a>, <a href="#local-6989586621679038622">n</a>)) <a href="#local-6989586621679038622">n</a>,

645+<a name="line-645"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038621">p</a>, <a href="#local-6989586621679038623">q</a>))),

646+<a name="line-646"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038619">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038621">p</a>, <a href="#local-6989586621679038623">q</a>)) <a href="#local-6989586621679038621">p</a>,

647+<a name="line-647"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038619">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038621">p</a>, <a href="#local-6989586621679038623">q</a>)) <a href="#local-6989586621679038623">q</a>

648+<a name="line-648"></a> )

649+<a name="line-649"></a> => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038619">e</a> <a href="#local-6989586621679038620">m</a> <a href="#local-6989586621679038621">p</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038619">e</a> <a href="#local-6989586621679038622">n</a> <a href="#local-6989586621679038623">q</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038619">e</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038620">m</a>, <a href="#local-6989586621679038622">n</a>)) (<a href="Matrix.Internal.html#Normalize">Normalize</a> (<a href="#local-6989586621679038621">p</a>, <a href="#local-6989586621679038623">q</a>))

650+<a name="line-650"></a>(<a name="%3E%3C"><a href="Matrix.Internal.html#%3E%3C">><</a></a>) <a name="local-6989586621679038976"><a href="#local-6989586621679038976">a</a></a> <a name="local-6989586621679038977"><a href="#local-6989586621679038977">b</a></a> =

651+<a name="line-651"></a> let <a name="local-6989586621679038978"><a href="#local-6989586621679038978">kp1'</a></a> = <a href="Matrix.Internal.html#kp1">kp1</a> @<a href="#local-6989586621679038619">e</a> @<a href="#local-6989586621679038620">m</a> @<a href="#local-6989586621679038622">n</a>

652+<a name="line-652"></a> <a name="local-6989586621679038979"><a href="#local-6989586621679038979">kp2'</a></a> = <a href="Matrix.Internal.html#kp2">kp2</a> @<a href="#local-6989586621679038619">e</a> @<a href="#local-6989586621679038620">m</a> @<a href="#local-6989586621679038622">n</a>

653+<a name="line-653"></a> in <a href="Matrix.Internal.html#khatri">khatri</a> (<a href="#local-6989586621679038976">a</a> . <a href="#local-6989586621679038978">kp1'</a>) (<a href="#local-6989586621679038977">b</a> . <a href="#local-6989586621679038979">kp2'</a>)

654+<a name="line-654"></a>

655+<a name="line-655"></a>-- Matrix abide Junc Split

656+<a name="line-656"></a>

657+<a name="line-657"></a>-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.

658+<a name="line-658"></a>--

659+<a name="line-659"></a>-- Law:

660+<a name="line-660"></a>--

661+<a name="line-661"></a>-- @

662+<a name="line-662"></a>-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)

663+<a name="line-663"></a>-- @

664+<a name="line-664"></a>abideJS :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038616">e</a> <a href="#local-6989586621679038617">cols</a> <a href="#local-6989586621679038618">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038616">e</a> <a href="#local-6989586621679038617">cols</a> <a href="#local-6989586621679038618">rows</a>

665+<a name="line-665"></a><a name="abideJS"><a href="Matrix.Internal.html#abideJS">abideJS</a></a> (<a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038980"><a href="#local-6989586621679038980">a</a></a> <a name="local-6989586621679038981"><a href="#local-6989586621679038981">c</a></a>) (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038982"><a href="#local-6989586621679038982">b</a></a> <a name="local-6989586621679038983"><a href="#local-6989586621679038983">d</a></a>)) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038980">a</a>) (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038982">b</a>)) (<a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038981">c</a>) (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038983">d</a>)) -- Junc-Split abide law

666+<a name="line-666"></a>abideJS <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

667+<a name="line-667"></a>abideJS (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038984"><a href="#local-6989586621679038984">e</a></a>) = <a href="Matrix.Internal.html#One">One</a> <a href="#local-6989586621679038984">e</a>

668+<a name="line-668"></a>abideJS (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038985"><a href="#local-6989586621679038985">a</a></a> <a name="local-6989586621679038986"><a href="#local-6989586621679038986">b</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038985">a</a>) (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038986">b</a>)

669+<a name="line-669"></a>abideJS (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038987"><a href="#local-6989586621679038987">a</a></a> <a name="local-6989586621679038988"><a href="#local-6989586621679038988">b</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038987">a</a>) (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679038988">b</a>)

670+<a name="line-670"></a>

671+<a name="line-671"></a>-- Matrix abide Split Junc

672+<a name="line-672"></a>

673+<a name="line-673"></a>-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.

674+<a name="line-674"></a>--

675+<a name="line-675"></a>-- @

676+<a name="line-676"></a>-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)

677+<a name="line-677"></a>-- @

678+<a name="line-678"></a>abideSJ :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038613">e</a> <a href="#local-6989586621679038614">cols</a> <a href="#local-6989586621679038615">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038613">e</a> <a href="#local-6989586621679038614">cols</a> <a href="#local-6989586621679038615">rows</a>

679+<a name="line-679"></a><a name="abideSJ"><a href="Matrix.Internal.html#abideSJ">abideSJ</a></a> (<a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038989"><a href="#local-6989586621679038989">a</a></a> <a name="local-6989586621679038990"><a href="#local-6989586621679038990">b</a></a>) (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038991"><a href="#local-6989586621679038991">c</a></a> <a name="local-6989586621679038992"><a href="#local-6989586621679038992">d</a></a>)) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#abideSJ">abideSJ</a> <a href="#local-6989586621679038989">a</a>) (<a href="Matrix.Internal.html#abideSJ">abideSJ</a> <a href="#local-6989586621679038991">c</a>)) (<a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#abideSJ">abideSJ</a> <a href="#local-6989586621679038990">b</a>) (<a href="Matrix.Internal.html#abideSJ">abideSJ</a> <a href="#local-6989586621679038992">d</a>)) -- Split-Junc abide law

680+<a name="line-680"></a>abideSJ <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

681+<a name="line-681"></a>abideSJ (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038993"><a href="#local-6989586621679038993">e</a></a>) = <a href="Matrix.Internal.html#One">One</a> <a href="#local-6989586621679038993">e</a>

682+<a name="line-682"></a>abideSJ (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038994"><a href="#local-6989586621679038994">a</a></a> <a name="local-6989586621679038995"><a href="#local-6989586621679038995">b</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#abideSJ">abideSJ</a> <a href="#local-6989586621679038994">a</a>) (<a href="Matrix.Internal.html#abideSJ">abideSJ</a> <a href="#local-6989586621679038995">b</a>)

683+<a name="line-683"></a>abideSJ (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679038996"><a href="#local-6989586621679038996">a</a></a> <a name="local-6989586621679038997"><a href="#local-6989586621679038997">b</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#abideSJ">abideSJ</a> <a href="#local-6989586621679038996">a</a>) (<a href="Matrix.Internal.html#abideSJ">abideSJ</a> <a href="#local-6989586621679038997">b</a>)

684+<a name="line-684"></a>

685+<a name="line-685"></a>-- Matrix transposition

686+<a name="line-686"></a>

687+<a name="line-687"></a>-- | Matrix transposition.

688+<a name="line-688"></a>tr :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038610">e</a> <a href="#local-6989586621679038611">cols</a> <a href="#local-6989586621679038612">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038610">e</a> <a href="#local-6989586621679038612">rows</a> <a href="#local-6989586621679038611">cols</a>

689+<a name="line-689"></a><a name="tr"><a href="Matrix.Internal.html#tr">tr</a></a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

690+<a name="line-690"></a>tr (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679038998"><a href="#local-6989586621679038998">e</a></a>) = <a href="Matrix.Internal.html#One">One</a> <a href="#local-6989586621679038998">e</a>

691+<a name="line-691"></a>tr (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679038999"><a href="#local-6989586621679038999">a</a></a> <a name="local-6989586621679039000"><a href="#local-6989586621679039000">b</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#tr">tr</a> <a href="#local-6989586621679038999">a</a>) (<a href="Matrix.Internal.html#tr">tr</a> <a href="#local-6989586621679039000">b</a>)

692+<a name="line-692"></a>tr (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039001"><a href="#local-6989586621679039001">a</a></a> <a name="local-6989586621679039002"><a href="#local-6989586621679039002">b</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#tr">tr</a> <a href="#local-6989586621679039001">a</a>) (<a href="Matrix.Internal.html#tr">tr</a> <a href="#local-6989586621679039002">b</a>)

693+<a name="line-693"></a>

694+<a name="line-694"></a>-- Selective 'select' operator

695+<a name="line-695"></a>

696+<a name="line-696"></a>-- | Selective functors 'select' operator equivalent inspired by the

697+<a name="line-697"></a>-- ArrowMonad solution presented in the paper.

698+<a name="line-698"></a>select :: (Num <a href="#local-6989586621679038606">e</a>, <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038606">e</a> <a href="#local-6989586621679038607">b</a> <a href="#local-6989586621679038607">b</a>, KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038607">b</a>)) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038606">e</a> <a href="#local-6989586621679038608">cols</a> (Either <a href="#local-6989586621679038609">a</a> <a href="#local-6989586621679038607">b</a>) -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038606">e</a> <a href="#local-6989586621679038609">a</a> <a href="#local-6989586621679038607">b</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038606">e</a> <a href="#local-6989586621679038608">cols</a> <a href="#local-6989586621679038607">b</a>

699+<a name="line-699"></a><a name="select"><a href="Matrix.Internal.html#select">select</a></a> <a name="local-6989586621679039003"><a href="#local-6989586621679039003">m</a></a> <a name="local-6989586621679039004"><a href="#local-6989586621679039004">y</a></a> = <a href="Matrix.Internal.html#junc">junc</a> <a href="#local-6989586621679039004">y</a> <a href="Matrix.Internal.html#identity">identity</a> . <a href="#local-6989586621679039003">m</a>

700+<a name="line-700"></a>

701+<a name="line-701"></a>-- McCarthy's Conditional

702+<a name="line-702"></a>

703+<a name="line-703"></a>-- | McCarthy's Conditional expresses probabilistic choice.

704+<a name="line-704"></a>cond ::

705+<a name="line-705"></a> ( cols ~ <a href="Matrix.Internal.html#FromNat">FromNat</a> (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038602">cols</a>),

706+<a name="line-706"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038602">cols</a>),

707+<a name="line-707"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038603">e</a> () <a href="#local-6989586621679038602">cols</a>,

708+<a name="line-708"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038603">e</a> <a href="#local-6989586621679038602">cols</a> (),

709+<a name="line-709"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038603">e</a> <a href="#local-6989586621679038602">cols</a> <a href="#local-6989586621679038602">cols</a>,

710+<a name="line-710"></a> Bounded <a href="#local-6989586621679038604">a</a>,

711+<a name="line-711"></a> Enum <a href="#local-6989586621679038604">a</a>,

712+<a name="line-712"></a> Num <a href="#local-6989586621679038603">e</a>,

713+<a name="line-713"></a> Ord <a href="#local-6989586621679038603">e</a>

714+<a name="line-714"></a> )

715+<a name="line-715"></a> =>

716+<a name="line-716"></a> (<a href="#local-6989586621679038604">a</a> -> Bool) -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038603">e</a> <a href="#local-6989586621679038602">cols</a> <a href="#local-6989586621679038605">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038603">e</a> <a href="#local-6989586621679038602">cols</a> <a href="#local-6989586621679038605">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038603">e</a> <a href="#local-6989586621679038602">cols</a> <a href="#local-6989586621679038605">rows</a>

717+<a name="line-717"></a><a name="cond"><a href="Matrix.Internal.html#cond">cond</a></a> <a name="local-6989586621679039005"><a href="#local-6989586621679039005">p</a></a> <a name="local-6989586621679039006"><a href="#local-6989586621679039006">f</a></a> <a name="local-6989586621679039007"><a href="#local-6989586621679039007">g</a></a> = <a href="Matrix.Internal.html#junc">junc</a> <a href="#local-6989586621679039006">f</a> <a href="#local-6989586621679039007">g</a> . <a href="Matrix.Internal.html#grd">grd</a> <a href="#local-6989586621679039005">p</a>

718+<a name="line-718"></a>

719+<a name="line-719"></a>grd ::

720+<a name="line-720"></a> ( q ~ <a href="Matrix.Internal.html#FromNat">FromNat</a> (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038599">q</a>),

721+<a name="line-721"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038599">q</a>),

722+<a name="line-722"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038600">e</a> () <a href="#local-6989586621679038599">q</a>,

723+<a name="line-723"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038600">e</a> <a href="#local-6989586621679038599">q</a> (),

724+<a name="line-724"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038600">e</a> <a href="#local-6989586621679038599">q</a> <a href="#local-6989586621679038599">q</a>,

725+<a name="line-725"></a> Bounded <a href="#local-6989586621679038601">a</a>,

726+<a name="line-726"></a> Enum <a href="#local-6989586621679038601">a</a>,

727+<a name="line-727"></a> Num <a href="#local-6989586621679038600">e</a>,

728+<a name="line-728"></a> Ord <a href="#local-6989586621679038600">e</a>

729+<a name="line-729"></a> )

730+<a name="line-730"></a> =>

731+<a name="line-731"></a> (<a href="#local-6989586621679038601">a</a> -> Bool) -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038600">e</a> <a href="#local-6989586621679038599">q</a> (Either <a href="#local-6989586621679038599">q</a> <a href="#local-6989586621679038599">q</a>)

732+<a name="line-732"></a><a name="grd"><a href="Matrix.Internal.html#grd">grd</a></a> <a name="local-6989586621679039008"><a href="#local-6989586621679039008">f</a></a> = <a href="Matrix.Internal.html#split">split</a> (<a href="Matrix.Internal.html#corr">corr</a> <a href="#local-6989586621679039008">f</a>) (<a href="Matrix.Internal.html#corr">corr</a> (not . <a href="#local-6989586621679039008">f</a>))

733+<a name="line-733"></a>

734+<a name="line-734"></a>corr ::

735+<a name="line-735"></a> forall <a name="local-6989586621679038596"><a href="#local-6989586621679038596">e</a></a> <a name="local-6989586621679038597"><a href="#local-6989586621679038597">a</a></a> <a name="local-6989586621679038598"><a href="#local-6989586621679038598">q</a></a> .

736+<a name="line-736"></a> ( q ~ <a href="Matrix.Internal.html#FromNat">FromNat</a> (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038598">q</a>),

737+<a name="line-737"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038598">q</a>),

738+<a name="line-738"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038596">e</a> () <a href="#local-6989586621679038598">q</a>,

739+<a name="line-739"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038596">e</a> <a href="#local-6989586621679038598">q</a> (),

740+<a name="line-740"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> <a href="#local-6989586621679038596">e</a> <a href="#local-6989586621679038598">q</a> <a href="#local-6989586621679038598">q</a>,

741+<a name="line-741"></a> Bounded <a href="#local-6989586621679038597">a</a>,

742+<a name="line-742"></a> Enum <a href="#local-6989586621679038597">a</a>,

743+<a name="line-743"></a> Num <a href="#local-6989586621679038596">e</a>,

744+<a name="line-744"></a> Ord <a href="#local-6989586621679038596">e</a>

745+<a name="line-745"></a> )

746+<a name="line-746"></a> => (<a href="#local-6989586621679038597">a</a> -> Bool) -> <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038596">e</a> <a href="#local-6989586621679038598">q</a> <a href="#local-6989586621679038598">q</a>

747+<a name="line-747"></a><a name="corr"><a href="Matrix.Internal.html#corr">corr</a></a> <a name="local-6989586621679039009"><a href="#local-6989586621679039009">p</a></a> = let <a name="local-6989586621679039010"><a href="#local-6989586621679039010">f</a></a> = <a href="Matrix.Internal.html#fromF">fromF</a> <a href="#local-6989586621679039009">p</a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038596">e</a> <a href="#local-6989586621679038598">q</a> ()

748+<a name="line-748"></a> in <a href="Matrix.Internal.html#khatri">khatri</a> <a href="#local-6989586621679039010">f</a> (<a href="Matrix.Internal.html#identity">identity</a> :: <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038596">e</a> <a href="#local-6989586621679038598">q</a> <a href="#local-6989586621679038598">q</a>)

749+<a name="line-749"></a>

750+<a name="line-750"></a>-- Pretty print

751+<a name="line-751"></a>

752+<a name="line-752"></a>prettyAux :: Show <a href="#local-6989586621679038595">e</a> => [[<a href="#local-6989586621679038595">e</a>]] -> [[<a href="#local-6989586621679038595">e</a>]] -> String

753+<a name="line-753"></a><a name="prettyAux"><a href="Matrix.Internal.html#prettyAux">prettyAux</a></a> [] _ = ""

754+<a name="line-754"></a>prettyAux [[<a name="local-6989586621679039011"><a href="#local-6989586621679039011">e</a></a>]] <a name="local-6989586621679039012"><a href="#local-6989586621679039012">m</a></a> = "│ " ++ <a href="#local-6989586621679039015">fill</a> (show <a href="#local-6989586621679039011">e</a>) ++ " │\n"

755+<a name="line-755"></a> where

756+<a name="line-756"></a> <a name="local-6989586621679039013"><a href="#local-6989586621679039013">v</a></a> = fmap show <a href="#local-6989586621679039012">m</a>

757+<a name="line-757"></a> <a name="local-6989586621679039014"><a href="#local-6989586621679039014">widest</a></a> = maximum $ fmap length <a href="#local-6989586621679039013">v</a>

758+<a name="line-758"></a> <a name="local-6989586621679039015"><a href="#local-6989586621679039015">fill</a></a> <a name="local-6989586621679039016"><a href="#local-6989586621679039016">str</a></a> = replicate (<a href="#local-6989586621679039014">widest</a> - length <a href="#local-6989586621679039016">str</a> - 2) ' ' ++ <a href="#local-6989586621679039016">str</a>

759+<a name="line-759"></a>prettyAux [<a name="local-6989586621679039017"><a href="#local-6989586621679039017">h</a></a>] <a name="local-6989586621679039018"><a href="#local-6989586621679039018">m</a></a> = "│ " ++ <a href="#local-6989586621679039021">fill</a> (unwords $ map show <a href="#local-6989586621679039017">h</a>) ++ " │\n"

760+<a name="line-760"></a> where

761+<a name="line-761"></a> <a name="local-6989586621679039019"><a href="#local-6989586621679039019">v</a></a> = fmap show <a href="#local-6989586621679039018">m</a>

762+<a name="line-762"></a> <a name="local-6989586621679039020"><a href="#local-6989586621679039020">widest</a></a> = maximum $ fmap length <a href="#local-6989586621679039019">v</a>

763+<a name="line-763"></a> <a name="local-6989586621679039021"><a href="#local-6989586621679039021">fill</a></a> <a name="local-6989586621679039022"><a href="#local-6989586621679039022">str</a></a> = replicate (<a href="#local-6989586621679039020">widest</a> - length <a href="#local-6989586621679039022">str</a> - 2) ' ' ++ <a href="#local-6989586621679039022">str</a>

764+<a name="line-764"></a>prettyAux (<a name="local-6989586621679039023"><a href="#local-6989586621679039023">h</a></a> : <a name="local-6989586621679039024"><a href="#local-6989586621679039024">t</a></a>) <a name="local-6989586621679039025"><a href="#local-6989586621679039025">l</a></a> = "│ " ++ <a href="#local-6989586621679039028">fill</a> (unwords $ map show <a href="#local-6989586621679039023">h</a>) ++ " │\n" ++

765+<a name="line-765"></a> <a href="Matrix.Internal.html#prettyAux">prettyAux</a> <a href="#local-6989586621679039024">t</a> <a href="#local-6989586621679039025">l</a>

766+<a name="line-766"></a> where

767+<a name="line-767"></a> <a name="local-6989586621679039026"><a href="#local-6989586621679039026">v</a></a> = fmap show <a href="#local-6989586621679039025">l</a>

768+<a name="line-768"></a> <a name="local-6989586621679039027"><a href="#local-6989586621679039027">widest</a></a> = maximum $ fmap length <a href="#local-6989586621679039026">v</a>

769+<a name="line-769"></a> <a name="local-6989586621679039028"><a href="#local-6989586621679039028">fill</a></a> <a name="local-6989586621679039029"><a href="#local-6989586621679039029">str</a></a> = replicate (<a href="#local-6989586621679039027">widest</a> - length <a href="#local-6989586621679039029">str</a> - 2) ' ' ++ <a href="#local-6989586621679039029">str</a>

770+<a name="line-770"></a>

771+<a name="line-771"></a>-- | Matrix pretty printer

772+<a name="line-772"></a>pretty :: (KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038592">cols</a>), Show <a href="#local-6989586621679038593">e</a>) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038593">e</a> <a href="#local-6989586621679038592">cols</a> <a href="#local-6989586621679038594">rows</a> -> String

773+<a name="line-773"></a><a name="pretty"><a href="Matrix.Internal.html#pretty">pretty</a></a> <a name="local-6989586621679039030"><a href="#local-6989586621679039030">m</a></a> = "┌ " ++ unwords (replicate (<a href="Matrix.Internal.html#columns">columns</a> <a href="#local-6989586621679039030">m</a>) <a href="#local-6989586621679039034">blank</a>) ++ " ┐\n" ++

774+<a name="line-774"></a> <a href="Matrix.Internal.html#prettyAux">prettyAux</a> (<a href="Matrix.Internal.html#toLists">toLists</a> <a href="#local-6989586621679039030">m</a>) (<a href="Matrix.Internal.html#toLists">toLists</a> <a href="#local-6989586621679039030">m</a>) ++

775+<a name="line-775"></a> "└ " ++ unwords (replicate (<a href="Matrix.Internal.html#columns">columns</a> <a href="#local-6989586621679039030">m</a>) <a href="#local-6989586621679039034">blank</a>) ++ " ┘"

776+<a name="line-776"></a> where

777+<a name="line-777"></a> <a name="local-6989586621679039031"><a href="#local-6989586621679039031">v</a></a> = fmap show (<a href="Matrix.Internal.html#toList">toList</a> <a href="#local-6989586621679039030">m</a>)

778+<a name="line-778"></a> <a name="local-6989586621679039032"><a href="#local-6989586621679039032">widest</a></a> = maximum $ fmap length <a href="#local-6989586621679039031">v</a>

779+<a name="line-779"></a> <a name="local-6989586621679039033"><a href="#local-6989586621679039033">fill</a></a> <a name="local-6989586621679039035"><a href="#local-6989586621679039035">str</a></a> = replicate (<a href="#local-6989586621679039032">widest</a> - length <a href="#local-6989586621679039035">str</a>) ' ' ++ <a href="#local-6989586621679039035">str</a>

780+<a name="line-780"></a> <a name="local-6989586621679039034"><a href="#local-6989586621679039034">blank</a></a> = <a href="#local-6989586621679039033">fill</a> ""

781+<a name="line-781"></a>

782+<a name="line-782"></a>-- | Matrix pretty printer

783+<a name="line-783"></a>prettyPrint :: (KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038589">cols</a>), Show <a href="#local-6989586621679038590">e</a>) => <a href="Matrix.Internal.html#Matrix">Matrix</a> <a href="#local-6989586621679038590">e</a> <a href="#local-6989586621679038589">cols</a> <a href="#local-6989586621679038591">rows</a> -> IO ()

784+<a name="line-784"></a><a name="prettyPrint"><a href="Matrix.Internal.html#prettyPrint">prettyPrint</a></a> = putStrLn . <a href="Matrix.Internal.html#pretty">pretty</a>

785+<a name="line-785"></a>

786+<a name="line-786"></a>-- Relational operators functions

787+<a name="line-787"></a>

788+<a name="line-788"></a>-- | Helper conversion function

789+<a name="line-789"></a>toBool :: (Num <a href="#local-6989586621679038588">e</a>, Eq <a href="#local-6989586621679038588">e</a>) => <a href="#local-6989586621679038588">e</a> -> Bool

790+<a name="line-790"></a><a name="toBool"><a href="Matrix.Internal.html#toBool">toBool</a></a> <a name="local-6989586621679039207"><a href="#local-6989586621679039207">n</a></a>

791+<a name="line-791"></a> | <a href="#local-6989586621679039207">n</a> == 0 = False

792+<a name="line-792"></a> | <a href="#local-6989586621679039207">n</a> == 1 = True

793+<a name="line-793"></a>

794+<a name="line-794"></a>-- | Helper conversion function

795+<a name="line-795"></a>fromBool :: Bool -> <a href="Utils.Internal.html#Natural">Natural</a> 0 1

796+<a name="line-796"></a><a name="fromBool"><a href="Matrix.Internal.html#fromBool">fromBool</a></a> True = <a href="Utils.Internal.html#nat">nat</a> 1

797+<a name="line-797"></a>fromBool False = <a href="Utils.Internal.html#nat">nat</a> 0

798+<a name="line-798"></a>

799+<a name="line-799"></a>-- | Relational addition

800+<a name="line-800"></a>orM :: <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038586">cols</a> <a href="#local-6989586621679038587">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038586">cols</a> <a href="#local-6989586621679038587">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038586">cols</a> <a href="#local-6989586621679038587">rows</a>

801+<a name="line-801"></a><a name="orM"><a href="Matrix.Internal.html#orM">orM</a></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

802+<a name="line-802"></a>orM (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679039208"><a href="#local-6989586621679039208">a</a></a>) (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679039209"><a href="#local-6989586621679039209">b</a></a>) = <a href="Matrix.Internal.html#One">One</a> (<a href="Matrix.Internal.html#fromBool">fromBool</a> (<a href="Matrix.Internal.html#toBool">toBool</a> <a href="#local-6989586621679039208">a</a> || <a href="Matrix.Internal.html#toBool">toBool</a> <a href="#local-6989586621679039209">b</a>))

803+<a name="line-803"></a>orM (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679039210"><a href="#local-6989586621679039210">a</a></a> <a name="local-6989586621679039211"><a href="#local-6989586621679039211">b</a></a>) (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679039212"><a href="#local-6989586621679039212">c</a></a> <a name="local-6989586621679039213"><a href="#local-6989586621679039213">d</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#orM">orM</a> <a href="#local-6989586621679039210">a</a> <a href="#local-6989586621679039212">c</a>) (<a href="Matrix.Internal.html#orM">orM</a> <a href="#local-6989586621679039211">b</a> <a href="#local-6989586621679039213">d</a>)

804+<a name="line-804"></a>orM (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039214"><a href="#local-6989586621679039214">a</a></a> <a name="local-6989586621679039215"><a href="#local-6989586621679039215">b</a></a>) (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039216"><a href="#local-6989586621679039216">c</a></a> <a name="local-6989586621679039217"><a href="#local-6989586621679039217">d</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#orM">orM</a> <a href="#local-6989586621679039214">a</a> <a href="#local-6989586621679039216">c</a>) (<a href="Matrix.Internal.html#orM">orM</a> <a href="#local-6989586621679039215">b</a> <a href="#local-6989586621679039217">d</a>)

805+<a name="line-805"></a>orM <a name="local-6989586621679039218"><a href="#local-6989586621679039218">x</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) <a name="local-6989586621679039219"><a href="#local-6989586621679039219">y</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) = <a href="Matrix.Internal.html#orM">orM</a> <a href="#local-6989586621679039218">x</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679039219">y</a>)

806+<a name="line-806"></a>orM <a name="local-6989586621679039220"><a href="#local-6989586621679039220">x</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) <a name="local-6989586621679039221"><a href="#local-6989586621679039221">y</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) = <a href="Matrix.Internal.html#orM">orM</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679039220">x</a>) <a href="#local-6989586621679039221">y</a>

807+<a name="line-807"></a>

808+<a name="line-808"></a>-- | Relational multiplication

809+<a name="line-809"></a>andM :: <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038584">cols</a> <a href="#local-6989586621679038585">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038584">cols</a> <a href="#local-6989586621679038585">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038584">cols</a> <a href="#local-6989586621679038585">rows</a>

810+<a name="line-810"></a><a name="andM"><a href="Matrix.Internal.html#andM">andM</a></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

811+<a name="line-811"></a>andM (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679039222"><a href="#local-6989586621679039222">a</a></a>) (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679039223"><a href="#local-6989586621679039223">b</a></a>) = <a href="Matrix.Internal.html#One">One</a> (<a href="Matrix.Internal.html#fromBool">fromBool</a> (<a href="Matrix.Internal.html#toBool">toBool</a> <a href="#local-6989586621679039222">a</a> && <a href="Matrix.Internal.html#toBool">toBool</a> <a href="#local-6989586621679039223">b</a>))

812+<a name="line-812"></a>andM (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679039224"><a href="#local-6989586621679039224">a</a></a> <a name="local-6989586621679039225"><a href="#local-6989586621679039225">b</a></a>) (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679039226"><a href="#local-6989586621679039226">c</a></a> <a name="local-6989586621679039227"><a href="#local-6989586621679039227">d</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#andM">andM</a> <a href="#local-6989586621679039224">a</a> <a href="#local-6989586621679039226">c</a>) (<a href="Matrix.Internal.html#andM">andM</a> <a href="#local-6989586621679039225">b</a> <a href="#local-6989586621679039227">d</a>)

813+<a name="line-813"></a>andM (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039228"><a href="#local-6989586621679039228">a</a></a> <a name="local-6989586621679039229"><a href="#local-6989586621679039229">b</a></a>) (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039230"><a href="#local-6989586621679039230">c</a></a> <a name="local-6989586621679039231"><a href="#local-6989586621679039231">d</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#andM">andM</a> <a href="#local-6989586621679039228">a</a> <a href="#local-6989586621679039230">c</a>) (<a href="Matrix.Internal.html#andM">andM</a> <a href="#local-6989586621679039229">b</a> <a href="#local-6989586621679039231">d</a>)

814+<a name="line-814"></a>andM <a name="local-6989586621679039232"><a href="#local-6989586621679039232">x</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) <a name="local-6989586621679039233"><a href="#local-6989586621679039233">y</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) = <a href="Matrix.Internal.html#andM">andM</a> <a href="#local-6989586621679039232">x</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679039233">y</a>)

815+<a name="line-815"></a>andM <a name="local-6989586621679039234"><a href="#local-6989586621679039234">x</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) <a name="local-6989586621679039235"><a href="#local-6989586621679039235">y</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) = <a href="Matrix.Internal.html#andM">andM</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679039234">x</a>) <a href="#local-6989586621679039235">y</a>

816+<a name="line-816"></a>

817+<a name="line-817"></a>-- | Relational subtraction

818+<a name="line-818"></a>subM :: <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038582">cols</a> <a href="#local-6989586621679038583">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038582">cols</a> <a href="#local-6989586621679038583">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038582">cols</a> <a href="#local-6989586621679038583">rows</a>

819+<a name="line-819"></a><a name="subM"><a href="Matrix.Internal.html#subM">subM</a></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

820+<a name="line-820"></a>subM (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679039236"><a href="#local-6989586621679039236">a</a></a>) (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679039237"><a href="#local-6989586621679039237">b</a></a>) = if <a href="#local-6989586621679039236">a</a> - <a href="#local-6989586621679039237">b</a> < <a href="Utils.Internal.html#nat">nat</a> 0 then <a href="Matrix.Internal.html#One">One</a> (<a href="Utils.Internal.html#nat">nat</a> 0) else <a href="Matrix.Internal.html#One">One</a> (<a href="#local-6989586621679039236">a</a> - <a href="#local-6989586621679039237">b</a>)

821+<a name="line-821"></a>subM (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679039238"><a href="#local-6989586621679039238">a</a></a> <a name="local-6989586621679039239"><a href="#local-6989586621679039239">b</a></a>) (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679039240"><a href="#local-6989586621679039240">c</a></a> <a name="local-6989586621679039241"><a href="#local-6989586621679039241">d</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#subM">subM</a> <a href="#local-6989586621679039238">a</a> <a href="#local-6989586621679039240">c</a>) (<a href="Matrix.Internal.html#subM">subM</a> <a href="#local-6989586621679039239">b</a> <a href="#local-6989586621679039241">d</a>)

822+<a name="line-822"></a>subM (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039242"><a href="#local-6989586621679039242">a</a></a> <a name="local-6989586621679039243"><a href="#local-6989586621679039243">b</a></a>) (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039244"><a href="#local-6989586621679039244">c</a></a> <a name="local-6989586621679039245"><a href="#local-6989586621679039245">d</a></a>) = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#subM">subM</a> <a href="#local-6989586621679039242">a</a> <a href="#local-6989586621679039244">c</a>) (<a href="Matrix.Internal.html#subM">subM</a> <a href="#local-6989586621679039243">b</a> <a href="#local-6989586621679039245">d</a>)

823+<a name="line-823"></a>subM <a name="local-6989586621679039246"><a href="#local-6989586621679039246">x</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) <a name="local-6989586621679039247"><a href="#local-6989586621679039247">y</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) = <a href="Matrix.Internal.html#subM">subM</a> <a href="#local-6989586621679039246">x</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679039247">y</a>)

824+<a name="line-824"></a>subM <a name="local-6989586621679039248"><a href="#local-6989586621679039248">x</a></a>@(<a href="Matrix.Internal.html#Junc">Junc</a> _ _) <a name="local-6989586621679039249"><a href="#local-6989586621679039249">y</a></a>@(<a href="Matrix.Internal.html#Split">Split</a> _ _) = <a href="Matrix.Internal.html#subM">subM</a> (<a href="Matrix.Internal.html#abideJS">abideJS</a> <a href="#local-6989586621679039248">x</a>) <a href="#local-6989586621679039249">y</a>

825+<a name="line-825"></a>

826+<a name="line-826"></a>-- | Matrix relational composition.

827+<a name="line-827"></a>compRel :: <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038579">cr</a> <a href="#local-6989586621679038580">rows</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038581">cols</a> <a href="#local-6989586621679038579">cr</a> -> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038581">cols</a> <a href="#local-6989586621679038580">rows</a>

828+<a name="line-828"></a><a name="compRel"><a href="Matrix.Internal.html#compRel">compRel</a></a> <a href="Matrix.Internal.html#Empty">Empty</a> <a href="Matrix.Internal.html#Empty">Empty</a> = <a href="Matrix.Internal.html#Empty">Empty</a>

829+<a name="line-829"></a>compRel (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679039250"><a href="#local-6989586621679039250">a</a></a>) (<a href="Matrix.Internal.html#One">One</a> <a name="local-6989586621679039251"><a href="#local-6989586621679039251">b</a></a>) = <a href="Matrix.Internal.html#One">One</a> (<a href="Matrix.Internal.html#fromBool">fromBool</a> (<a href="Matrix.Internal.html#toBool">toBool</a> <a href="#local-6989586621679039250">a</a> && <a href="Matrix.Internal.html#toBool">toBool</a> <a href="#local-6989586621679039251">b</a>))

830+<a name="line-830"></a>compRel (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679039252"><a href="#local-6989586621679039252">a</a></a> <a name="local-6989586621679039253"><a href="#local-6989586621679039253">b</a></a>) (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039254"><a href="#local-6989586621679039254">c</a></a> <a name="local-6989586621679039255"><a href="#local-6989586621679039255">d</a></a>) = <a href="Matrix.Internal.html#orM">orM</a> (<a href="Matrix.Internal.html#compRel">compRel</a> <a href="#local-6989586621679039252">a</a> <a href="#local-6989586621679039254">c</a>) (<a href="Matrix.Internal.html#compRel">compRel</a> <a href="#local-6989586621679039253">b</a> <a href="#local-6989586621679039255">d</a>) -- Divide-and-conquer law

831+<a name="line-831"></a>compRel (<a href="Matrix.Internal.html#Split">Split</a> <a name="local-6989586621679039256"><a href="#local-6989586621679039256">a</a></a> <a name="local-6989586621679039257"><a href="#local-6989586621679039257">b</a></a>) <a name="local-6989586621679039258"><a href="#local-6989586621679039258">c</a></a> = <a href="Matrix.Internal.html#Split">Split</a> (<a href="Matrix.Internal.html#compRel">compRel</a> <a href="#local-6989586621679039256">a</a> <a href="#local-6989586621679039258">c</a>) (<a href="Matrix.Internal.html#compRel">compRel</a> <a href="#local-6989586621679039257">b</a> <a href="#local-6989586621679039258">c</a>) -- Split fusion law

832+<a name="line-832"></a>compRel <a name="local-6989586621679039259"><a href="#local-6989586621679039259">c</a></a> (<a href="Matrix.Internal.html#Junc">Junc</a> <a name="local-6989586621679039260"><a href="#local-6989586621679039260">a</a></a> <a name="local-6989586621679039261"><a href="#local-6989586621679039261">b</a></a>) = <a href="Matrix.Internal.html#Junc">Junc</a> (<a href="Matrix.Internal.html#compRel">compRel</a> <a href="#local-6989586621679039259">c</a> <a href="#local-6989586621679039260">a</a>) (<a href="Matrix.Internal.html#compRel">compRel</a> <a href="#local-6989586621679039259">c</a> <a href="#local-6989586621679039261">b</a>) -- Junc fusion law

833+<a name="line-833"></a>

834+<a name="line-834"></a>-- | Lifts functions to relations with arbitrary dimensions.

835+<a name="line-835"></a>--

836+<a name="line-836"></a>-- NOTE: Be careful to not ask for a relation bigger than the cardinality of

837+<a name="line-837"></a>-- types @a@ or @b@ allows.

838+<a name="line-838"></a>fromFRel ::

839+<a name="line-839"></a> forall <a name="local-6989586621679038575"><a href="#local-6989586621679038575">a</a></a> <a name="local-6989586621679038576"><a href="#local-6989586621679038576">b</a></a> <a name="local-6989586621679038577"><a href="#local-6989586621679038577">cols</a></a> <a name="local-6989586621679038578"><a href="#local-6989586621679038578">rows</a></a>.

840+<a name="line-840"></a> ( Bounded <a href="#local-6989586621679038575">a</a>,

841+<a name="line-841"></a> Bounded <a href="#local-6989586621679038576">b</a>,

842+<a name="line-842"></a> Enum <a href="#local-6989586621679038575">a</a>,

843+<a name="line-843"></a> Enum <a href="#local-6989586621679038576">b</a>,

844+<a name="line-844"></a> Eq <a href="#local-6989586621679038576">b</a>,

845+<a name="line-845"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038577">cols</a>),

846+<a name="line-846"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038578">rows</a>),

847+<a name="line-847"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038578">rows</a> <a href="#local-6989586621679038577">cols</a>

848+<a name="line-848"></a> ) =>

849+<a name="line-849"></a> (<a href="#local-6989586621679038575">a</a> -> <a href="#local-6989586621679038576">b</a>) ->

850+<a name="line-850"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) <a href="#local-6989586621679038577">cols</a> <a href="#local-6989586621679038578">rows</a>

851+<a name="line-851"></a><a name="fromFRel"><a href="Matrix.Internal.html#fromFRel">fromFRel</a></a> <a name="local-6989586621679039262"><a href="#local-6989586621679039262">f</a></a> =

852+<a name="line-852"></a> let <a name="local-6989586621679039266"><a href="#local-6989586621679039266">minA</a></a> = minBound @<a href="#local-6989586621679038575">a</a>

853+<a name="line-853"></a> <a name="local-6989586621679039267"><a href="#local-6989586621679039267">maxA</a></a> = maxBound @<a href="#local-6989586621679038575">a</a>

854+<a name="line-854"></a> <a name="local-6989586621679039268"><a href="#local-6989586621679039268">minB</a></a> = minBound @<a href="#local-6989586621679038576">b</a>

855+<a name="line-855"></a> <a name="local-6989586621679039269"><a href="#local-6989586621679039269">maxB</a></a> = maxBound @<a href="#local-6989586621679038576">b</a>

856+<a name="line-856"></a> <a name="local-6989586621679039270"><a href="#local-6989586621679039270">ccols</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038577">cols</a>))

857+<a name="line-857"></a> <a name="local-6989586621679039271"><a href="#local-6989586621679039271">rrows</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> <a href="#local-6989586621679038578">rows</a>))

858+<a name="line-858"></a> <a name="local-6989586621679039272"><a href="#local-6989586621679039272">elementsA</a></a> = take <a href="#local-6989586621679039270">ccols</a> [<a href="#local-6989586621679039266">minA</a> .. <a href="#local-6989586621679039267">maxA</a>]

859+<a name="line-859"></a> <a name="local-6989586621679039273"><a href="#local-6989586621679039273">elementsB</a></a> = take <a href="#local-6989586621679039271">rrows</a> [<a href="#local-6989586621679039268">minB</a> .. <a href="#local-6989586621679039269">maxB</a>]

860+<a name="line-860"></a> <a name="local-6989586621679039274"><a href="#local-6989586621679039274">combinations</a></a> = (,) <$> <a href="#local-6989586621679039272">elementsA</a> <*> <a href="#local-6989586621679039273">elementsB</a>

861+<a name="line-861"></a> <a name="local-6989586621679039275"><a href="#local-6989586621679039275">combAp</a></a> = map snd . sort . map (\(<a name="local-6989586621679039277"><a href="#local-6989586621679039277">a</a></a>, <a name="local-6989586621679039278"><a href="#local-6989586621679039278">b</a></a>) -> if <a href="#local-6989586621679039262">f</a> <a href="#local-6989586621679039277">a</a> == <a href="#local-6989586621679039278">b</a>

862+<a name="line-862"></a> then ((fromEnum <a href="#local-6989586621679039277">a</a>, fromEnum <a href="#local-6989586621679039278">b</a>), <a href="Utils.Internal.html#nat">nat</a> 1)

863+<a name="line-863"></a> else ((fromEnum <a href="#local-6989586621679039277">a</a>, fromEnum <a href="#local-6989586621679039278">b</a>), <a href="Utils.Internal.html#nat">nat</a> 0)) $ <a href="#local-6989586621679039274">combinations</a>

864+<a name="line-864"></a> <a name="local-6989586621679039276"><a href="#local-6989586621679039276">mList</a></a> = <a href="#local-6989586621679039263">buildList</a> <a href="#local-6989586621679039275">combAp</a> <a href="#local-6989586621679039271">rrows</a>

865+<a name="line-865"></a> in <a href="Matrix.Internal.html#tr">tr</a> $ <a href="Matrix.Internal.html#fromLists">fromLists</a> <a href="#local-6989586621679039276">mList</a>

866+<a name="line-866"></a> where

867+<a name="line-867"></a> <a name="local-6989586621679039263"><a href="#local-6989586621679039263">buildList</a></a> [] _ = []

868+<a name="line-868"></a> buildList <a name="local-6989586621679039264"><a href="#local-6989586621679039264">l</a></a> <a name="local-6989586621679039265"><a href="#local-6989586621679039265">r</a></a> = take <a href="#local-6989586621679039265">r</a> <a href="#local-6989586621679039264">l</a> : <a href="#local-6989586621679039263">buildList</a> (drop <a href="#local-6989586621679039265">r</a> <a href="#local-6989586621679039264">l</a>) <a href="#local-6989586621679039265">r</a>

869+<a name="line-869"></a>

870+<a name="line-870"></a>-- | Lifts functions to relations with dimensions matching @a@ and @b@

871+<a name="line-871"></a>-- cardinality's.

872+<a name="line-872"></a>fromFRel' ::

873+<a name="line-873"></a> forall <a name="local-6989586621679038573"><a href="#local-6989586621679038573">a</a></a> <a name="local-6989586621679038574"><a href="#local-6989586621679038574">b</a></a>.

874+<a name="line-874"></a> ( Bounded <a href="#local-6989586621679038573">a</a>,

875+<a name="line-875"></a> Bounded <a href="#local-6989586621679038574">b</a>,

876+<a name="line-876"></a> Enum <a href="#local-6989586621679038573">a</a>,

877+<a name="line-877"></a> Enum <a href="#local-6989586621679038574">b</a>,

878+<a name="line-878"></a> Eq <a href="#local-6989586621679038574">b</a>,

879+<a name="line-879"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038573">a</a>)),

880+<a name="line-880"></a> KnownNat (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038574">b</a>)),

881+<a name="line-881"></a> <a href="Matrix.Internal.html#FromLists">FromLists</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038574">b</a>) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038573">a</a>)

882+<a name="line-882"></a> ) =>

883+<a name="line-883"></a> (<a href="#local-6989586621679038573">a</a> -> <a href="#local-6989586621679038574">b</a>) ->

884+<a name="line-884"></a> <a href="Matrix.Internal.html#Matrix">Matrix</a> (<a href="Utils.Internal.html#Natural">Natural</a> 0 1) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038573">a</a>) (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038574">b</a>)

885+<a name="line-885"></a><a name="fromFRel%27"><a href="Matrix.Internal.html#fromFRel%27">fromFRel'</a></a> <a name="local-6989586621679039279"><a href="#local-6989586621679039279">f</a></a> =

886+<a name="line-886"></a> let <a name="local-6989586621679039283"><a href="#local-6989586621679039283">minA</a></a> = minBound @<a href="#local-6989586621679038573">a</a>

887+<a name="line-887"></a> <a name="local-6989586621679039284"><a href="#local-6989586621679039284">maxA</a></a> = maxBound @<a href="#local-6989586621679038573">a</a>

888+<a name="line-888"></a> <a name="local-6989586621679039285"><a href="#local-6989586621679039285">minB</a></a> = minBound @<a href="#local-6989586621679038574">b</a>

889+<a name="line-889"></a> <a name="local-6989586621679039286"><a href="#local-6989586621679039286">maxB</a></a> = maxBound @<a href="#local-6989586621679038574">b</a>

890+<a name="line-890"></a> <a name="local-6989586621679039287"><a href="#local-6989586621679039287">ccols</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038573">a</a>)))

891+<a name="line-891"></a> <a name="local-6989586621679039288"><a href="#local-6989586621679039288">rrows</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">Count</a> (<a href="Matrix.Internal.html#Normalize">Normalize</a> <a href="#local-6989586621679038574">b</a>)))

892+<a name="line-892"></a> <a name="local-6989586621679039289"><a href="#local-6989586621679039289">elementsA</a></a> = take <a href="#local-6989586621679039287">ccols</a> [<a href="#local-6989586621679039283">minA</a> .. <a href="#local-6989586621679039284">maxA</a>]

893+<a name="line-893"></a> <a name="local-6989586621679039290"><a href="#local-6989586621679039290">elementsB</a></a> = take <a href="#local-6989586621679039288">rrows</a> [<a href="#local-6989586621679039285">minB</a> .. <a href="#local-6989586621679039286">maxB</a>]

894+<a name="line-894"></a> <a name="local-6989586621679039291"><a href="#local-6989586621679039291">combinations</a></a> = (,) <$> <a href="#local-6989586621679039289">elementsA</a> <*> <a href="#local-6989586621679039290">elementsB</a>

895+<a name="line-895"></a> <a name="local-6989586621679039292"><a href="#local-6989586621679039292">combAp</a></a> = map snd . sort . map (\(<a name="local-6989586621679039294"><a href="#local-6989586621679039294">a</a></a>, <a name="local-6989586621679039295"><a href="#local-6989586621679039295">b</a></a>) -> if <a href="#local-6989586621679039279">f</a> <a href="#local-6989586621679039294">a</a> == <a href="#local-6989586621679039295">b</a>

896+<a name="line-896"></a> then ((fromEnum <a href="#local-6989586621679039294">a</a>, fromEnum <a href="#local-6989586621679039295">b</a>), <a href="Utils.Internal.html#nat">nat</a> 1)

897+<a name="line-897"></a> else ((fromEnum <a href="#local-6989586621679039294">a</a>, fromEnum <a href="#local-6989586621679039295">b</a>), <a href="Utils.Internal.html#nat">nat</a> 0)) $ <a href="#local-6989586621679039291">combinations</a>

898+<a name="line-898"></a> <a name="local-6989586621679039293"><a href="#local-6989586621679039293">mList</a></a> = <a href="#local-6989586621679039280">buildList</a> <a href="#local-6989586621679039292">combAp</a> <a href="#local-6989586621679039288">rrows</a>

899+<a name="line-899"></a> in <a href="Matrix.Internal.html#tr">tr</a> $ <a href="Matrix.Internal.html#fromLists">fromLists</a> <a href="#local-6989586621679039293">mList</a>

900+<a name="line-900"></a> where

901+<a name="line-901"></a> <a name="local-6989586621679039280"><a href="#local-6989586621679039280">buildList</a></a> [] _ = []

902+<a name="line-902"></a> buildList <a name="local-6989586621679039281"><a href="#local-6989586621679039281">l</a></a> <a name="local-6989586621679039282"><a href="#local-6989586621679039282">r</a></a> = take <a href="#local-6989586621679039282">r</a> <a href="#local-6989586621679039281">l</a> : <a href="#local-6989586621679039280">buildList</a> (drop <a href="#local-6989586621679039282">r</a> <a href="#local-6989586621679039281">l</a>) <a href="#local-6989586621679039282">r</a>

903+<a name="line-903"></a></pre></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/src/Matrix.Nat.htmlnew file+484

@@ -0,0 +1,484 @@

1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="style.css" /><script type="text/javascript" src="highlight.js"></script></head><body><pre>{-# LANGUAGE AllowAmbiguousTypes #-}

2+<a name="line-2"></a>{-# LANGUAGE DataKinds #-}

3+<a name="line-3"></a>{-# LANGUAGE DerivingVia #-}

4+<a name="line-4"></a>{-# LANGUAGE FlexibleContexts #-}

5+<a name="line-5"></a>{-# LANGUAGE FlexibleInstances #-}

6+<a name="line-6"></a>{-# LANGUAGE GADTs #-}

7+<a name="line-7"></a>{-# LANGUAGE KindSignatures #-}

8+<a name="line-8"></a>{-# LANGUAGE MultiParamTypeClasses #-}

9+<a name="line-9"></a>{-# LANGUAGE NoStarIsType #-}

10+<a name="line-10"></a>{-# LANGUAGE RankNTypes #-}

11+<a name="line-11"></a>{-# LANGUAGE ScopedTypeVariables #-}

12+<a name="line-12"></a>{-# LANGUAGE TypeApplications #-}

13+<a name="line-13"></a>{-# LANGUAGE TypeOperators #-}

14+<a name="line-14"></a>{-# LANGUAGE UndecidableInstances #-}

15+<a name="line-15"></a>

16+<a name="line-16"></a>-----------------------------------------------------------------------------

17+<a name="line-17"></a>-- |

18+<a name="line-18"></a>-- Module : Matrix.Nat

19+<a name="line-19"></a>-- Copyright : (c) Armando Santos 2019-2020

20+<a name="line-20"></a>-- Maintainer : armandoifsantos@gmail.com

21+<a name="line-21"></a>-- Stability : experimental

22+<a name="line-22"></a>--

23+<a name="line-23"></a>-- The LAoP discipline generalises relations and functions treating them as

24+<a name="line-24"></a>-- Boolean matrices and in turn consider these as arrows.

25+<a name="line-25"></a>--

26+<a name="line-26"></a>-- __LAoP__ is a library for algebraic (inductive) construction and manipulation of matrices

27+<a name="line-27"></a>-- in Haskell. See <https://github.com/bolt12/master-thesis my Msc Thesis> for the

28+<a name="line-28"></a>-- motivation behind the library, the underlying theory, and implementation details.

29+<a name="line-29"></a>--

30+<a name="line-30"></a>-- This module offers a newtype wrapper around 'Matrix.Type.Matrix' that

31+<a name="line-31"></a>-- uses type level naturals instead of standard data types for the matrices

32+<a name="line-32"></a>-- dimensions.

33+<a name="line-33"></a>--

34+<a name="line-34"></a>-----------------------------------------------------------------------------

35+<a name="line-35"></a>

36+<a name="line-36"></a>module Matrix.Nat

37+<a name="line-37"></a> ( -- | LAoP (Linear Algebra of Programming) Inductive Matrix definition.

38+<a name="line-38"></a> --

39+<a name="line-39"></a> -- LAoP generalises relations and functions treating them as

40+<a name="line-40"></a> -- Boolean matrices and in turn consider these as arrows.

41+<a name="line-41"></a> -- This library offers many of the combinators mentioned in the work of

42+<a name="line-42"></a> -- Macedo (2012) and Oliveira (2012).

43+<a name="line-43"></a> --

44+<a name="line-44"></a> -- This definition is a wrapper around 'Matrix.Type' but

45+<a name="line-45"></a> -- dimensions are type level Naturals. Type inference might not

46+<a name="line-46"></a> -- be as desired.

47+<a name="line-47"></a> --

48+<a name="line-48"></a> -- There exists two type families that make it easier to write

49+<a name="line-49"></a> -- matrix dimensions: 'FromNat' and 'Count'. This approach

50+<a name="line-50"></a> -- leads to a very straightforward implementation

51+<a name="line-51"></a> -- of LAoP combinators.

52+<a name="line-52"></a>

53+<a name="line-53"></a> -- * Type safe matrix representation

54+<a name="line-54"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> (..),

55+<a name="line-55"></a>

56+<a name="line-56"></a> -- * Primitives

57+<a name="line-57"></a> <a href="Matrix.Nat.html#empty">empty</a>,

58+<a name="line-58"></a> <a href="Matrix.Nat.html#one">one</a>,

59+<a name="line-59"></a> <a href="Matrix.Nat.html#junc">junc</a>,

60+<a name="line-60"></a> <a href="Matrix.Nat.html#split">split</a>,

61+<a name="line-61"></a>

62+<a name="line-62"></a> -- * Auxiliary type families

63+<a name="line-63"></a> <a href="Matrix.Internal.html#FromNat">I.FromNat</a>,

64+<a name="line-64"></a> <a href="Matrix.Internal.html#Count">I.Count</a>,

65+<a name="line-65"></a> <a href="Matrix.Internal.html#Normalize">I.Normalize</a>,

66+<a name="line-66"></a>

67+<a name="line-67"></a> -- * Matrix construction and conversion

68+<a name="line-68"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a>,

69+<a name="line-69"></a> <a href="Matrix.Nat.html#fromLists">fromLists</a>,

70+<a name="line-70"></a> <a href="Matrix.Nat.html#toLists">toLists</a>,

71+<a name="line-71"></a> <a href="Matrix.Nat.html#toList">toList</a>,

72+<a name="line-72"></a> <a href="Matrix.Nat.html#matrixBuilder">matrixBuilder</a>,

73+<a name="line-73"></a> <a href="Matrix.Nat.html#row">row</a>,

74+<a name="line-74"></a> <a href="Matrix.Nat.html#col">col</a>,

75+<a name="line-75"></a> <a href="Matrix.Nat.html#zeros">zeros</a>,

76+<a name="line-76"></a> <a href="Matrix.Nat.html#ones">ones</a>,

77+<a name="line-77"></a> <a href="Matrix.Nat.html#bang">bang</a>,

78+<a name="line-78"></a> <a href="Matrix.Nat.html#constant">constant</a>,

79+<a name="line-79"></a>

80+<a name="line-80"></a> -- * Misc

81+<a name="line-81"></a> -- ** Get dimensions

82+<a name="line-82"></a> <a href="Matrix.Nat.html#columns">columns</a>,

83+<a name="line-83"></a> <a href="Matrix.Nat.html#rows">rows</a>,

84+<a name="line-84"></a>

85+<a name="line-85"></a> -- ** Matrix Transposition

86+<a name="line-86"></a> <a href="Matrix.Nat.html#tr">tr</a>,

87+<a name="line-87"></a>

88+<a name="line-88"></a> -- ** Selective operator

89+<a name="line-89"></a> <a href="Matrix.Nat.html#select">select</a>,

90+<a name="line-90"></a>

91+<a name="line-91"></a> -- ** McCarthy's Conditional

92+<a name="line-92"></a> <a href="Matrix.Nat.html#cond">cond</a>,

93+<a name="line-93"></a>

94+<a name="line-94"></a> -- ** Matrix "abiding"

95+<a name="line-95"></a> <a href="Matrix.Nat.html#abideJS">abideJS</a>,

96+<a name="line-96"></a> <a href="Matrix.Nat.html#abideSJ">abideSJ</a>,

97+<a name="line-97"></a>

98+<a name="line-98"></a> -- * Biproduct approach

99+<a name="line-99"></a> -- ** Split

100+<a name="line-100"></a> (<a href="Matrix.Nat.html#%3D%3D%3D">===</a>),

101+<a name="line-101"></a> -- *** Projections

102+<a name="line-102"></a> <a href="Matrix.Nat.html#p1">p1</a>,

103+<a name="line-103"></a> <a href="Matrix.Nat.html#p2">p2</a>,

104+<a name="line-104"></a> -- ** Junc

105+<a name="line-105"></a> (<a href="Matrix.Nat.html#%7C%7C%7C">|||</a>),

106+<a name="line-106"></a> -- *** Injections

107+<a name="line-107"></a> <a href="Matrix.Nat.html#i1">i1</a>,

108+<a name="line-108"></a> <a href="Matrix.Nat.html#i2">i2</a>,

109+<a name="line-109"></a> -- ** Bifunctors

110+<a name="line-110"></a> (<a href="Matrix.Nat.html#-%7C-">-|-</a>),

111+<a name="line-111"></a> (<a href="Matrix.Nat.html#%3E%3C">><</a>),

112+<a name="line-112"></a>

113+<a name="line-113"></a> -- ** Applicative matrix combinators

114+<a name="line-114"></a>

115+<a name="line-115"></a> -- | Note that given the restrictions imposed it is not possible to

116+<a name="line-116"></a> -- implement the standard type classes present in standard Haskell.

117+<a name="line-117"></a> -- *** Matrix pairing projections

118+<a name="line-118"></a> <a href="Matrix.Nat.html#kp1">kp1</a>,

119+<a name="line-119"></a> <a href="Matrix.Nat.html#kp2">kp2</a>,

120+<a name="line-120"></a>

121+<a name="line-121"></a> -- *** Matrix pairing

122+<a name="line-122"></a> <a href="Matrix.Nat.html#khatri">khatri</a>,

123+<a name="line-123"></a>

124+<a name="line-124"></a> -- * Matrix composition and lifting

125+<a name="line-125"></a>

126+<a name="line-126"></a> -- ** Arrow matrix combinators

127+<a name="line-127"></a>

128+<a name="line-128"></a> -- | Note that given the restrictions imposed it is not possible to

129+<a name="line-129"></a> -- implement the standard type classes present in standard Haskell.

130+<a name="line-130"></a> <a href="Matrix.Nat.html#identity">identity</a>,

131+<a name="line-131"></a> <a href="Matrix.Nat.html#comp">comp</a>,

132+<a name="line-132"></a> <a href="Matrix.Nat.html#fromF">fromF</a>,

133+<a name="line-133"></a> <a href="Matrix.Nat.html#fromF%27">fromF'</a>,

134+<a name="line-134"></a>

135+<a name="line-135"></a> -- * Matrix printing

136+<a name="line-136"></a> <a href="Matrix.Nat.html#pretty">pretty</a>,

137+<a name="line-137"></a> <a href="Matrix.Nat.html#prettyPrint">prettyPrint</a>

138+<a name="line-138"></a> )

139+<a name="line-139"></a>where

140+<a name="line-140"></a>

141+<a name="line-141"></a>import Data.Proxy

142+<a name="line-142"></a>import GHC.TypeLits

143+<a name="line-143"></a>import Control.DeepSeq

144+<a name="line-144"></a>import qualified Control.Category as C

145+<a name="line-145"></a>import qualified <a href="Matrix.Internal.html">Matrix.Internal</a> as I

146+<a name="line-146"></a>

147+<a name="line-147"></a>newtype <a name="Matrix"><a href="Matrix.Nat.html#Matrix">Matrix</a></a> <a name="local-6989586621679063540"><a href="#local-6989586621679063540">e</a></a> (<a name="local-6989586621679063541"><a href="#local-6989586621679063541">cols</a></a> :: Nat) (<a name="local-6989586621679063542"><a href="#local-6989586621679063542">rows</a></a> :: Nat) = <a name="M"><a href="Matrix.Nat.html#M">M</a></a> (<a href="Matrix.Internal.html#Matrix">I.Matrix</a> <a href="#local-6989586621679063540">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063541">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063542">rows</a>))

148+<a name="line-148"></a> deriving (Show, Num, Eq, Ord, NFData) via (<a href="Matrix.Internal.html#Matrix">I.Matrix</a> <a href="#local-6989586621679063540">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063541">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063542">rows</a>))

149+<a name="line-149"></a>

150+<a name="line-150"></a>-- | It isn't possible to implement the 'id' function so it's

151+<a name="line-151"></a>-- implementation is 'undefined'. However 'comp' can be and this partial

152+<a name="line-152"></a>-- class implementation exists just to make the code more readable.

153+<a name="line-153"></a>--

154+<a name="line-154"></a>-- Please use 'identity' instead.

155+<a name="line-155"></a>instance (Num <a href="#local-6989586621679063543">e</a>) => C.Category (<a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063543">e</a>) where

156+<a name="line-156"></a> <a name="local-8214565720323789508">id</a> = undefined

157+<a name="line-157"></a> (<a name="local-8214565720323789507">.</a>) = <a href="Matrix.Nat.html#comp">comp</a>

158+<a name="line-158"></a>

159+<a name="line-159"></a>-- Primitives

160+<a name="line-160"></a>

161+<a name="line-161"></a>empty :: <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063670">e</a> 0 0

162+<a name="line-162"></a><a name="empty"><a href="Matrix.Nat.html#empty">empty</a></a> = <a href="Matrix.Nat.html#M">M</a> <a href="Matrix.Internal.html#Empty">I.Empty</a>

163+<a name="line-163"></a>

164+<a name="line-164"></a>one :: <a href="#local-6989586621679063669">e</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063669">e</a> 1 1

165+<a name="line-165"></a><a name="one"><a href="Matrix.Nat.html#one">one</a></a> = <a href="Matrix.Nat.html#M">M</a> . <a href="Matrix.Internal.html#One">I.One</a>

166+<a name="line-166"></a>

167+<a name="line-167"></a>junc ::

168+<a name="line-168"></a> (I.FromNat <a href="#local-6989586621679063664">cols3</a> ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063665">cols1</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063666">cols2</a>)) =>

169+<a name="line-169"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063667">e</a> <a href="#local-6989586621679063665">cols1</a> <a href="#local-6989586621679063668">rows</a> ->

170+<a name="line-170"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063667">e</a> <a href="#local-6989586621679063666">cols2</a> <a href="#local-6989586621679063668">rows</a> ->

171+<a name="line-171"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063667">e</a> <a href="#local-6989586621679063664">cols3</a> <a href="#local-6989586621679063668">rows</a>

172+<a name="line-172"></a><a name="junc"><a href="Matrix.Nat.html#junc">junc</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063671"><a href="#local-6989586621679063671">a</a></a>) (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063672"><a href="#local-6989586621679063672">b</a></a>) = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#Junc">I.Junc</a> <a href="#local-6989586621679063671">a</a> <a href="#local-6989586621679063672">b</a>)

173+<a name="line-173"></a>

174+<a name="line-174"></a>infixl 3 <a href="Matrix.Nat.html#%7C%7C%7C">|||</a>

175+<a name="line-175"></a>(|||) ::

176+<a name="line-176"></a> (I.FromNat <a href="#local-6989586621679063659">cols3</a> ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063660">cols1</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063661">cols2</a>)) =>

177+<a name="line-177"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063662">e</a> <a href="#local-6989586621679063660">cols1</a> <a href="#local-6989586621679063663">rows</a> ->

178+<a name="line-178"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063662">e</a> <a href="#local-6989586621679063661">cols2</a> <a href="#local-6989586621679063663">rows</a> ->

179+<a name="line-179"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063662">e</a> <a href="#local-6989586621679063659">cols3</a> <a href="#local-6989586621679063663">rows</a>

180+<a name="line-180"></a>(<a name="%7C%7C%7C"><a href="Matrix.Nat.html#%7C%7C%7C">|||</a></a>) = <a href="Matrix.Nat.html#junc">junc</a>

181+<a name="line-181"></a>

182+<a name="line-182"></a>split ::

183+<a name="line-183"></a> (I.FromNat <a href="#local-6989586621679063654">rows3</a> ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063655">rows1</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063656">rows2</a>)) =>

184+<a name="line-184"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063657">e</a> <a href="#local-6989586621679063658">cols</a> <a href="#local-6989586621679063655">rows1</a> ->

185+<a name="line-185"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063657">e</a> <a href="#local-6989586621679063658">cols</a> <a href="#local-6989586621679063656">rows2</a> ->

186+<a name="line-186"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063657">e</a> <a href="#local-6989586621679063658">cols</a> <a href="#local-6989586621679063654">rows3</a>

187+<a name="line-187"></a><a name="split"><a href="Matrix.Nat.html#split">split</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063673"><a href="#local-6989586621679063673">a</a></a>) (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063674"><a href="#local-6989586621679063674">b</a></a>) = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#Split">I.Split</a> <a href="#local-6989586621679063673">a</a> <a href="#local-6989586621679063674">b</a>)

188+<a name="line-188"></a>

189+<a name="line-189"></a>infixl 2 <a href="Matrix.Nat.html#%3D%3D%3D">===</a>

190+<a name="line-190"></a>(===) ::

191+<a name="line-191"></a> (I.FromNat <a href="#local-6989586621679063649">rows3</a> ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063650">rows1</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063651">rows2</a>)) =>

192+<a name="line-192"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063652">e</a> <a href="#local-6989586621679063653">cols</a> <a href="#local-6989586621679063650">rows1</a> ->

193+<a name="line-193"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063652">e</a> <a href="#local-6989586621679063653">cols</a> <a href="#local-6989586621679063651">rows2</a> ->

194+<a name="line-194"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063652">e</a> <a href="#local-6989586621679063653">cols</a> <a href="#local-6989586621679063649">rows3</a>

195+<a name="line-195"></a>(<a name="%3D%3D%3D"><a href="Matrix.Nat.html#%3D%3D%3D">===</a></a>) = <a href="Matrix.Nat.html#split">split</a>

196+<a name="line-196"></a>

197+<a name="line-197"></a>-- Construction

198+<a name="line-198"></a>

199+<a name="line-199"></a>fromLists :: (<a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063646">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063647">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063648">rows</a>)) => [[<a href="#local-6989586621679063646">e</a>]] -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063646">e</a> <a href="#local-6989586621679063647">cols</a> <a href="#local-6989586621679063648">rows</a>

200+<a name="line-200"></a><a name="fromLists"><a href="Matrix.Nat.html#fromLists">fromLists</a></a> = <a href="Matrix.Nat.html#M">M</a> . <a href="Matrix.Internal.html#fromLists">I.fromLists</a>

201+<a name="line-201"></a>

202+<a name="line-202"></a>matrixBuilder ::

203+<a name="line-203"></a> (<a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063643">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063644">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063645">rows</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063644">cols</a>)), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063645">rows</a>))) =>

204+<a name="line-204"></a> ((Int, Int) -> <a href="#local-6989586621679063643">e</a>) ->

205+<a name="line-205"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063643">e</a> <a href="#local-6989586621679063644">cols</a> <a href="#local-6989586621679063645">rows</a>

206+<a name="line-206"></a><a name="matrixBuilder"><a href="Matrix.Nat.html#matrixBuilder">matrixBuilder</a></a> = <a href="Matrix.Nat.html#M">M</a> . <a href="Matrix.Internal.html#matrixBuilder">I.matrixBuilder</a>

207+<a name="line-207"></a>

208+<a name="line-208"></a>col :: (<a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063641">e</a> () (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063642">rows</a>)) => [<a href="#local-6989586621679063641">e</a>] -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063641">e</a> 1 <a href="#local-6989586621679063642">rows</a>

209+<a name="line-209"></a><a name="col"><a href="Matrix.Nat.html#col">col</a></a> = <a href="Matrix.Nat.html#M">M</a> . <a href="Matrix.Internal.html#col">I.col</a>

210+<a name="line-210"></a>

211+<a name="line-211"></a>row :: (<a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063639">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063640">cols</a>) ()) => [<a href="#local-6989586621679063639">e</a>] -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063639">e</a> <a href="#local-6989586621679063640">cols</a> 1

212+<a name="line-212"></a><a name="row"><a href="Matrix.Nat.html#row">row</a></a> = <a href="Matrix.Nat.html#M">M</a> . <a href="Matrix.Internal.html#row">I.row</a>

213+<a name="line-213"></a>

214+<a name="line-214"></a>fromF ::

215+<a name="line-215"></a> ( Bounded <a href="#local-6989586621679063634">a</a>,

216+<a name="line-216"></a> Bounded <a href="#local-6989586621679063635">b</a>,

217+<a name="line-217"></a> Enum <a href="#local-6989586621679063634">a</a>,

218+<a name="line-218"></a> Enum <a href="#local-6989586621679063635">b</a>,

219+<a name="line-219"></a> Eq <a href="#local-6989586621679063635">b</a>,

220+<a name="line-220"></a> Num <a href="#local-6989586621679063636">e</a>,

221+<a name="line-221"></a> Ord <a href="#local-6989586621679063636">e</a>,

222+<a name="line-222"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063637">cols</a>)),

223+<a name="line-223"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063638">rows</a>)),

224+<a name="line-224"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063636">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063638">rows</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063637">cols</a>)

225+<a name="line-225"></a> ) =>

226+<a name="line-226"></a> (<a href="#local-6989586621679063634">a</a> -> <a href="#local-6989586621679063635">b</a>) ->

227+<a name="line-227"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063636">e</a> <a href="#local-6989586621679063637">cols</a> <a href="#local-6989586621679063638">rows</a>

228+<a name="line-228"></a><a name="fromF"><a href="Matrix.Nat.html#fromF">fromF</a></a> = <a href="Matrix.Nat.html#M">M</a> . <a href="Matrix.Internal.html#fromF">I.fromF</a>

229+<a name="line-229"></a>

230+<a name="line-230"></a>fromF' ::

231+<a name="line-231"></a> ( Bounded <a href="#local-6989586621679063631">a</a>,

232+<a name="line-232"></a> Bounded <a href="#local-6989586621679063632">b</a>,

233+<a name="line-233"></a> Enum <a href="#local-6989586621679063631">a</a>,

234+<a name="line-234"></a> Enum <a href="#local-6989586621679063632">b</a>,

235+<a name="line-235"></a> Eq <a href="#local-6989586621679063632">b</a>,

236+<a name="line-236"></a> Num <a href="#local-6989586621679063633">e</a>,

237+<a name="line-237"></a> Ord <a href="#local-6989586621679063633">e</a>,

238+<a name="line-238"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679063631">a</a>)),

239+<a name="line-239"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679063632">b</a>)),

240+<a name="line-240"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063633">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679063632">b</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679063631">a</a>)

241+<a name="line-241"></a> ) =>

242+<a name="line-242"></a> (<a href="#local-6989586621679063631">a</a> -> <a href="#local-6989586621679063632">b</a>) ->

243+<a name="line-243"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063633">e</a> (<a href="Matrix.Internal.html#Count">I.Count</a> <a href="#local-6989586621679063631">a</a>) (<a href="Matrix.Internal.html#Count">I.Count</a> <a href="#local-6989586621679063632">b</a>)

244+<a name="line-244"></a><a name="fromF%27"><a href="Matrix.Nat.html#fromF%27">fromF'</a></a> = <a href="Matrix.Nat.html#M">M</a> . <a href="Matrix.Internal.html#fromF%27">I.fromF'</a>

245+<a name="line-245"></a>

246+<a name="line-246"></a>-- Conversion

247+<a name="line-247"></a>

248+<a name="line-248"></a>toLists :: <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063628">e</a> <a href="#local-6989586621679063629">cols</a> <a href="#local-6989586621679063630">rows</a> -> [[<a href="#local-6989586621679063628">e</a>]]

249+<a name="line-249"></a><a name="toLists"><a href="Matrix.Nat.html#toLists">toLists</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063675"><a href="#local-6989586621679063675">m</a></a>) = <a href="Matrix.Internal.html#toLists">I.toLists</a> <a href="#local-6989586621679063675">m</a>

250+<a name="line-250"></a>

251+<a name="line-251"></a>toList :: <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063625">e</a> <a href="#local-6989586621679063626">cols</a> <a href="#local-6989586621679063627">rows</a> -> [<a href="#local-6989586621679063625">e</a>]

252+<a name="line-252"></a><a name="toList"><a href="Matrix.Nat.html#toList">toList</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063676"><a href="#local-6989586621679063676">m</a></a>) = <a href="Matrix.Internal.html#toList">I.toList</a> <a href="#local-6989586621679063676">m</a>

253+<a name="line-253"></a>

254+<a name="line-254"></a>-- Zeros Matrix

255+<a name="line-255"></a>

256+<a name="line-256"></a>zeros ::

257+<a name="line-257"></a> (Num <a href="#local-6989586621679063622">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063622">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063623">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063624">rows</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063623">cols</a>)), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063624">rows</a>))) =>

258+<a name="line-258"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063622">e</a> <a href="#local-6989586621679063623">cols</a> <a href="#local-6989586621679063624">rows</a>

259+<a name="line-259"></a><a name="zeros"><a href="Matrix.Nat.html#zeros">zeros</a></a> = <a href="Matrix.Nat.html#M">M</a> <a href="Matrix.Internal.html#zeros">I.zeros</a>

260+<a name="line-260"></a>

261+<a name="line-261"></a>-- Ones Matrix

262+<a name="line-262"></a>

263+<a name="line-263"></a>ones ::

264+<a name="line-264"></a> (Num <a href="#local-6989586621679063619">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063619">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063620">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063621">rows</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063620">cols</a>)), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063621">rows</a>))) =>

265+<a name="line-265"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063619">e</a> <a href="#local-6989586621679063620">cols</a> <a href="#local-6989586621679063621">rows</a>

266+<a name="line-266"></a><a name="ones"><a href="Matrix.Nat.html#ones">ones</a></a> = <a href="Matrix.Nat.html#M">M</a> <a href="Matrix.Internal.html#ones">I.ones</a>

267+<a name="line-267"></a>

268+<a name="line-268"></a>-- Const Matrix

269+<a name="line-269"></a>

270+<a name="line-270"></a>constant ::

271+<a name="line-271"></a> (Num <a href="#local-6989586621679063616">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063616">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063617">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063618">rows</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063617">cols</a>)), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063618">rows</a>))) =>

272+<a name="line-272"></a> <a href="#local-6989586621679063616">e</a> ->

273+<a name="line-273"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063616">e</a> <a href="#local-6989586621679063617">cols</a> <a href="#local-6989586621679063618">rows</a>

274+<a name="line-274"></a><a name="constant"><a href="Matrix.Nat.html#constant">constant</a></a> = <a href="Matrix.Nat.html#M">M</a> . <a href="Matrix.Internal.html#constant">I.constant</a>

275+<a name="line-275"></a>

276+<a name="line-276"></a>-- Bang Matrix

277+<a name="line-277"></a>

278+<a name="line-278"></a>bang ::

279+<a name="line-279"></a> forall <a name="local-6989586621679063614"><a href="#local-6989586621679063614">e</a></a> <a name="local-6989586621679063615"><a href="#local-6989586621679063615">cols</a></a>.

280+<a name="line-280"></a> (Num <a href="#local-6989586621679063614">e</a>, Enum <a href="#local-6989586621679063614">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063614">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063615">cols</a>) (), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063615">cols</a>))) =>

281+<a name="line-281"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063614">e</a> <a href="#local-6989586621679063615">cols</a> 1

282+<a name="line-282"></a><a name="bang"><a href="Matrix.Nat.html#bang">bang</a></a> = <a href="Matrix.Nat.html#M">M</a> <a href="Matrix.Internal.html#bang">I.bang</a>

283+<a name="line-283"></a>

284+<a name="line-284"></a>-- Identity Matrix

285+<a name="line-285"></a>

286+<a name="line-286"></a>identity ::

287+<a name="line-287"></a> (Num <a href="#local-6989586621679063612">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063612">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063613">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063613">cols</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063613">cols</a>))) =>

288+<a name="line-288"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063612">e</a> <a href="#local-6989586621679063613">cols</a> <a href="#local-6989586621679063613">cols</a>

289+<a name="line-289"></a><a name="identity"><a href="Matrix.Nat.html#identity">identity</a></a> = <a href="Matrix.Nat.html#M">M</a> <a href="Matrix.Internal.html#identity">I.identity</a>

290+<a name="line-290"></a>

291+<a name="line-291"></a>-- Matrix composition (MMM)

292+<a name="line-292"></a>

293+<a name="line-293"></a>comp :: (Num <a href="#local-6989586621679063608">e</a>) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063608">e</a> <a href="#local-6989586621679063609">cr</a> <a href="#local-6989586621679063610">rows</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063608">e</a> <a href="#local-6989586621679063611">cols</a> <a href="#local-6989586621679063609">cr</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063608">e</a> <a href="#local-6989586621679063611">cols</a> <a href="#local-6989586621679063610">rows</a>

294+<a name="line-294"></a><a name="comp"><a href="Matrix.Nat.html#comp">comp</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063677"><a href="#local-6989586621679063677">a</a></a>) (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063678"><a href="#local-6989586621679063678">b</a></a>) = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#comp">I.comp</a> <a href="#local-6989586621679063677">a</a> <a href="#local-6989586621679063678">b</a>)

295+<a name="line-295"></a>

296+<a name="line-296"></a>p1 ::

297+<a name="line-297"></a> ( Num <a href="#local-6989586621679063605">e</a>,

298+<a name="line-298"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063606">n</a>)),

299+<a name="line-299"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063607">m</a>)),

300+<a name="line-300"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063605">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063606">n</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063607">m</a>),

301+<a name="line-301"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063605">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063607">m</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063607">m</a>),

302+<a name="line-302"></a> I.FromNat (m + <a href="#local-6989586621679063606">n</a>) ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063607">m</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063606">n</a>)

303+<a name="line-303"></a> ) =>

304+<a name="line-304"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063605">e</a> (m + <a href="#local-6989586621679063606">n</a>) <a href="#local-6989586621679063607">m</a>

305+<a name="line-305"></a><a name="p1"><a href="Matrix.Nat.html#p1">p1</a></a> = <a href="Matrix.Nat.html#M">M</a> <a href="Matrix.Internal.html#p1">I.p1</a>

306+<a name="line-306"></a>

307+<a name="line-307"></a>p2 ::

308+<a name="line-308"></a> ( Num <a href="#local-6989586621679063602">e</a>,

309+<a name="line-309"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063603">n</a>)),

310+<a name="line-310"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063604">m</a>)),

311+<a name="line-311"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063602">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063604">m</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063603">n</a>),

312+<a name="line-312"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063602">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063603">n</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063603">n</a>),

313+<a name="line-313"></a> I.FromNat (m + <a href="#local-6989586621679063603">n</a>) ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063604">m</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063603">n</a>)

314+<a name="line-314"></a> ) =>

315+<a name="line-315"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063602">e</a> (m + <a href="#local-6989586621679063603">n</a>) <a href="#local-6989586621679063603">n</a>

316+<a name="line-316"></a><a name="p2"><a href="Matrix.Nat.html#p2">p2</a></a> = <a href="Matrix.Nat.html#M">M</a> <a href="Matrix.Internal.html#p2">I.p2</a>

317+<a name="line-317"></a>

318+<a name="line-318"></a>-- Injections

319+<a name="line-319"></a>

320+<a name="line-320"></a>i1 ::

321+<a name="line-321"></a> ( Num <a href="#local-6989586621679063599">e</a>,

322+<a name="line-322"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063600">n</a>)),

323+<a name="line-323"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063601">rows</a>)),

324+<a name="line-324"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063599">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063600">n</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063601">rows</a>),

325+<a name="line-325"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063599">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063601">rows</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063601">rows</a>),

326+<a name="line-326"></a> I.FromNat (rows + <a href="#local-6989586621679063600">n</a>) ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063601">rows</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063600">n</a>)

327+<a name="line-327"></a> ) =>

328+<a name="line-328"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063599">e</a> <a href="#local-6989586621679063601">rows</a> (rows + <a href="#local-6989586621679063600">n</a>)

329+<a name="line-329"></a><a name="i1"><a href="Matrix.Nat.html#i1">i1</a></a> = <a href="Matrix.Nat.html#tr">tr</a> <a href="Matrix.Nat.html#p1">p1</a>

330+<a name="line-330"></a>

331+<a name="line-331"></a>i2 ::

332+<a name="line-332"></a> ( Num <a href="#local-6989586621679063596">e</a>,

333+<a name="line-333"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063597">rows</a>)),

334+<a name="line-334"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063598">m</a>)),

335+<a name="line-335"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063596">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063598">m</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063597">rows</a>),

336+<a name="line-336"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063596">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063597">rows</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063597">rows</a>),

337+<a name="line-337"></a> I.FromNat (m + <a href="#local-6989586621679063597">rows</a>) ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063598">m</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063597">rows</a>)

338+<a name="line-338"></a> ) =>

339+<a name="line-339"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063596">e</a> <a href="#local-6989586621679063597">rows</a> (m + <a href="#local-6989586621679063597">rows</a>)

340+<a name="line-340"></a><a name="i2"><a href="Matrix.Nat.html#i2">i2</a></a> = <a href="Matrix.Nat.html#tr">tr</a> <a href="Matrix.Nat.html#p2">p2</a>

341+<a name="line-341"></a>

342+<a name="line-342"></a>-- Dimensions

343+<a name="line-343"></a>

344+<a name="line-344"></a>rows :: (KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063593">rows</a>))) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063594">e</a> <a href="#local-6989586621679063595">cols</a> <a href="#local-6989586621679063593">rows</a> -> Int

345+<a name="line-345"></a><a name="rows"><a href="Matrix.Nat.html#rows">rows</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063679"><a href="#local-6989586621679063679">m</a></a>) = <a href="Matrix.Internal.html#rows">I.rows</a> <a href="#local-6989586621679063679">m</a>

346+<a name="line-346"></a>

347+<a name="line-347"></a>columns :: (KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063590">cols</a>))) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063591">e</a> <a href="#local-6989586621679063590">cols</a> <a href="#local-6989586621679063592">rows</a> -> Int

348+<a name="line-348"></a><a name="columns"><a href="Matrix.Nat.html#columns">columns</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063680"><a href="#local-6989586621679063680">m</a></a>) = <a href="Matrix.Internal.html#columns">I.columns</a> <a href="#local-6989586621679063680">m</a>

349+<a name="line-349"></a>

350+<a name="line-350"></a>-- Coproduct Bifunctor

351+<a name="line-351"></a>

352+<a name="line-352"></a>infixl 5 <a href="Matrix.Nat.html#-%7C-">-|-</a>

353+<a name="line-353"></a>

354+<a name="line-354"></a>(-|-) ::

355+<a name="line-355"></a> ( Num <a href="#local-6989586621679063585">e</a>,

356+<a name="line-356"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063586">j</a>)),

357+<a name="line-357"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063587">k</a>)),

358+<a name="line-358"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063585">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063587">k</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063587">k</a>),

359+<a name="line-359"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063585">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063586">j</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063587">k</a>),

360+<a name="line-360"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063585">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063587">k</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063586">j</a>),

361+<a name="line-361"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063585">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063586">j</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063586">j</a>),

362+<a name="line-362"></a> I.FromNat (n + <a href="#local-6989586621679063589">m</a>) ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063588">n</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063589">m</a>),

363+<a name="line-363"></a> I.FromNat (k + <a href="#local-6989586621679063586">j</a>) ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063587">k</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063586">j</a>)

364+<a name="line-364"></a> ) =>

365+<a name="line-365"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063585">e</a> <a href="#local-6989586621679063588">n</a> <a href="#local-6989586621679063587">k</a> ->

366+<a name="line-366"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063585">e</a> <a href="#local-6989586621679063589">m</a> <a href="#local-6989586621679063586">j</a> ->

367+<a name="line-367"></a> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063585">e</a> (n + <a href="#local-6989586621679063589">m</a>) (k + <a href="#local-6989586621679063586">j</a>)

368+<a name="line-368"></a>(<a name="-%7C-"><a href="Matrix.Nat.html#-%7C-">-|-</a></a>) (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063681"><a href="#local-6989586621679063681">a</a></a>) (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063682"><a href="#local-6989586621679063682">b</a></a>) = <a href="Matrix.Nat.html#M">M</a> ((<a href="Matrix.Internal.html#-%7C-">I.-|-</a>) <a href="#local-6989586621679063681">a</a> <a href="#local-6989586621679063682">b</a>)

369+<a name="line-369"></a>

370+<a name="line-370"></a>-- Khatri Rao Product and projections

371+<a name="line-371"></a>

372+<a name="line-372"></a>kp1 ::

373+<a name="line-373"></a> forall <a name="local-6989586621679063582"><a href="#local-6989586621679063582">e</a></a> <a name="local-6989586621679063583"><a href="#local-6989586621679063583">m</a></a> <a name="local-6989586621679063584"><a href="#local-6989586621679063584">k</a></a> .

374+<a name="line-374"></a> ( Num <a href="#local-6989586621679063582">e</a>,

375+<a name="line-375"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063583">m</a>)),

376+<a name="line-376"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063584">k</a>)),

377+<a name="line-377"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (m * <a href="#local-6989586621679063584">k</a>))),

378+<a name="line-378"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063582">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (m * <a href="#local-6989586621679063584">k</a>)) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063583">m</a>),

379+<a name="line-379"></a> I.FromNat (m * <a href="#local-6989586621679063584">k</a>) ~ <a href="Matrix.Internal.html#FromNat">I.FromNat</a> (I.Count (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063583">m</a>) * <a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063584">k</a>))

380+<a name="line-380"></a> ) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063582">e</a> (m * <a href="#local-6989586621679063584">k</a>) <a href="#local-6989586621679063583">m</a>

381+<a name="line-381"></a><a name="kp1"><a href="Matrix.Nat.html#kp1">kp1</a></a> = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#kp1">I.kp1</a> @<a href="#local-6989586621679063582">e</a> @(<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063583">m</a>) @(<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063584">k</a>))

382+<a name="line-382"></a>

383+<a name="line-383"></a>kp2 ::

384+<a name="line-384"></a> forall <a name="local-6989586621679063579"><a href="#local-6989586621679063579">e</a></a> <a name="local-6989586621679063580"><a href="#local-6989586621679063580">m</a></a> <a name="local-6989586621679063581"><a href="#local-6989586621679063581">k</a></a>.

385+<a name="line-385"></a> ( Num <a href="#local-6989586621679063579">e</a>,

386+<a name="line-386"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063581">k</a>)),

387+<a name="line-387"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063579">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (m * <a href="#local-6989586621679063581">k</a>)) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063581">k</a>),

388+<a name="line-388"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063580">m</a>)),

389+<a name="line-389"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (m * <a href="#local-6989586621679063581">k</a>))),

390+<a name="line-390"></a> I.FromNat (m * <a href="#local-6989586621679063581">k</a>) ~ <a href="Matrix.Internal.html#FromNat">I.FromNat</a> (I.Count (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063580">m</a>) * <a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063581">k</a>))

391+<a name="line-391"></a> ) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063579">e</a> (m * <a href="#local-6989586621679063581">k</a>) <a href="#local-6989586621679063581">k</a>

392+<a name="line-392"></a><a name="kp2"><a href="Matrix.Nat.html#kp2">kp2</a></a> = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#kp2">I.kp2</a> @<a href="#local-6989586621679063579">e</a> @(<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063580">m</a>) @(<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063581">k</a>))

393+<a name="line-393"></a>

394+<a name="line-394"></a>khatri ::

395+<a name="line-395"></a> forall <a name="local-6989586621679063575"><a href="#local-6989586621679063575">e</a></a> <a name="local-6989586621679063576"><a href="#local-6989586621679063576">cols</a></a> <a name="local-6989586621679063577"><a href="#local-6989586621679063577">a</a></a> <a name="local-6989586621679063578"><a href="#local-6989586621679063578">b</a></a>.

396+<a name="line-396"></a> ( Num <a href="#local-6989586621679063575">e</a>,

397+<a name="line-397"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063577">a</a>)),

398+<a name="line-398"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063578">b</a>)),

399+<a name="line-399"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (a * <a href="#local-6989586621679063578">b</a>))),

400+<a name="line-400"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063575">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (a * <a href="#local-6989586621679063578">b</a>)) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063577">a</a>),

401+<a name="line-401"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063575">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (a * <a href="#local-6989586621679063578">b</a>)) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063578">b</a>),

402+<a name="line-402"></a> I.FromNat (a * <a href="#local-6989586621679063578">b</a>) ~ <a href="Matrix.Internal.html#FromNat">I.FromNat</a> (I.Count (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063577">a</a>) * <a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063578">b</a>))

403+<a name="line-403"></a> ) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063575">e</a> <a href="#local-6989586621679063576">cols</a> <a href="#local-6989586621679063577">a</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063575">e</a> <a href="#local-6989586621679063576">cols</a> <a href="#local-6989586621679063578">b</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063575">e</a> <a href="#local-6989586621679063576">cols</a> (a * <a href="#local-6989586621679063578">b</a>)

404+<a name="line-404"></a><a name="khatri"><a href="Matrix.Nat.html#khatri">khatri</a></a> <a name="local-6989586621679063683"><a href="#local-6989586621679063683">a</a></a> <a name="local-6989586621679063684"><a href="#local-6989586621679063684">b</a></a> =

405+<a name="line-405"></a> let <a name="local-6989586621679063685"><a href="#local-6989586621679063685">kp1'</a></a> = <a href="Matrix.Nat.html#kp1">kp1</a> @<a href="#local-6989586621679063575">e</a> @<a href="#local-6989586621679063577">a</a> @<a href="#local-6989586621679063578">b</a>

406+<a name="line-406"></a> <a name="local-6989586621679063686"><a href="#local-6989586621679063686">kp2'</a></a> = <a href="Matrix.Nat.html#kp2">kp2</a> @<a href="#local-6989586621679063575">e</a> @<a href="#local-6989586621679063577">a</a> @<a href="#local-6989586621679063578">b</a>

407+<a name="line-407"></a> in <a href="Matrix.Nat.html#comp">comp</a> (<a href="Matrix.Nat.html#tr">tr</a> <a href="#local-6989586621679063685">kp1'</a>) <a href="#local-6989586621679063683">a</a> * <a href="Matrix.Nat.html#comp">comp</a> (<a href="Matrix.Nat.html#tr">tr</a> <a href="#local-6989586621679063686">kp2'</a>) <a href="#local-6989586621679063684">b</a>

408+<a name="line-408"></a>

409+<a name="line-409"></a>-- Product Bifunctor (Kronecker)

410+<a name="line-410"></a>

411+<a name="line-411"></a>infixl 4 <a href="Matrix.Nat.html#%3E%3C">><</a>

412+<a name="line-412"></a>

413+<a name="line-413"></a>(><) ::

414+<a name="line-414"></a> forall <a name="local-6989586621679063570"><a href="#local-6989586621679063570">e</a></a> <a name="local-6989586621679063571"><a href="#local-6989586621679063571">m</a></a> <a name="local-6989586621679063572"><a href="#local-6989586621679063572">p</a></a> <a name="local-6989586621679063573"><a href="#local-6989586621679063573">n</a></a> <a name="local-6989586621679063574"><a href="#local-6989586621679063574">q</a></a>.

415+<a name="line-415"></a> ( Num <a href="#local-6989586621679063570">e</a>,

416+<a name="line-416"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063571">m</a>)),

417+<a name="line-417"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063573">n</a>)),

418+<a name="line-418"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063572">p</a>)),

419+<a name="line-419"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063574">q</a>)),

420+<a name="line-420"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (m * <a href="#local-6989586621679063573">n</a>))),

421+<a name="line-421"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (p * <a href="#local-6989586621679063574">q</a>))),

422+<a name="line-422"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063570">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (m * <a href="#local-6989586621679063573">n</a>)) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063571">m</a>),

423+<a name="line-423"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063570">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (m * <a href="#local-6989586621679063573">n</a>)) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063573">n</a>),

424+<a name="line-424"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063570">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (p * <a href="#local-6989586621679063574">q</a>)) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063572">p</a>),

425+<a name="line-425"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063570">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> (p * <a href="#local-6989586621679063574">q</a>)) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063574">q</a>),

426+<a name="line-426"></a> I.FromNat (m * <a href="#local-6989586621679063573">n</a>) ~ <a href="Matrix.Internal.html#FromNat">I.FromNat</a> (I.Count (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063571">m</a>) * <a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063573">n</a>)),

427+<a name="line-427"></a> I.FromNat (p * <a href="#local-6989586621679063574">q</a>) ~ <a href="Matrix.Internal.html#FromNat">I.FromNat</a> (I.Count (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063572">p</a>) * <a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063574">q</a>))

428+<a name="line-428"></a> ) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063570">e</a> <a href="#local-6989586621679063571">m</a> <a href="#local-6989586621679063572">p</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063570">e</a> <a href="#local-6989586621679063573">n</a> <a href="#local-6989586621679063574">q</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063570">e</a> (m * <a href="#local-6989586621679063573">n</a>) (p * <a href="#local-6989586621679063574">q</a>)

429+<a name="line-429"></a>(<a name="%3E%3C"><a href="Matrix.Nat.html#%3E%3C">><</a></a>) <a name="local-6989586621679063687"><a href="#local-6989586621679063687">a</a></a> <a name="local-6989586621679063688"><a href="#local-6989586621679063688">b</a></a> =

430+<a name="line-430"></a> let <a name="local-6989586621679063689"><a href="#local-6989586621679063689">kp1'</a></a> = <a href="Matrix.Nat.html#kp1">kp1</a> @<a href="#local-6989586621679063570">e</a> @<a href="#local-6989586621679063571">m</a> @<a href="#local-6989586621679063573">n</a>

431+<a name="line-431"></a> <a name="local-6989586621679063690"><a href="#local-6989586621679063690">kp2'</a></a> = <a href="Matrix.Nat.html#kp2">kp2</a> @<a href="#local-6989586621679063570">e</a> @<a href="#local-6989586621679063571">m</a> @<a href="#local-6989586621679063573">n</a>

432+<a name="line-432"></a> in <a href="Matrix.Nat.html#khatri">khatri</a> (<a href="Matrix.Nat.html#comp">comp</a> <a href="#local-6989586621679063687">a</a> <a href="#local-6989586621679063689">kp1'</a>) (<a href="Matrix.Nat.html#comp">comp</a> <a href="#local-6989586621679063688">b</a> <a href="#local-6989586621679063690">kp2'</a>)

433+<a name="line-433"></a>

434+<a name="line-434"></a>-- Matrix abide Junc Split

435+<a name="line-435"></a>

436+<a name="line-436"></a>abideJS :: <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063567">e</a> <a href="#local-6989586621679063568">cols</a> <a href="#local-6989586621679063569">rows</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063567">e</a> <a href="#local-6989586621679063568">cols</a> <a href="#local-6989586621679063569">rows</a>

437+<a name="line-437"></a><a name="abideJS"><a href="Matrix.Nat.html#abideJS">abideJS</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063691"><a href="#local-6989586621679063691">m</a></a>) = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#abideJS">I.abideJS</a> <a href="#local-6989586621679063691">m</a>)

438+<a name="line-438"></a>

439+<a name="line-439"></a>-- Matrix abide Split Junc

440+<a name="line-440"></a>

441+<a name="line-441"></a>abideSJ :: <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063564">e</a> <a href="#local-6989586621679063565">cols</a> <a href="#local-6989586621679063566">rows</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063564">e</a> <a href="#local-6989586621679063565">cols</a> <a href="#local-6989586621679063566">rows</a>

442+<a name="line-442"></a><a name="abideSJ"><a href="Matrix.Nat.html#abideSJ">abideSJ</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063692"><a href="#local-6989586621679063692">m</a></a>) = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#abideSJ">I.abideSJ</a> <a href="#local-6989586621679063692">m</a>)

443+<a name="line-443"></a>

444+<a name="line-444"></a>-- Matrix transposition

445+<a name="line-445"></a>

446+<a name="line-446"></a>tr :: <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063561">e</a> <a href="#local-6989586621679063562">cols</a> <a href="#local-6989586621679063563">rows</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063561">e</a> <a href="#local-6989586621679063563">rows</a> <a href="#local-6989586621679063562">cols</a>

447+<a name="line-447"></a><a name="tr"><a href="Matrix.Nat.html#tr">tr</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063693"><a href="#local-6989586621679063693">m</a></a>) = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#tr">I.tr</a> <a href="#local-6989586621679063693">m</a>)

448+<a name="line-448"></a>

449+<a name="line-449"></a>-- Selective 'select' operator

450+<a name="line-450"></a>select ::

451+<a name="line-451"></a> ( Num <a href="#local-6989586621679063554">e</a>,

452+<a name="line-452"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063554">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063555">rows1</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063555">rows1</a>),

453+<a name="line-453"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063555">rows1</a>)),

454+<a name="line-454"></a> I.FromNat <a href="#local-6989586621679063556">rows2</a> ~ <a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063555">rows1</a>,

455+<a name="line-455"></a> I.FromNat <a href="#local-6989586621679063557">cols1</a> ~ <a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063558">cols2</a>,

456+<a name="line-456"></a> I.FromNat <a href="#local-6989586621679063559">rows3</a> ~ Either (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063560">cols3</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063555">rows1</a>)

457+<a name="line-457"></a> ) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063554">e</a> <a href="#local-6989586621679063557">cols1</a> <a href="#local-6989586621679063559">rows3</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063554">e</a> <a href="#local-6989586621679063560">cols3</a> <a href="#local-6989586621679063555">rows1</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063554">e</a> <a href="#local-6989586621679063558">cols2</a> <a href="#local-6989586621679063556">rows2</a>

458+<a name="line-458"></a><a name="select"><a href="Matrix.Nat.html#select">select</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063694"><a href="#local-6989586621679063694">m</a></a>) (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063695"><a href="#local-6989586621679063695">y</a></a>) = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#select">I.select</a> <a href="#local-6989586621679063694">m</a> <a href="#local-6989586621679063695">y</a>)

459+<a name="line-459"></a>

460+<a name="line-460"></a>-- McCarthy's Conditional

461+<a name="line-461"></a>

462+<a name="line-462"></a>cond ::

463+<a name="line-463"></a> ( I.FromNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063550">cols</a>)) ~ <a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063550">cols</a>,

464+<a name="line-464"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063550">cols</a>)),

465+<a name="line-465"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063551">e</a> () (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063550">cols</a>),

466+<a name="line-466"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063551">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063550">cols</a>) (),

467+<a name="line-467"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679063551">e</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063550">cols</a>) (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063550">cols</a>),

468+<a name="line-468"></a> Bounded <a href="#local-6989586621679063552">a</a>,

469+<a name="line-469"></a> Enum <a href="#local-6989586621679063552">a</a>,

470+<a name="line-470"></a> Num <a href="#local-6989586621679063551">e</a>,

471+<a name="line-471"></a> Ord <a href="#local-6989586621679063551">e</a>

472+<a name="line-472"></a> )

473+<a name="line-473"></a> =>

474+<a name="line-474"></a> (<a href="#local-6989586621679063552">a</a> -> Bool) -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063551">e</a> <a href="#local-6989586621679063550">cols</a> <a href="#local-6989586621679063553">rows</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063551">e</a> <a href="#local-6989586621679063550">cols</a> <a href="#local-6989586621679063553">rows</a> -> <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063551">e</a> <a href="#local-6989586621679063550">cols</a> <a href="#local-6989586621679063553">rows</a>

475+<a name="line-475"></a><a name="cond"><a href="Matrix.Nat.html#cond">cond</a></a> <a name="local-6989586621679063696"><a href="#local-6989586621679063696">p</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063697"><a href="#local-6989586621679063697">a</a></a>) (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063698"><a href="#local-6989586621679063698">b</a></a>) = <a href="Matrix.Nat.html#M">M</a> (<a href="Matrix.Internal.html#cond">I.cond</a> <a href="#local-6989586621679063696">p</a> <a href="#local-6989586621679063697">a</a> <a href="#local-6989586621679063698">b</a>)

476+<a name="line-476"></a>

477+<a name="line-477"></a>-- Pretty print

478+<a name="line-478"></a>

479+<a name="line-479"></a>pretty :: (KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063547">cols</a>)), Show <a href="#local-6989586621679063548">e</a>) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063548">e</a> <a href="#local-6989586621679063547">cols</a> <a href="#local-6989586621679063549">rows</a> -> String

480+<a name="line-480"></a><a name="pretty"><a href="Matrix.Nat.html#pretty">pretty</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063699"><a href="#local-6989586621679063699">m</a></a>) = <a href="Matrix.Internal.html#pretty">I.pretty</a> <a href="#local-6989586621679063699">m</a>

481+<a name="line-481"></a>

482+<a name="line-482"></a>prettyPrint :: (KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#FromNat">I.FromNat</a> <a href="#local-6989586621679063544">cols</a>)), Show <a href="#local-6989586621679063545">e</a>) => <a href="Matrix.Nat.html#Matrix">Matrix</a> <a href="#local-6989586621679063545">e</a> <a href="#local-6989586621679063544">cols</a> <a href="#local-6989586621679063546">rows</a> -> IO ()

483+<a name="line-483"></a><a name="prettyPrint"><a href="Matrix.Nat.html#prettyPrint">prettyPrint</a></a> (<a href="Matrix.Nat.html#M">M</a> <a name="local-6989586621679063700"><a href="#local-6989586621679063700">m</a></a>) = <a href="Matrix.Internal.html#prettyPrint">I.prettyPrint</a> <a href="#local-6989586621679063700">m</a>

484+<a name="line-484"></a></pre></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/src/Matrix.Type.htmlnew file+648

@@ -0,0 +1,648 @@

1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="style.css" /><script type="text/javascript" src="highlight.js"></script></head><body><pre>{-# LANGUAGE AllowAmbiguousTypes #-}

2+<a name="line-2"></a>{-# LANGUAGE DataKinds #-}

3+<a name="line-3"></a>{-# LANGUAGE DerivingVia #-}

4+<a name="line-4"></a>{-# LANGUAGE FlexibleContexts #-}

5+<a name="line-5"></a>{-# LANGUAGE FlexibleInstances #-}

6+<a name="line-6"></a>{-# LANGUAGE GADTs #-}

7+<a name="line-7"></a>{-# LANGUAGE KindSignatures #-}

8+<a name="line-8"></a>{-# LANGUAGE MultiParamTypeClasses #-}

9+<a name="line-9"></a>{-# LANGUAGE NoStarIsType #-}

10+<a name="line-10"></a>{-# LANGUAGE RankNTypes #-}

11+<a name="line-11"></a>{-# LANGUAGE ScopedTypeVariables #-}

12+<a name="line-12"></a>{-# LANGUAGE TypeApplications #-}

13+<a name="line-13"></a>{-# LANGUAGE TypeOperators #-}

14+<a name="line-14"></a>{-# LANGUAGE UndecidableInstances #-}

15+<a name="line-15"></a>

16+<a name="line-16"></a>-----------------------------------------------------------------------------

17+<a name="line-17"></a>-- |

18+<a name="line-18"></a>-- Module : Matrix.Type

19+<a name="line-19"></a>-- Copyright : (c) Armando Santos 2019-2020

20+<a name="line-20"></a>-- Maintainer : armandoifsantos@gmail.com

21+<a name="line-21"></a>-- Stability : experimental

22+<a name="line-22"></a>--

23+<a name="line-23"></a>-- The LAoP discipline generalises relations and functions treating them as

24+<a name="line-24"></a>-- Boolean matrices and in turn consider these as arrows.

25+<a name="line-25"></a>--

26+<a name="line-26"></a>-- __LAoP__ is a library for algebraic (inductive) construction and manipulation of matrices

27+<a name="line-27"></a>-- in Haskell. See <https://github.com/bolt12/master-thesis my Msc Thesis> for the

28+<a name="line-28"></a>-- motivation behind the library, the underlying theory, and implementation details.

29+<a name="line-29"></a>--

30+<a name="line-30"></a>-- This module offers a newtype wrapper around 'Matrix.Type.Matrix' that

31+<a name="line-31"></a>-- uses arbitrary types instead of canonical data types for the matrices

32+<a name="line-32"></a>-- dimensions.

33+<a name="line-33"></a>--

34+<a name="line-34"></a>-- __NOTE__: If the types in the dimensions are custom they must need to

35+<a name="line-35"></a>-- implement a 'Generic' instance.

36+<a name="line-36"></a>--

37+<a name="line-37"></a>-----------------------------------------------------------------------------

38+<a name="line-38"></a>

39+<a name="line-39"></a>module Matrix.Type

40+<a name="line-40"></a> ( -- | LAoP (Linear Algebra of Programming) Inductive Matrix definition.

41+<a name="line-41"></a> --

42+<a name="line-42"></a> -- LAoP generalises relations and functions treating them as

43+<a name="line-43"></a> -- Boolean matrices and in turn consider these as arrows.

44+<a name="line-44"></a> -- This library offers many of the combinators mentioned in the work of

45+<a name="line-45"></a> -- Macedo (2012) and Oliveira (2012).

46+<a name="line-46"></a> --

47+<a name="line-47"></a> -- This definition is a wrapper around 'Matrix.Type' but

48+<a name="line-48"></a> -- dimensions are arbitrary data types. Type inference might not

49+<a name="line-49"></a> -- be as desired.

50+<a name="line-50"></a>

51+<a name="line-51"></a> -- __NOTE__: If the types in the dimensions are custom they must need to

52+<a name="line-52"></a> -- implement a 'Generic' instance.

53+<a name="line-53"></a> --

54+<a name="line-54"></a>

55+<a name="line-55"></a> -- * Type safe matrix representation

56+<a name="line-56"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> (..),

57+<a name="line-57"></a>

58+<a name="line-58"></a> -- * Type aliases

59+<a name="line-59"></a> <a href="Matrix.Type.html#Zero">Zero</a>,

60+<a name="line-60"></a> <a href="Matrix.Type.html#One">One</a>,

61+<a name="line-61"></a>

62+<a name="line-62"></a> -- * Primitives

63+<a name="line-63"></a> <a href="Matrix.Type.html#empty">empty</a>,

64+<a name="line-64"></a> <a href="Matrix.Type.html#one">one</a>,

65+<a name="line-65"></a> <a href="Matrix.Type.html#junc">junc</a>,

66+<a name="line-66"></a> <a href="Matrix.Type.html#split">split</a>,

67+<a name="line-67"></a>

68+<a name="line-68"></a> -- * Auxiliary type families

69+<a name="line-69"></a> <a href="Matrix.Internal.html#FromNat">I.FromNat</a>,

70+<a name="line-70"></a> <a href="Matrix.Internal.html#Count">I.Count</a>,

71+<a name="line-71"></a> <a href="Matrix.Internal.html#Normalize">I.Normalize</a>,

72+<a name="line-72"></a>

73+<a name="line-73"></a> -- * Matrix construction and conversion

74+<a name="line-74"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a>,

75+<a name="line-75"></a> <a href="Matrix.Type.html#fromLists">fromLists</a>,

76+<a name="line-76"></a> <a href="Matrix.Type.html#toLists">toLists</a>,

77+<a name="line-77"></a> <a href="Matrix.Type.html#toList">toList</a>,

78+<a name="line-78"></a> <a href="Matrix.Type.html#matrixBuilder">matrixBuilder</a>,

79+<a name="line-79"></a> <a href="Matrix.Type.html#row">row</a>,

80+<a name="line-80"></a> <a href="Matrix.Type.html#col">col</a>,

81+<a name="line-81"></a> <a href="Matrix.Type.html#zeros">zeros</a>,

82+<a name="line-82"></a> <a href="Matrix.Type.html#ones">ones</a>,

83+<a name="line-83"></a> <a href="Matrix.Type.html#bang">bang</a>,

84+<a name="line-84"></a> <a href="Matrix.Type.html#constant">constant</a>,

85+<a name="line-85"></a>

86+<a name="line-86"></a> -- * Functor instance equivalent function

87+<a name="line-87"></a> <a href="Matrix.Type.html#fmapM">fmapM</a>,

88+<a name="line-88"></a>

89+<a name="line-89"></a> -- * Applicative/Monoidal instance equivalent functions

90+<a name="line-90"></a> <a href="Matrix.Type.html#unitM">unitM</a>,

91+<a name="line-91"></a> <a href="Matrix.Type.html#multM">multM</a>,

92+<a name="line-92"></a>

93+<a name="line-93"></a> -- * Selective equivalent instance function

94+<a name="line-94"></a> <a href="Matrix.Type.html#selectM">selectM</a>,

95+<a name="line-95"></a>

96+<a name="line-96"></a> -- * Monad equivalent instance function

97+<a name="line-97"></a> <a href="Matrix.Type.html#returnM">returnM</a>,

98+<a name="line-98"></a> <a href="Matrix.Type.html#bindM">bindM</a>,

99+<a name="line-99"></a>

100+<a name="line-100"></a> -- * Misc

101+<a name="line-101"></a> -- ** Get dimensions

102+<a name="line-102"></a> <a href="Matrix.Type.html#columns">columns</a>,

103+<a name="line-103"></a> <a href="Matrix.Type.html#rows">rows</a>,

104+<a name="line-104"></a>

105+<a name="line-105"></a> -- ** Matrix Transposition

106+<a name="line-106"></a> <a href="Matrix.Type.html#tr">tr</a>,

107+<a name="line-107"></a>

108+<a name="line-108"></a> -- ** McCarthy's Conditional

109+<a name="line-109"></a> <a href="Matrix.Type.html#cond">cond</a>,

110+<a name="line-110"></a>

111+<a name="line-111"></a> -- ** Matrix "abiding"

112+<a name="line-112"></a> <a href="Matrix.Type.html#abideJS">abideJS</a>,

113+<a name="line-113"></a> <a href="Matrix.Type.html#abideSJ">abideSJ</a>,

114+<a name="line-114"></a>

115+<a name="line-115"></a> -- * Biproduct approach

116+<a name="line-116"></a> -- ** Split

117+<a name="line-117"></a> (<a href="Matrix.Type.html#%3D%3D%3D">===</a>),

118+<a name="line-118"></a> -- *** Projections

119+<a name="line-119"></a> <a href="Matrix.Type.html#p1">p1</a>,

120+<a name="line-120"></a> <a href="Matrix.Type.html#p2">p2</a>,

121+<a name="line-121"></a> -- ** Junc

122+<a name="line-122"></a> (<a href="Matrix.Type.html#%7C%7C%7C">|||</a>),

123+<a name="line-123"></a> -- *** Injections

124+<a name="line-124"></a> <a href="Matrix.Type.html#i1">i1</a>,

125+<a name="line-125"></a> <a href="Matrix.Type.html#i2">i2</a>,

126+<a name="line-126"></a> -- ** Bifunctors

127+<a name="line-127"></a> (<a href="Matrix.Type.html#-%7C-">-|-</a>),

128+<a name="line-128"></a> (<a href="Matrix.Type.html#%3E%3C">><</a>),

129+<a name="line-129"></a>

130+<a name="line-130"></a> -- ** Applicative matrix combinators

131+<a name="line-131"></a>

132+<a name="line-132"></a> -- | Note that given the restrictions imposed it is not possible to

133+<a name="line-133"></a> -- implement the standard type classes present in standard Haskell.

134+<a name="line-134"></a> -- *** Matrix pairing projections

135+<a name="line-135"></a> <a href="Matrix.Type.html#kp1">kp1</a>,

136+<a name="line-136"></a> <a href="Matrix.Type.html#kp2">kp2</a>,

137+<a name="line-137"></a>

138+<a name="line-138"></a> -- *** Matrix pairing

139+<a name="line-139"></a> <a href="Matrix.Type.html#khatri">khatri</a>,

140+<a name="line-140"></a>

141+<a name="line-141"></a> -- * Matrix composition and lifting

142+<a name="line-142"></a>

143+<a name="line-143"></a> -- ** Arrow matrix combinators

144+<a name="line-144"></a>

145+<a name="line-145"></a> -- | Note that given the restrictions imposed it is not possible to

146+<a name="line-146"></a> -- implement the standard type classes present in standard Haskell.

147+<a name="line-147"></a> <a href="Matrix.Type.html#identity">identity</a>,

148+<a name="line-148"></a> <a href="Matrix.Type.html#comp">comp</a>,

149+<a name="line-149"></a> <a href="Matrix.Type.html#fromF">fromF</a>,

150+<a name="line-150"></a> <a href="Matrix.Type.html#fromF%27">fromF'</a>,

151+<a name="line-151"></a>

152+<a name="line-152"></a> -- * Matrix printing

153+<a name="line-153"></a> <a href="Matrix.Type.html#pretty">pretty</a>,

154+<a name="line-154"></a> <a href="Matrix.Type.html#prettyPrint">prettyPrint</a>

155+<a name="line-155"></a> )

156+<a name="line-156"></a>where

157+<a name="line-157"></a>

158+<a name="line-158"></a>import Data.Void

159+<a name="line-159"></a>import Data.Proxy

160+<a name="line-160"></a>import Data.Kind

161+<a name="line-161"></a>import GHC.TypeLits

162+<a name="line-162"></a>import Control.DeepSeq

163+<a name="line-163"></a>import qualified Control.Category as C

164+<a name="line-164"></a>import qualified <a href="Matrix.Internal.html">Matrix.Internal</a> as I

165+<a name="line-165"></a>

166+<a name="line-166"></a>newtype <a name="Matrix"><a href="Matrix.Type.html#Matrix">Matrix</a></a> <a name="local-6989586621679046459"><a href="#local-6989586621679046459">e</a></a> (<a name="local-6989586621679046460"><a href="#local-6989586621679046460">cols</a></a> :: Type) (<a name="local-6989586621679046461"><a href="#local-6989586621679046461">rows</a></a> :: Type) = <a name="M"><a href="Matrix.Type.html#M">M</a></a> (<a href="Matrix.Internal.html#Matrix">I.Matrix</a> <a href="#local-6989586621679046459">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046460">cols</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046461">rows</a>))

167+<a name="line-167"></a> deriving (Show, Num, Eq, Ord, NFData) via (<a href="Matrix.Internal.html#Matrix">I.Matrix</a> <a href="#local-6989586621679046459">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046460">cols</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046461">rows</a>))

168+<a name="line-168"></a>

169+<a name="line-169"></a>-- | It isn't possible to implement the 'id' function so it's

170+<a name="line-170"></a>-- implementation is 'undefined'. However 'comp' can be and this partial

171+<a name="line-171"></a>-- class implementation exists just to make the code more readable.

172+<a name="line-172"></a>--

173+<a name="line-173"></a>-- Please use 'identity' instead.

174+<a name="line-174"></a>instance (Num <a href="#local-6989586621679046462">e</a>) => C.Category (<a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046462">e</a>) where

175+<a name="line-175"></a> <a name="local-8214565720323789508">id</a> = undefined

176+<a name="line-176"></a> (<a name="local-8214565720323789507">.</a>) = <a href="Matrix.Type.html#comp">comp</a>

177+<a name="line-177"></a>

178+<a name="line-178"></a>-- | Zero type alias

179+<a name="line-179"></a>type <a name="Zero"><a href="Matrix.Type.html#Zero">Zero</a></a> = Void

180+<a name="line-180"></a>

181+<a name="line-181"></a>-- | One type alias

182+<a name="line-182"></a>type <a name="One"><a href="Matrix.Type.html#One">One</a></a> = ()

183+<a name="line-183"></a>

184+<a name="line-184"></a>-- Primitives

185+<a name="line-185"></a>

186+<a name="line-186"></a>-- | Empty matrix constructor

187+<a name="line-187"></a>empty :: <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046596">e</a> <a href="Matrix.Type.html#Zero">Zero</a> <a href="Matrix.Type.html#Zero">Zero</a>

188+<a name="line-188"></a><a name="empty"><a href="Matrix.Type.html#empty">empty</a></a> = <a href="Matrix.Type.html#M">M</a> <a href="Matrix.Internal.html#Empty">I.Empty</a>

189+<a name="line-189"></a>

190+<a name="line-190"></a>-- | Unit matrix constructor

191+<a name="line-191"></a>one :: <a href="#local-6989586621679046595">e</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046595">e</a> <a href="Matrix.Type.html#One">One</a> <a href="Matrix.Type.html#One">One</a>

192+<a name="line-192"></a><a name="one"><a href="Matrix.Type.html#one">one</a></a> = <a href="Matrix.Type.html#M">M</a> . <a href="Matrix.Internal.html#One">I.One</a>

193+<a name="line-193"></a>

194+<a name="line-194"></a>-- | Matrix 'Junc' constructor

195+<a name="line-195"></a>junc ::

196+<a name="line-196"></a> (I.Normalize (Either <a href="#local-6989586621679046591">a</a> <a href="#local-6989586621679046592">b</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046591">a</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046592">b</a>)) =>

197+<a name="line-197"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046593">e</a> <a href="#local-6989586621679046591">a</a> <a href="#local-6989586621679046594">rows</a> ->

198+<a name="line-198"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046593">e</a> <a href="#local-6989586621679046592">b</a> <a href="#local-6989586621679046594">rows</a> ->

199+<a name="line-199"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046593">e</a> (Either <a href="#local-6989586621679046591">a</a> <a href="#local-6989586621679046592">b</a>) <a href="#local-6989586621679046594">rows</a>

200+<a name="line-200"></a><a name="junc"><a href="Matrix.Type.html#junc">junc</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046597"><a href="#local-6989586621679046597">a</a></a>) (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046598"><a href="#local-6989586621679046598">b</a></a>) = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#Junc">I.Junc</a> <a href="#local-6989586621679046597">a</a> <a href="#local-6989586621679046598">b</a>)

201+<a name="line-201"></a>

202+<a name="line-202"></a>infixl 3 <a href="Matrix.Type.html#%7C%7C%7C">|||</a>

203+<a name="line-203"></a>-- | Matrix 'Junc' constructor

204+<a name="line-204"></a>(|||) ::

205+<a name="line-205"></a> (I.Normalize (Either <a href="#local-6989586621679046587">a</a> <a href="#local-6989586621679046588">b</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046587">a</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046588">b</a>)) =>

206+<a name="line-206"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046589">e</a> <a href="#local-6989586621679046587">a</a> <a href="#local-6989586621679046590">rows</a> ->

207+<a name="line-207"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046589">e</a> <a href="#local-6989586621679046588">b</a> <a href="#local-6989586621679046590">rows</a> ->

208+<a name="line-208"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046589">e</a> (Either <a href="#local-6989586621679046587">a</a> <a href="#local-6989586621679046588">b</a>) <a href="#local-6989586621679046590">rows</a>

209+<a name="line-209"></a>(<a name="%7C%7C%7C"><a href="Matrix.Type.html#%7C%7C%7C">|||</a></a>) = <a href="Matrix.Type.html#junc">junc</a>

210+<a name="line-210"></a>

211+<a name="line-211"></a>-- | Matrix 'Split' constructor

212+<a name="line-212"></a>split ::

213+<a name="line-213"></a> (I.Normalize (Either <a href="#local-6989586621679046583">a</a> <a href="#local-6989586621679046584">b</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046583">a</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046584">b</a>)) =>

214+<a name="line-214"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046585">e</a> <a href="#local-6989586621679046586">cols</a> <a href="#local-6989586621679046583">a</a> ->

215+<a name="line-215"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046585">e</a> <a href="#local-6989586621679046586">cols</a> <a href="#local-6989586621679046584">b</a> ->

216+<a name="line-216"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046585">e</a> <a href="#local-6989586621679046586">cols</a> (Either <a href="#local-6989586621679046583">a</a> <a href="#local-6989586621679046584">b</a>)

217+<a name="line-217"></a><a name="split"><a href="Matrix.Type.html#split">split</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046599"><a href="#local-6989586621679046599">a</a></a>) (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046600"><a href="#local-6989586621679046600">b</a></a>) = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#Split">I.Split</a> <a href="#local-6989586621679046599">a</a> <a href="#local-6989586621679046600">b</a>)

218+<a name="line-218"></a>

219+<a name="line-219"></a>infixl 2 <a href="Matrix.Type.html#%3D%3D%3D">===</a>

220+<a name="line-220"></a>-- | Matrix 'Split' constructor

221+<a name="line-221"></a>(===) ::

222+<a name="line-222"></a> (I.Normalize (Either <a href="#local-6989586621679046579">a</a> <a href="#local-6989586621679046580">b</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046579">a</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046580">b</a>)) =>

223+<a name="line-223"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046581">e</a> <a href="#local-6989586621679046582">cols</a> <a href="#local-6989586621679046579">a</a> ->

224+<a name="line-224"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046581">e</a> <a href="#local-6989586621679046582">cols</a> <a href="#local-6989586621679046580">b</a> ->

225+<a name="line-225"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046581">e</a> <a href="#local-6989586621679046582">cols</a> (Either <a href="#local-6989586621679046579">a</a> <a href="#local-6989586621679046580">b</a>)

226+<a name="line-226"></a>(<a name="%3D%3D%3D"><a href="Matrix.Type.html#%3D%3D%3D">===</a></a>) = <a href="Matrix.Type.html#split">split</a>

227+<a name="line-227"></a>

228+<a name="line-228"></a>-- Functor hierarchy

229+<a name="line-229"></a>

230+<a name="line-230"></a>-- | Functor instance equivalent function

231+<a name="line-231"></a>fmapM ::

232+<a name="line-232"></a> ( Bounded <a href="#local-6989586621679046575">a</a>,

233+<a name="line-233"></a> Bounded <a href="#local-6989586621679046576">b</a>,

234+<a name="line-234"></a> Enum <a href="#local-6989586621679046575">a</a>,

235+<a name="line-235"></a> Enum <a href="#local-6989586621679046576">b</a>,

236+<a name="line-236"></a> Eq <a href="#local-6989586621679046576">b</a>,

237+<a name="line-237"></a> Num <a href="#local-6989586621679046577">e</a>,

238+<a name="line-238"></a> Ord <a href="#local-6989586621679046577">e</a>,

239+<a name="line-239"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046575">a</a>)),

240+<a name="line-240"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046576">b</a>)),

241+<a name="line-241"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046577">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046576">b</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046575">a</a>)

242+<a name="line-242"></a> )

243+<a name="line-243"></a> =>

244+<a name="line-244"></a> (<a href="#local-6989586621679046575">a</a> -> <a href="#local-6989586621679046576">b</a>) -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046577">e</a> <a href="#local-6989586621679046578">c</a> <a href="#local-6989586621679046575">a</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046577">e</a> <a href="#local-6989586621679046578">c</a> <a href="#local-6989586621679046576">b</a>

245+<a name="line-245"></a><a name="fmapM"><a href="Matrix.Type.html#fmapM">fmapM</a></a> <a name="local-6989586621679046601"><a href="#local-6989586621679046601">f</a></a> <a name="local-6989586621679046602"><a href="#local-6989586621679046602">m</a></a> = <a href="Matrix.Type.html#fromF%27">fromF'</a> <a href="#local-6989586621679046601">f</a> `<a href="Matrix.Type.html#comp">comp</a>` <a href="#local-6989586621679046602">m</a>

246+<a name="line-246"></a>

247+<a name="line-247"></a>-- | Applicative instance equivalent 'unit' function,

248+<a name="line-248"></a>unitM :: (Num <a href="#local-6989586621679046574">e</a>) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046574">e</a> () ()

249+<a name="line-249"></a><a name="unitM"><a href="Matrix.Type.html#unitM">unitM</a></a> = <a href="Matrix.Type.html#one">one</a> 1

250+<a name="line-250"></a>

251+<a name="line-251"></a>-- | Applicative instance equivalent 'unit' function,

252+<a name="line-252"></a>multM ::

253+<a name="line-253"></a> ( KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046570">a</a>)),

254+<a name="line-254"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046571">b</a>)),

255+<a name="line-255"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046570">a</a>, <a href="#local-6989586621679046571">b</a>))),

256+<a name="line-256"></a> Num <a href="#local-6989586621679046572">e</a>,

257+<a name="line-257"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046572">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046570">a</a>, <a href="#local-6989586621679046571">b</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046570">a</a>),

258+<a name="line-258"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046572">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046570">a</a>, <a href="#local-6989586621679046571">b</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046571">b</a>),

259+<a name="line-259"></a> I.Normalize (<a href="#local-6989586621679046570">a</a>, <a href="#local-6989586621679046571">b</a>) ~ <a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046570">a</a>, <a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046571">b</a>)

260+<a name="line-260"></a> ) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046572">e</a> <a href="#local-6989586621679046573">c</a> <a href="#local-6989586621679046570">a</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046572">e</a> <a href="#local-6989586621679046573">c</a> <a href="#local-6989586621679046571">b</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046572">e</a> <a href="#local-6989586621679046573">c</a> (<a href="#local-6989586621679046570">a</a>, <a href="#local-6989586621679046571">b</a>)

261+<a name="line-261"></a><a name="multM"><a href="Matrix.Type.html#multM">multM</a></a> <a name="local-6989586621679046603"><a href="#local-6989586621679046603">a</a></a> <a name="local-6989586621679046604"><a href="#local-6989586621679046604">b</a></a> = <a href="Matrix.Type.html#khatri">khatri</a> <a href="#local-6989586621679046603">a</a> <a href="#local-6989586621679046604">b</a>

262+<a name="line-262"></a>

263+<a name="line-263"></a>

264+<a name="line-264"></a>-- | Monad instance equivalent 'return' function,

265+<a name="line-265"></a>returnM ::

266+<a name="line-266"></a> forall <a name="local-6989586621679046568"><a href="#local-6989586621679046568">e</a></a> <a name="local-6989586621679046569"><a href="#local-6989586621679046569">a</a></a> .

267+<a name="line-267"></a> ( Num <a href="#local-6989586621679046568">e</a>,

268+<a name="line-268"></a> Enum <a href="#local-6989586621679046568">e</a>,

269+<a name="line-269"></a> Enum <a href="#local-6989586621679046569">a</a>,

270+<a name="line-270"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046568">e</a> () (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046569">a</a>),

271+<a name="line-271"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> <a href="#local-6989586621679046569">a</a>)

272+<a name="line-272"></a> ) => <a href="#local-6989586621679046569">a</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046568">e</a> <a href="Matrix.Type.html#One">One</a> <a href="#local-6989586621679046569">a</a>

273+<a name="line-273"></a><a name="returnM"><a href="Matrix.Type.html#returnM">returnM</a></a> <a name="local-6989586621679046605"><a href="#local-6989586621679046605">a</a></a> = <a href="Matrix.Type.html#col">col</a> <a href="#local-6989586621679046608">l</a>

274+<a name="line-274"></a> where

275+<a name="line-275"></a> <a name="local-6989586621679046606"><a href="#local-6989586621679046606">i</a></a> = fromInteger $ natVal (Proxy :: Proxy (<a href="Matrix.Internal.html#Count">I.Count</a> <a href="#local-6989586621679046569">a</a>))

276+<a name="line-276"></a> <a name="local-6989586621679046607"><a href="#local-6989586621679046607">x</a></a> = fromEnum <a href="#local-6989586621679046605">a</a>

277+<a name="line-277"></a> <a name="local-6989586621679046608"><a href="#local-6989586621679046608">l</a></a> = take <a href="#local-6989586621679046607">x</a> [0,0..] ++ [1] ++ take (<a href="#local-6989586621679046606">i</a> - <a href="#local-6989586621679046607">x</a> - 1) [0,0..]

278+<a name="line-278"></a>

279+<a name="line-279"></a>-- | Monad instance equivalent '(>>=)' function,

280+<a name="line-280"></a>bindM :: (Num <a href="#local-6989586621679046564">e</a>) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046564">e</a> <a href="#local-6989586621679046565">a</a> <a href="#local-6989586621679046566">b</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046564">e</a> <a href="#local-6989586621679046566">b</a> <a href="#local-6989586621679046567">c</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046564">e</a> <a href="#local-6989586621679046565">a</a> <a href="#local-6989586621679046567">c</a>

281+<a name="line-281"></a><a name="bindM"><a href="Matrix.Type.html#bindM">bindM</a></a> = flip <a href="Matrix.Type.html#comp">comp</a>

282+<a name="line-282"></a>

283+<a name="line-283"></a>-- Construction

284+<a name="line-284"></a>

285+<a name="line-285"></a>-- | Build a matrix out of a list of list of elements. Throws a runtime

286+<a name="line-286"></a>-- error if the dimensions do not match.

287+<a name="line-287"></a>fromLists :: (<a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046561">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046562">cols</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046563">rows</a>)) => [[<a href="#local-6989586621679046561">e</a>]] -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046561">e</a> <a href="#local-6989586621679046562">cols</a> <a href="#local-6989586621679046563">rows</a>

288+<a name="line-288"></a><a name="fromLists"><a href="Matrix.Type.html#fromLists">fromLists</a></a> = <a href="Matrix.Type.html#M">M</a> . <a href="Matrix.Internal.html#fromLists">I.fromLists</a>

289+<a name="line-289"></a>

290+<a name="line-290"></a>-- | Matrix builder function. Constructs a matrix provided with

291+<a name="line-291"></a>-- a construction function.

292+<a name="line-292"></a>matrixBuilder ::

293+<a name="line-293"></a> (<a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046558">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046559">cols</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046560">rows</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046559">cols</a>)), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046560">rows</a>))) =>

294+<a name="line-294"></a> ((Int, Int) -> <a href="#local-6989586621679046558">e</a>) ->

295+<a name="line-295"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046558">e</a> <a href="#local-6989586621679046559">cols</a> <a href="#local-6989586621679046560">rows</a>

296+<a name="line-296"></a><a name="matrixBuilder"><a href="Matrix.Type.html#matrixBuilder">matrixBuilder</a></a> = <a href="Matrix.Type.html#M">M</a> . <a href="Matrix.Internal.html#matrixBuilder">I.matrixBuilder</a>

297+<a name="line-297"></a>

298+<a name="line-298"></a>-- | Constructs a column vector matrix

299+<a name="line-299"></a>col :: (<a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046556">e</a> () (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046557">rows</a>)) => [<a href="#local-6989586621679046556">e</a>] -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046556">e</a> <a href="Matrix.Type.html#One">One</a> <a href="#local-6989586621679046557">rows</a>

300+<a name="line-300"></a><a name="col"><a href="Matrix.Type.html#col">col</a></a> = <a href="Matrix.Type.html#M">M</a> . <a href="Matrix.Internal.html#col">I.col</a>

301+<a name="line-301"></a>

302+<a name="line-302"></a>-- | Constructs a row vector matrix

303+<a name="line-303"></a>row :: (<a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046554">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046555">cols</a>) ()) => [<a href="#local-6989586621679046554">e</a>] -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046554">e</a> <a href="#local-6989586621679046555">cols</a> <a href="Matrix.Type.html#One">One</a>

304+<a name="line-304"></a><a name="row"><a href="Matrix.Type.html#row">row</a></a> = <a href="Matrix.Type.html#M">M</a> . <a href="Matrix.Internal.html#row">I.row</a>

305+<a name="line-305"></a>

306+<a name="line-306"></a>-- | Lifts functions to matrices with arbitrary dimensions.

307+<a name="line-307"></a>--

308+<a name="line-308"></a>-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of

309+<a name="line-309"></a>-- types @a@ or @b@ allows.

310+<a name="line-310"></a>fromF ::

311+<a name="line-311"></a> ( Bounded <a href="#local-6989586621679046549">a</a>,

312+<a name="line-312"></a> Bounded <a href="#local-6989586621679046550">b</a>,

313+<a name="line-313"></a> Enum <a href="#local-6989586621679046549">a</a>,

314+<a name="line-314"></a> Enum <a href="#local-6989586621679046550">b</a>,

315+<a name="line-315"></a> Eq <a href="#local-6989586621679046550">b</a>,

316+<a name="line-316"></a> Num <a href="#local-6989586621679046551">e</a>,

317+<a name="line-317"></a> Ord <a href="#local-6989586621679046551">e</a>,

318+<a name="line-318"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046552">cols</a>)),

319+<a name="line-319"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046553">rows</a>)),

320+<a name="line-320"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046551">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046553">rows</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046552">cols</a>)

321+<a name="line-321"></a> ) =>

322+<a name="line-322"></a> (<a href="#local-6989586621679046549">a</a> -> <a href="#local-6989586621679046550">b</a>) ->

323+<a name="line-323"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046551">e</a> <a href="#local-6989586621679046552">cols</a> <a href="#local-6989586621679046553">rows</a>

324+<a name="line-324"></a><a name="fromF"><a href="Matrix.Type.html#fromF">fromF</a></a> = <a href="Matrix.Type.html#M">M</a> . <a href="Matrix.Internal.html#fromF">I.fromF</a>

325+<a name="line-325"></a>

326+<a name="line-326"></a>-- | Lifts functions to matrices with dimensions matching @a@ and @b@

327+<a name="line-327"></a>-- cardinality's.

328+<a name="line-328"></a>fromF' ::

329+<a name="line-329"></a> ( Bounded <a href="#local-6989586621679046546">a</a>,

330+<a name="line-330"></a> Bounded <a href="#local-6989586621679046547">b</a>,

331+<a name="line-331"></a> Enum <a href="#local-6989586621679046546">a</a>,

332+<a name="line-332"></a> Enum <a href="#local-6989586621679046547">b</a>,

333+<a name="line-333"></a> Eq <a href="#local-6989586621679046547">b</a>,

334+<a name="line-334"></a> Num <a href="#local-6989586621679046548">e</a>,

335+<a name="line-335"></a> Ord <a href="#local-6989586621679046548">e</a>,

336+<a name="line-336"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046546">a</a>)),

337+<a name="line-337"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046547">b</a>)),

338+<a name="line-338"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046548">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046547">b</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046546">a</a>)

339+<a name="line-339"></a> ) =>

340+<a name="line-340"></a> (<a href="#local-6989586621679046546">a</a> -> <a href="#local-6989586621679046547">b</a>) ->

341+<a name="line-341"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046548">e</a> <a href="#local-6989586621679046546">a</a> <a href="#local-6989586621679046547">b</a>

342+<a name="line-342"></a><a name="fromF%27"><a href="Matrix.Type.html#fromF%27">fromF'</a></a> = <a href="Matrix.Type.html#M">M</a> . <a href="Matrix.Internal.html#fromF%27">I.fromF'</a>

343+<a name="line-343"></a>

344+<a name="line-344"></a>-- Conversion

345+<a name="line-345"></a>

346+<a name="line-346"></a>-- | Converts a matrix to a list of lists of elements.

347+<a name="line-347"></a>toLists :: <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046543">e</a> <a href="#local-6989586621679046544">cols</a> <a href="#local-6989586621679046545">rows</a> -> [[<a href="#local-6989586621679046543">e</a>]]

348+<a name="line-348"></a><a name="toLists"><a href="Matrix.Type.html#toLists">toLists</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046609"><a href="#local-6989586621679046609">m</a></a>) = <a href="Matrix.Internal.html#toLists">I.toLists</a> <a href="#local-6989586621679046609">m</a>

349+<a name="line-349"></a>

350+<a name="line-350"></a>-- | Converts a matrix to a list of elements.

351+<a name="line-351"></a>toList :: <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046540">e</a> <a href="#local-6989586621679046541">cols</a> <a href="#local-6989586621679046542">rows</a> -> [<a href="#local-6989586621679046540">e</a>]

352+<a name="line-352"></a><a name="toList"><a href="Matrix.Type.html#toList">toList</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046610"><a href="#local-6989586621679046610">m</a></a>) = <a href="Matrix.Internal.html#toList">I.toList</a> <a href="#local-6989586621679046610">m</a>

353+<a name="line-353"></a>

354+<a name="line-354"></a>-- Zeros Matrix

355+<a name="line-355"></a>

356+<a name="line-356"></a>-- | The zero matrix. A matrix wholly filled with zeros.

357+<a name="line-357"></a>zeros ::

358+<a name="line-358"></a> (Num <a href="#local-6989586621679046537">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046537">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046538">cols</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046539">rows</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046538">cols</a>)), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046539">rows</a>))) =>

359+<a name="line-359"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046537">e</a> <a href="#local-6989586621679046538">cols</a> <a href="#local-6989586621679046539">rows</a>

360+<a name="line-360"></a><a name="zeros"><a href="Matrix.Type.html#zeros">zeros</a></a> = <a href="Matrix.Type.html#M">M</a> <a href="Matrix.Internal.html#zeros">I.zeros</a>

361+<a name="line-361"></a>

362+<a name="line-362"></a>-- Ones Matrix

363+<a name="line-363"></a>

364+<a name="line-364"></a>-- | The ones matrix. A matrix wholly filled with ones.

365+<a name="line-365"></a>--

366+<a name="line-366"></a>-- Also known as T (Top) matrix.

367+<a name="line-367"></a>ones ::

368+<a name="line-368"></a> (Num <a href="#local-6989586621679046534">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046534">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046535">cols</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046536">rows</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046535">cols</a>)), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046536">rows</a>))) =>

369+<a name="line-369"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046534">e</a> <a href="#local-6989586621679046535">cols</a> <a href="#local-6989586621679046536">rows</a>

370+<a name="line-370"></a><a name="ones"><a href="Matrix.Type.html#ones">ones</a></a> = <a href="Matrix.Type.html#M">M</a> <a href="Matrix.Internal.html#ones">I.ones</a>

371+<a name="line-371"></a>

372+<a name="line-372"></a>-- Const Matrix

373+<a name="line-373"></a>

374+<a name="line-374"></a>-- | The constant matrix constructor. A matrix wholly filled with a given

375+<a name="line-375"></a>-- value.

376+<a name="line-376"></a>constant ::

377+<a name="line-377"></a> (Num <a href="#local-6989586621679046531">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046531">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046532">cols</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046533">rows</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046532">cols</a>)), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046533">rows</a>))) =>

378+<a name="line-378"></a> <a href="#local-6989586621679046531">e</a> ->

379+<a name="line-379"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046531">e</a> <a href="#local-6989586621679046532">cols</a> <a href="#local-6989586621679046533">rows</a>

380+<a name="line-380"></a><a name="constant"><a href="Matrix.Type.html#constant">constant</a></a> = <a href="Matrix.Type.html#M">M</a> . <a href="Matrix.Internal.html#constant">I.constant</a>

381+<a name="line-381"></a>

382+<a name="line-382"></a>-- Bang Matrix

383+<a name="line-383"></a>

384+<a name="line-384"></a>-- | The T (Top) row vector matrix.

385+<a name="line-385"></a>bang ::

386+<a name="line-386"></a> forall <a name="local-6989586621679046529"><a href="#local-6989586621679046529">e</a></a> <a name="local-6989586621679046530"><a href="#local-6989586621679046530">cols</a></a>.

387+<a name="line-387"></a> (Num <a href="#local-6989586621679046529">e</a>, Enum <a href="#local-6989586621679046529">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046529">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046530">cols</a>) (), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046530">cols</a>))) =>

388+<a name="line-388"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046529">e</a> <a href="#local-6989586621679046530">cols</a> <a href="Matrix.Type.html#One">One</a>

389+<a name="line-389"></a><a name="bang"><a href="Matrix.Type.html#bang">bang</a></a> = <a href="Matrix.Type.html#M">M</a> <a href="Matrix.Internal.html#bang">I.bang</a>

390+<a name="line-390"></a>

391+<a name="line-391"></a>-- Identity Matrix

392+<a name="line-392"></a>

393+<a name="line-393"></a>-- | Identity matrix

394+<a name="line-394"></a>identity ::

395+<a name="line-395"></a> (Num <a href="#local-6989586621679046527">e</a>, <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046527">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046528">a</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046528">a</a>), KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046528">a</a>))) =>

396+<a name="line-396"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046527">e</a> <a href="#local-6989586621679046528">a</a> <a href="#local-6989586621679046528">a</a>

397+<a name="line-397"></a><a name="identity"><a href="Matrix.Type.html#identity">identity</a></a> = <a href="Matrix.Type.html#M">M</a> <a href="Matrix.Internal.html#identity">I.identity</a>

398+<a name="line-398"></a>

399+<a name="line-399"></a>-- Matrix composition (MMM)

400+<a name="line-400"></a>

401+<a name="line-401"></a>-- | Matrix composition. Equivalent to matrix-matrix multiplication.

402+<a name="line-402"></a>--

403+<a name="line-403"></a>-- This definition takes advantage of divide-and-conquer and fusion laws

404+<a name="line-404"></a>-- from LAoP.

405+<a name="line-405"></a>comp :: (Num <a href="#local-6989586621679046523">e</a>) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046523">e</a> <a href="#local-6989586621679046524">cr</a> <a href="#local-6989586621679046525">rows</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046523">e</a> <a href="#local-6989586621679046526">cols</a> <a href="#local-6989586621679046524">cr</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046523">e</a> <a href="#local-6989586621679046526">cols</a> <a href="#local-6989586621679046525">rows</a>

406+<a name="line-406"></a><a name="comp"><a href="Matrix.Type.html#comp">comp</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046611"><a href="#local-6989586621679046611">a</a></a>) (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046612"><a href="#local-6989586621679046612">b</a></a>) = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#comp">I.comp</a> <a href="#local-6989586621679046611">a</a> <a href="#local-6989586621679046612">b</a>)

407+<a name="line-407"></a>

408+<a name="line-408"></a>-- | Biproduct first component projection

409+<a name="line-409"></a>p1 ::

410+<a name="line-410"></a> ( Num <a href="#local-6989586621679046520">e</a>,

411+<a name="line-411"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046521">n</a>)),

412+<a name="line-412"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046522">m</a>)),

413+<a name="line-413"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046520">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046521">n</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046522">m</a>),

414+<a name="line-414"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046520">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046522">m</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046522">m</a>),

415+<a name="line-415"></a> I.Normalize (Either <a href="#local-6989586621679046522">m</a> <a href="#local-6989586621679046521">n</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046522">m</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046521">n</a>)

416+<a name="line-416"></a> ) =>

417+<a name="line-417"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046520">e</a> (Either <a href="#local-6989586621679046522">m</a> <a href="#local-6989586621679046521">n</a>) <a href="#local-6989586621679046522">m</a>

418+<a name="line-418"></a><a name="p1"><a href="Matrix.Type.html#p1">p1</a></a> = <a href="Matrix.Type.html#M">M</a> <a href="Matrix.Internal.html#p1">I.p1</a>

419+<a name="line-419"></a>

420+<a name="line-420"></a>-- | Biproduct second component projection

421+<a name="line-421"></a>p2 ::

422+<a name="line-422"></a> ( Num <a href="#local-6989586621679046517">e</a>,

423+<a name="line-423"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046518">n</a>)),

424+<a name="line-424"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046519">m</a>)),

425+<a name="line-425"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046517">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046519">m</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046518">n</a>),

426+<a name="line-426"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046517">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046518">n</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046518">n</a>),

427+<a name="line-427"></a> I.Normalize (Either <a href="#local-6989586621679046519">m</a> <a href="#local-6989586621679046518">n</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046519">m</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046518">n</a>)

428+<a name="line-428"></a> ) =>

429+<a name="line-429"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046517">e</a> (Either <a href="#local-6989586621679046519">m</a> <a href="#local-6989586621679046518">n</a>) <a href="#local-6989586621679046518">n</a>

430+<a name="line-430"></a><a name="p2"><a href="Matrix.Type.html#p2">p2</a></a> = <a href="Matrix.Type.html#M">M</a> <a href="Matrix.Internal.html#p2">I.p2</a>

431+<a name="line-431"></a>

432+<a name="line-432"></a>-- Injections

433+<a name="line-433"></a>

434+<a name="line-434"></a>-- | Biproduct first component injection

435+<a name="line-435"></a>i1 ::

436+<a name="line-436"></a> ( Num <a href="#local-6989586621679046514">e</a>,

437+<a name="line-437"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046515">n</a>)),

438+<a name="line-438"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046516">m</a>)),

439+<a name="line-439"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046514">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046515">n</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046516">m</a>),

440+<a name="line-440"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046514">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046516">m</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046516">m</a>),

441+<a name="line-441"></a> I.Normalize (Either <a href="#local-6989586621679046516">m</a> <a href="#local-6989586621679046515">n</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046516">m</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046515">n</a>)

442+<a name="line-442"></a> ) =>

443+<a name="line-443"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046514">e</a> <a href="#local-6989586621679046516">m</a> (Either <a href="#local-6989586621679046516">m</a> <a href="#local-6989586621679046515">n</a>)

444+<a name="line-444"></a><a name="i1"><a href="Matrix.Type.html#i1">i1</a></a> = <a href="Matrix.Type.html#tr">tr</a> <a href="Matrix.Type.html#p1">p1</a>

445+<a name="line-445"></a>

446+<a name="line-446"></a>-- | Biproduct second component injection

447+<a name="line-447"></a>i2 ::

448+<a name="line-448"></a> ( Num <a href="#local-6989586621679046511">e</a>,

449+<a name="line-449"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046512">n</a>)),

450+<a name="line-450"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046513">m</a>)),

451+<a name="line-451"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046511">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046513">m</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046512">n</a>),

452+<a name="line-452"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046511">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046512">n</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046512">n</a>),

453+<a name="line-453"></a> I.Normalize (Either <a href="#local-6989586621679046513">m</a> <a href="#local-6989586621679046512">n</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046513">m</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046512">n</a>)

454+<a name="line-454"></a> ) =>

455+<a name="line-455"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046511">e</a> <a href="#local-6989586621679046512">n</a> (Either <a href="#local-6989586621679046513">m</a> <a href="#local-6989586621679046512">n</a>)

456+<a name="line-456"></a><a name="i2"><a href="Matrix.Type.html#i2">i2</a></a> = <a href="Matrix.Type.html#tr">tr</a> <a href="Matrix.Type.html#p2">p2</a>

457+<a name="line-457"></a>

458+<a name="line-458"></a>-- Dimensions

459+<a name="line-459"></a>

460+<a name="line-460"></a>-- | Obtain the number of rows.

461+<a name="line-461"></a>--

462+<a name="line-462"></a>-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

463+<a name="line-463"></a>-- dimensions in constant time.

464+<a name="line-464"></a>--

465+<a name="line-465"></a>-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in

466+<a name="line-466"></a>-- exchange for performance.

467+<a name="line-467"></a>rows :: (KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046508">rows</a>))) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046509">e</a> <a href="#local-6989586621679046510">cols</a> <a href="#local-6989586621679046508">rows</a> -> Int

468+<a name="line-468"></a><a name="rows"><a href="Matrix.Type.html#rows">rows</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046613"><a href="#local-6989586621679046613">m</a></a>) = <a href="Matrix.Internal.html#rows">I.rows</a> <a href="#local-6989586621679046613">m</a>

469+<a name="line-469"></a>

470+<a name="line-470"></a>-- | Obtain the number of columns.

471+<a name="line-471"></a>--

472+<a name="line-472"></a>-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

473+<a name="line-473"></a>-- dimensions in constant time.

474+<a name="line-474"></a>--

475+<a name="line-475"></a>-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in

476+<a name="line-476"></a>-- exchange for performance.

477+<a name="line-477"></a>columns :: (KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046505">cols</a>))) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046506">e</a> <a href="#local-6989586621679046505">cols</a> <a href="#local-6989586621679046507">rows</a> -> Int

478+<a name="line-478"></a><a name="columns"><a href="Matrix.Type.html#columns">columns</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046614"><a href="#local-6989586621679046614">m</a></a>) = <a href="Matrix.Internal.html#columns">I.columns</a> <a href="#local-6989586621679046614">m</a>

479+<a name="line-479"></a>

480+<a name="line-480"></a>-- Coproduct Bifunctor

481+<a name="line-481"></a>

482+<a name="line-482"></a>infixl 5 <a href="Matrix.Type.html#-%7C-">-|-</a>

483+<a name="line-483"></a>

484+<a name="line-484"></a>-- | Matrix coproduct functor also known as matrix direct sum.

485+<a name="line-485"></a>(-|-) ::

486+<a name="line-486"></a> ( Num <a href="#local-6989586621679046500">e</a>,

487+<a name="line-487"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046501">j</a>)),

488+<a name="line-488"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046502">k</a>)),

489+<a name="line-489"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046500">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046502">k</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046502">k</a>),

490+<a name="line-490"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046500">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046501">j</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046502">k</a>),

491+<a name="line-491"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046500">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046502">k</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046501">j</a>),

492+<a name="line-492"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046500">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046501">j</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046501">j</a>),

493+<a name="line-493"></a> I.Normalize (Either <a href="#local-6989586621679046503">n</a> <a href="#local-6989586621679046504">m</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046503">n</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046504">m</a>),

494+<a name="line-494"></a> I.Normalize (Either <a href="#local-6989586621679046502">k</a> <a href="#local-6989586621679046501">j</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046502">k</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046501">j</a>)

495+<a name="line-495"></a> ) =>

496+<a name="line-496"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046500">e</a> <a href="#local-6989586621679046503">n</a> <a href="#local-6989586621679046502">k</a> ->

497+<a name="line-497"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046500">e</a> <a href="#local-6989586621679046504">m</a> <a href="#local-6989586621679046501">j</a> ->

498+<a name="line-498"></a> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046500">e</a> (Either <a href="#local-6989586621679046503">n</a> <a href="#local-6989586621679046504">m</a>) (Either <a href="#local-6989586621679046502">k</a> <a href="#local-6989586621679046501">j</a>)

499+<a name="line-499"></a>(<a name="-%7C-"><a href="Matrix.Type.html#-%7C-">-|-</a></a>) (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046615"><a href="#local-6989586621679046615">a</a></a>) (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046616"><a href="#local-6989586621679046616">b</a></a>) = <a href="Matrix.Type.html#M">M</a> ((<a href="Matrix.Internal.html#-%7C-">I.-|-</a>) <a href="#local-6989586621679046615">a</a> <a href="#local-6989586621679046616">b</a>)

500+<a name="line-500"></a>

501+<a name="line-501"></a>-- Khatri Rao Product and projections

502+<a name="line-502"></a>

503+<a name="line-503"></a>-- | Khatri Rao product first component projection matrix.

504+<a name="line-504"></a>kp1 ::

505+<a name="line-505"></a> forall <a name="local-6989586621679046497"><a href="#local-6989586621679046497">e</a></a> <a name="local-6989586621679046498"><a href="#local-6989586621679046498">m</a></a> <a name="local-6989586621679046499"><a href="#local-6989586621679046499">k</a></a> .

506+<a name="line-506"></a> ( Num <a href="#local-6989586621679046497">e</a>,

507+<a name="line-507"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046498">m</a>)),

508+<a name="line-508"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046499">k</a>)),

509+<a name="line-509"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046498">m</a>, <a href="#local-6989586621679046499">k</a>))),

510+<a name="line-510"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046497">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046498">m</a>, <a href="#local-6989586621679046499">k</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046498">m</a>),

511+<a name="line-511"></a> I.Normalize (<a href="#local-6989586621679046498">m</a>, <a href="#local-6989586621679046499">k</a>) ~ <a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046498">m</a>, <a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046499">k</a>)

512+<a name="line-512"></a> ) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046497">e</a> (<a href="#local-6989586621679046498">m</a>, <a href="#local-6989586621679046499">k</a>) <a href="#local-6989586621679046498">m</a>

513+<a name="line-513"></a><a name="kp1"><a href="Matrix.Type.html#kp1">kp1</a></a> = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#kp1">I.kp1</a> @<a href="#local-6989586621679046497">e</a> @(<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046498">m</a>) @(<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046499">k</a>))

514+<a name="line-514"></a>

515+<a name="line-515"></a>-- | Khatri Rao product second component projection matrix.

516+<a name="line-516"></a>kp2 ::

517+<a name="line-517"></a> forall <a name="local-6989586621679046494"><a href="#local-6989586621679046494">e</a></a> <a name="local-6989586621679046495"><a href="#local-6989586621679046495">m</a></a> <a name="local-6989586621679046496"><a href="#local-6989586621679046496">k</a></a>.

518+<a name="line-518"></a> ( Num <a href="#local-6989586621679046494">e</a>,

519+<a name="line-519"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046496">k</a>)),

520+<a name="line-520"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046495">m</a>)),

521+<a name="line-521"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046495">m</a>, <a href="#local-6989586621679046496">k</a>))),

522+<a name="line-522"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046494">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046495">m</a>, <a href="#local-6989586621679046496">k</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046496">k</a>),

523+<a name="line-523"></a> I.Normalize (<a href="#local-6989586621679046495">m</a>, <a href="#local-6989586621679046496">k</a>) ~ <a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046495">m</a>, <a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046496">k</a>)

524+<a name="line-524"></a> ) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046494">e</a> (<a href="#local-6989586621679046495">m</a>, <a href="#local-6989586621679046496">k</a>) <a href="#local-6989586621679046496">k</a>

525+<a name="line-525"></a><a name="kp2"><a href="Matrix.Type.html#kp2">kp2</a></a> = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#kp2">I.kp2</a> @<a href="#local-6989586621679046494">e</a> @(<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046495">m</a>) @(<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046496">k</a>))

526+<a name="line-526"></a>

527+<a name="line-527"></a>-- | Khatri Rao Matrix product also known as matrix pairing.

528+<a name="line-528"></a>--

529+<a name="line-529"></a>-- NOTE: That this is not a true categorical product, see for instance:

530+<a name="line-530"></a>--

531+<a name="line-531"></a>-- @

532+<a name="line-532"></a>-- | kp1 `comp` khatri a b == a

533+<a name="line-533"></a>-- khatri a b ==> |

534+<a name="line-534"></a>-- | kp2 `comp` khatri a b == b

535+<a name="line-535"></a>-- @

536+<a name="line-536"></a>--

537+<a name="line-537"></a>-- __Emphasis__ on the implication symbol.

538+<a name="line-538"></a>khatri ::

539+<a name="line-539"></a> forall <a name="local-6989586621679046490"><a href="#local-6989586621679046490">e</a></a> <a name="local-6989586621679046491"><a href="#local-6989586621679046491">cols</a></a> <a name="local-6989586621679046492"><a href="#local-6989586621679046492">a</a></a> <a name="local-6989586621679046493"><a href="#local-6989586621679046493">b</a></a>.

540+<a name="line-540"></a> ( Num <a href="#local-6989586621679046490">e</a>,

541+<a name="line-541"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046492">a</a>)),

542+<a name="line-542"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046493">b</a>)),

543+<a name="line-543"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046492">a</a>, <a href="#local-6989586621679046493">b</a>))),

544+<a name="line-544"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046490">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046492">a</a>, <a href="#local-6989586621679046493">b</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046492">a</a>),

545+<a name="line-545"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046490">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046492">a</a>, <a href="#local-6989586621679046493">b</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046493">b</a>),

546+<a name="line-546"></a> I.Normalize (<a href="#local-6989586621679046492">a</a>, <a href="#local-6989586621679046493">b</a>) ~ <a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046492">a</a>, <a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046493">b</a>)

547+<a name="line-547"></a> ) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046490">e</a> <a href="#local-6989586621679046491">cols</a> <a href="#local-6989586621679046492">a</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046490">e</a> <a href="#local-6989586621679046491">cols</a> <a href="#local-6989586621679046493">b</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046490">e</a> <a href="#local-6989586621679046491">cols</a> (<a href="#local-6989586621679046492">a</a>, <a href="#local-6989586621679046493">b</a>)

548+<a name="line-548"></a><a name="khatri"><a href="Matrix.Type.html#khatri">khatri</a></a> <a name="local-6989586621679046617"><a href="#local-6989586621679046617">a</a></a> <a name="local-6989586621679046618"><a href="#local-6989586621679046618">b</a></a> =

549+<a name="line-549"></a> let <a name="local-6989586621679046619"><a href="#local-6989586621679046619">kp1'</a></a> = <a href="Matrix.Type.html#kp1">kp1</a> @<a href="#local-6989586621679046490">e</a> @<a href="#local-6989586621679046492">a</a> @<a href="#local-6989586621679046493">b</a>

550+<a name="line-550"></a> <a name="local-6989586621679046620"><a href="#local-6989586621679046620">kp2'</a></a> = <a href="Matrix.Type.html#kp2">kp2</a> @<a href="#local-6989586621679046490">e</a> @<a href="#local-6989586621679046492">a</a> @<a href="#local-6989586621679046493">b</a>

551+<a name="line-551"></a> in <a href="Matrix.Type.html#comp">comp</a> (<a href="Matrix.Type.html#tr">tr</a> <a href="#local-6989586621679046619">kp1'</a>) <a href="#local-6989586621679046617">a</a> * <a href="Matrix.Type.html#comp">comp</a> (<a href="Matrix.Type.html#tr">tr</a> <a href="#local-6989586621679046620">kp2'</a>) <a href="#local-6989586621679046618">b</a>

552+<a name="line-552"></a>

553+<a name="line-553"></a>-- Product Bifunctor (Kronecker)

554+<a name="line-554"></a>

555+<a name="line-555"></a>infixl 4 <a href="Matrix.Type.html#%3E%3C">><</a>

556+<a name="line-556"></a>

557+<a name="line-557"></a>-- | Matrix product functor also known as kronecker product

558+<a name="line-558"></a>(><) ::

559+<a name="line-559"></a> forall <a name="local-6989586621679046485"><a href="#local-6989586621679046485">e</a></a> <a name="local-6989586621679046486"><a href="#local-6989586621679046486">m</a></a> <a name="local-6989586621679046487"><a href="#local-6989586621679046487">p</a></a> <a name="local-6989586621679046488"><a href="#local-6989586621679046488">n</a></a> <a name="local-6989586621679046489"><a href="#local-6989586621679046489">q</a></a>.

560+<a name="line-560"></a> ( Num <a href="#local-6989586621679046485">e</a>,

561+<a name="line-561"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046486">m</a>)),

562+<a name="line-562"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046488">n</a>)),

563+<a name="line-563"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046487">p</a>)),

564+<a name="line-564"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046489">q</a>)),

565+<a name="line-565"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046486">m</a>, <a href="#local-6989586621679046488">n</a>))),

566+<a name="line-566"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046487">p</a>, <a href="#local-6989586621679046489">q</a>))),

567+<a name="line-567"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046485">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046486">m</a>, <a href="#local-6989586621679046488">n</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046486">m</a>),

568+<a name="line-568"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046485">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046486">m</a>, <a href="#local-6989586621679046488">n</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046488">n</a>),

569+<a name="line-569"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046485">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046487">p</a>, <a href="#local-6989586621679046489">q</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046487">p</a>),

570+<a name="line-570"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046485">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="#local-6989586621679046487">p</a>, <a href="#local-6989586621679046489">q</a>)) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046489">q</a>),

571+<a name="line-571"></a> I.Normalize (<a href="#local-6989586621679046486">m</a>, <a href="#local-6989586621679046488">n</a>) ~ <a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046486">m</a>, <a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046488">n</a>),

572+<a name="line-572"></a> I.Normalize (<a href="#local-6989586621679046487">p</a>, <a href="#local-6989586621679046489">q</a>) ~ <a href="Matrix.Internal.html#Normalize">I.Normalize</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046487">p</a>, <a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046489">q</a>)

573+<a name="line-573"></a> ) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046485">e</a> <a href="#local-6989586621679046486">m</a> <a href="#local-6989586621679046487">p</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046485">e</a> <a href="#local-6989586621679046488">n</a> <a href="#local-6989586621679046489">q</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046485">e</a> (<a href="#local-6989586621679046486">m</a>, <a href="#local-6989586621679046488">n</a>) (<a href="#local-6989586621679046487">p</a>, <a href="#local-6989586621679046489">q</a>)

574+<a name="line-574"></a>(<a name="%3E%3C"><a href="Matrix.Type.html#%3E%3C">><</a></a>) <a name="local-6989586621679046621"><a href="#local-6989586621679046621">a</a></a> <a name="local-6989586621679046622"><a href="#local-6989586621679046622">b</a></a> =

575+<a name="line-575"></a> let <a name="local-6989586621679046623"><a href="#local-6989586621679046623">kp1'</a></a> = <a href="Matrix.Type.html#kp1">kp1</a> @<a href="#local-6989586621679046485">e</a> @<a href="#local-6989586621679046486">m</a> @<a href="#local-6989586621679046488">n</a>

576+<a name="line-576"></a> <a name="local-6989586621679046624"><a href="#local-6989586621679046624">kp2'</a></a> = <a href="Matrix.Type.html#kp2">kp2</a> @<a href="#local-6989586621679046485">e</a> @<a href="#local-6989586621679046486">m</a> @<a href="#local-6989586621679046488">n</a>

577+<a name="line-577"></a> in <a href="Matrix.Type.html#khatri">khatri</a> (<a href="Matrix.Type.html#comp">comp</a> <a href="#local-6989586621679046621">a</a> <a href="#local-6989586621679046623">kp1'</a>) (<a href="Matrix.Type.html#comp">comp</a> <a href="#local-6989586621679046622">b</a> <a href="#local-6989586621679046624">kp2'</a>)

578+<a name="line-578"></a>

579+<a name="line-579"></a>-- Matrix abide Junc Split

580+<a name="line-580"></a>

581+<a name="line-581"></a>-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.

582+<a name="line-582"></a>--

583+<a name="line-583"></a>-- Law:

584+<a name="line-584"></a>--

585+<a name="line-585"></a>-- @

586+<a name="line-586"></a>-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)

587+<a name="line-587"></a>-- @

588+<a name="line-588"></a>abideJS :: <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046482">e</a> <a href="#local-6989586621679046483">cols</a> <a href="#local-6989586621679046484">rows</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046482">e</a> <a href="#local-6989586621679046483">cols</a> <a href="#local-6989586621679046484">rows</a>

589+<a name="line-589"></a><a name="abideJS"><a href="Matrix.Type.html#abideJS">abideJS</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046625"><a href="#local-6989586621679046625">m</a></a>) = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#abideJS">I.abideJS</a> <a href="#local-6989586621679046625">m</a>)

590+<a name="line-590"></a>

591+<a name="line-591"></a>-- Matrix abide Split Junc

592+<a name="line-592"></a>

593+<a name="line-593"></a>-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.

594+<a name="line-594"></a>--

595+<a name="line-595"></a>-- Law:

596+<a name="line-596"></a>--

597+<a name="line-597"></a>-- @

598+<a name="line-598"></a>-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)

599+<a name="line-599"></a>-- @

600+<a name="line-600"></a>abideSJ :: <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046479">e</a> <a href="#local-6989586621679046480">cols</a> <a href="#local-6989586621679046481">rows</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046479">e</a> <a href="#local-6989586621679046480">cols</a> <a href="#local-6989586621679046481">rows</a>

601+<a name="line-601"></a><a name="abideSJ"><a href="Matrix.Type.html#abideSJ">abideSJ</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046626"><a href="#local-6989586621679046626">m</a></a>) = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#abideSJ">I.abideSJ</a> <a href="#local-6989586621679046626">m</a>)

602+<a name="line-602"></a>

603+<a name="line-603"></a>-- Matrix transposition

604+<a name="line-604"></a>

605+<a name="line-605"></a>-- | Matrix transposition.

606+<a name="line-606"></a>tr :: <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046476">e</a> <a href="#local-6989586621679046477">cols</a> <a href="#local-6989586621679046478">rows</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046476">e</a> <a href="#local-6989586621679046478">rows</a> <a href="#local-6989586621679046477">cols</a>

607+<a name="line-607"></a><a name="tr"><a href="Matrix.Type.html#tr">tr</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046627"><a href="#local-6989586621679046627">m</a></a>) = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#tr">I.tr</a> <a href="#local-6989586621679046627">m</a>)

608+<a name="line-608"></a>

609+<a name="line-609"></a>-- Selective 'select' operator

610+<a name="line-610"></a>

611+<a name="line-611"></a>-- | Selective functors 'select' operator equivalent inspired by the

612+<a name="line-612"></a>-- ArrowMonad solution presented in the paper.

613+<a name="line-613"></a>selectM ::

614+<a name="line-614"></a> ( Num <a href="#local-6989586621679046472">e</a>,

615+<a name="line-615"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046472">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046473">b</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046473">b</a>),

616+<a name="line-616"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046473">b</a>)),

617+<a name="line-617"></a> I.Normalize (Either <a href="#local-6989586621679046474">a</a> <a href="#local-6989586621679046473">b</a>) ~ Either (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046474">a</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046473">b</a>)

618+<a name="line-618"></a> ) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046472">e</a> <a href="#local-6989586621679046475">cols</a> (Either <a href="#local-6989586621679046474">a</a> <a href="#local-6989586621679046473">b</a>) -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046472">e</a> <a href="#local-6989586621679046474">a</a> <a href="#local-6989586621679046473">b</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046472">e</a> <a href="#local-6989586621679046475">cols</a> <a href="#local-6989586621679046473">b</a>

619+<a name="line-619"></a><a name="selectM"><a href="Matrix.Type.html#selectM">selectM</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046628"><a href="#local-6989586621679046628">m</a></a>) (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046629"><a href="#local-6989586621679046629">y</a></a>) = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#select">I.select</a> <a href="#local-6989586621679046628">m</a> <a href="#local-6989586621679046629">y</a>)

620+<a name="line-620"></a>

621+<a name="line-621"></a>-- McCarthy's Conditional

622+<a name="line-622"></a>

623+<a name="line-623"></a>-- | McCarthy's Conditional expresses probabilistic choice.

624+<a name="line-624"></a>cond ::

625+<a name="line-625"></a> ( I.Normalize (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046469">a</a>) ~ <a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046469">a</a>,

626+<a name="line-626"></a> KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046469">a</a>)),

627+<a name="line-627"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046470">e</a> () (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046469">a</a>),

628+<a name="line-628"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046470">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046469">a</a>) (),

629+<a name="line-629"></a> <a href="Matrix.Internal.html#FromLists">I.FromLists</a> <a href="#local-6989586621679046470">e</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046469">a</a>) (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046469">a</a>),

630+<a name="line-630"></a> Bounded <a href="#local-6989586621679046469">a</a>,

631+<a name="line-631"></a> Enum <a href="#local-6989586621679046469">a</a>,

632+<a name="line-632"></a> Num <a href="#local-6989586621679046470">e</a>,

633+<a name="line-633"></a> Ord <a href="#local-6989586621679046470">e</a>

634+<a name="line-634"></a> )

635+<a name="line-635"></a> =>

636+<a name="line-636"></a> (<a href="#local-6989586621679046469">a</a> -> Bool) -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046470">e</a> <a href="#local-6989586621679046469">a</a> <a href="#local-6989586621679046471">b</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046470">e</a> <a href="#local-6989586621679046469">a</a> <a href="#local-6989586621679046471">b</a> -> <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046470">e</a> <a href="#local-6989586621679046469">a</a> <a href="#local-6989586621679046471">b</a>

637+<a name="line-637"></a><a name="cond"><a href="Matrix.Type.html#cond">cond</a></a> <a name="local-6989586621679046630"><a href="#local-6989586621679046630">p</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046631"><a href="#local-6989586621679046631">a</a></a>) (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046632"><a href="#local-6989586621679046632">b</a></a>) = <a href="Matrix.Type.html#M">M</a> (<a href="Matrix.Internal.html#cond">I.cond</a> <a href="#local-6989586621679046630">p</a> <a href="#local-6989586621679046631">a</a> <a href="#local-6989586621679046632">b</a>)

638+<a name="line-638"></a>

639+<a name="line-639"></a>-- Pretty print

640+<a name="line-640"></a>

641+<a name="line-641"></a>-- | Matrix pretty printer

642+<a name="line-642"></a>pretty :: (KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046466">cols</a>)), Show <a href="#local-6989586621679046467">e</a>) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046467">e</a> <a href="#local-6989586621679046466">cols</a> <a href="#local-6989586621679046468">rows</a> -> String

643+<a name="line-643"></a><a name="pretty"><a href="Matrix.Type.html#pretty">pretty</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046633"><a href="#local-6989586621679046633">m</a></a>) = <a href="Matrix.Internal.html#pretty">I.pretty</a> <a href="#local-6989586621679046633">m</a>

644+<a name="line-644"></a>

645+<a name="line-645"></a>-- | Matrix pretty printer

646+<a name="line-646"></a>prettyPrint :: (KnownNat (<a href="Matrix.Internal.html#Count">I.Count</a> (<a href="Matrix.Internal.html#Normalize">I.Normalize</a> <a href="#local-6989586621679046463">cols</a>)), Show <a href="#local-6989586621679046464">e</a>) => <a href="Matrix.Type.html#Matrix">Matrix</a> <a href="#local-6989586621679046464">e</a> <a href="#local-6989586621679046463">cols</a> <a href="#local-6989586621679046465">rows</a> -> IO ()

647+<a name="line-647"></a><a name="prettyPrint"><a href="Matrix.Type.html#prettyPrint">prettyPrint</a></a> (<a href="Matrix.Type.html#M">M</a> <a name="local-6989586621679046634"><a href="#local-6989586621679046634">m</a></a>) = <a href="Matrix.Internal.html#prettyPrint">I.prettyPrint</a> <a href="#local-6989586621679046634">m</a>

648+<a name="line-648"></a></pre></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/src/Paths_laop.htmlnew file+51

@@ -0,0 +1,51 @@

1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="style.css" /><script type="text/javascript" src="highlight.js"></script></head><body><pre>{-# LANGUAGE CPP #-}

2+<a name="line-2"></a>{-# LANGUAGE NoRebindableSyntax #-}

3+<a name="line-3"></a>{-# OPTIONS_GHC -fno-warn-missing-import-lists #-}

4+<a name="line-4"></a>module Paths_laop (

5+<a name="line-5"></a> <a href="Paths_laop.html#version">version</a>,

6+<a name="line-6"></a> <a href="Paths_laop.html#getBinDir">getBinDir</a>, <a href="Paths_laop.html#getLibDir">getLibDir</a>, <a href="Paths_laop.html#getDynLibDir">getDynLibDir</a>, <a href="Paths_laop.html#getDataDir">getDataDir</a>, <a href="Paths_laop.html#getLibexecDir">getLibexecDir</a>,

7+<a name="line-7"></a> <a href="Paths_laop.html#getDataFileName">getDataFileName</a>, <a href="Paths_laop.html#getSysconfDir">getSysconfDir</a>

8+<a name="line-8"></a> ) where

9+<a name="line-9"></a>

10+<a name="line-10"></a>import qualified Control.Exception as Exception

11+<a name="line-11"></a>import Data.Version (Version(..))

12+<a name="line-12"></a>import System.Environment (getEnv)

13+<a name="line-13"></a>import Prelude

14+<a name="line-14"></a>

15+<a name="line-15"></a>#if defined(VERSION_base)

16+

17+<a name="line-17"></a>#if MIN_VERSION_base(4,0,0)

18+catchIO :: IO <a href="#local-6989586621679020005">a</a> -> (Exception.IOException -> IO <a href="#local-6989586621679020005">a</a>) -> IO <a href="#local-6989586621679020005">a</a>

19+<a name="line-19"></a>#else

20+catchIO :: IO a -> (Exception.Exception -> IO a) -> IO a

21+<a name="line-21"></a>#endif

22+

23+<a name="line-23"></a>#else

24+catchIO :: IO a -> (Exception.IOException -> IO a) -> IO a

25+<a name="line-25"></a>#endif

26+<a name="catchIO"><a href="Paths_laop.html#catchIO">catchIO</a></a> = Exception.catch

27+<a name="line-27"></a>

28+<a name="line-28"></a>version :: Version

29+<a name="line-29"></a><a name="version"><a href="Paths_laop.html#version">version</a></a> = Version [0,1,0,0] []

30+<a name="line-30"></a>bindir, libdir, dynlibdir, datadir, libexecdir, sysconfdir :: FilePath

31+<a name="line-31"></a>

32+<a name="line-32"></a><a name="bindir"><a href="Paths_laop.html#bindir">bindir</a></a> = "/home/bolt/.cabal/bin"

33+<a name="line-33"></a><a name="libdir"><a href="Paths_laop.html#libdir">libdir</a></a> = "/home/bolt/.cabal/lib/x86_64-linux-ghc-8.6.5/laop-0.1.0.0-inplace"

34+<a name="line-34"></a><a name="dynlibdir"><a href="Paths_laop.html#dynlibdir">dynlibdir</a></a> = "/home/bolt/.cabal/lib/x86_64-linux-ghc-8.6.5"

35+<a name="line-35"></a><a name="datadir"><a href="Paths_laop.html#datadir">datadir</a></a> = "/home/bolt/.cabal/share/x86_64-linux-ghc-8.6.5/laop-0.1.0.0"

36+<a name="line-36"></a><a name="libexecdir"><a href="Paths_laop.html#libexecdir">libexecdir</a></a> = "/home/bolt/.cabal/libexec/x86_64-linux-ghc-8.6.5/laop-0.1.0.0"

37+<a name="line-37"></a><a name="sysconfdir"><a href="Paths_laop.html#sysconfdir">sysconfdir</a></a> = "/home/bolt/.cabal/etc"

38+<a name="line-38"></a>

39+<a name="line-39"></a>getBinDir, getLibDir, getDynLibDir, getDataDir, getLibexecDir, getSysconfDir :: IO FilePath

40+<a name="line-40"></a><a name="getBinDir"><a href="Paths_laop.html#getBinDir">getBinDir</a></a> = <a href="Paths_laop.html#catchIO">catchIO</a> (getEnv "laop_bindir") (\_ -> return <a href="Paths_laop.html#bindir">bindir</a>)

41+<a name="line-41"></a><a name="getLibDir"><a href="Paths_laop.html#getLibDir">getLibDir</a></a> = <a href="Paths_laop.html#catchIO">catchIO</a> (getEnv "laop_libdir") (\_ -> return <a href="Paths_laop.html#libdir">libdir</a>)

42+<a name="line-42"></a><a name="getDynLibDir"><a href="Paths_laop.html#getDynLibDir">getDynLibDir</a></a> = <a href="Paths_laop.html#catchIO">catchIO</a> (getEnv "laop_dynlibdir") (\_ -> return <a href="Paths_laop.html#dynlibdir">dynlibdir</a>)

43+<a name="line-43"></a><a name="getDataDir"><a href="Paths_laop.html#getDataDir">getDataDir</a></a> = <a href="Paths_laop.html#catchIO">catchIO</a> (getEnv "laop_datadir") (\_ -> return <a href="Paths_laop.html#datadir">datadir</a>)

44+<a name="line-44"></a><a name="getLibexecDir"><a href="Paths_laop.html#getLibexecDir">getLibexecDir</a></a> = <a href="Paths_laop.html#catchIO">catchIO</a> (getEnv "laop_libexecdir") (\_ -> return <a href="Paths_laop.html#libexecdir">libexecdir</a>)

45+<a name="line-45"></a><a name="getSysconfDir"><a href="Paths_laop.html#getSysconfDir">getSysconfDir</a></a> = <a href="Paths_laop.html#catchIO">catchIO</a> (getEnv "laop_sysconfdir") (\_ -> return <a href="Paths_laop.html#sysconfdir">sysconfdir</a>)

46+<a name="line-46"></a>

47+<a name="line-47"></a>getDataFileName :: FilePath -> IO FilePath

48+<a name="line-48"></a><a name="getDataFileName"><a href="Paths_laop.html#getDataFileName">getDataFileName</a></a> <a name="local-6989586621679020854"><a href="#local-6989586621679020854">name</a></a> = do

49+<a name="line-49"></a> <a name="local-6989586621679020855"><a href="#local-6989586621679020855">dir</a></a> <- <a href="Paths_laop.html#getDataDir">getDataDir</a>

50+<a name="line-50"></a> return (<a href="#local-6989586621679020855">dir</a> ++ "/" ++ <a href="#local-6989586621679020854">name</a>)

51+<a name="line-51"></a></pre></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/src/Utils.Internal.htmlnew file+177

@@ -0,0 +1,177 @@

1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="style.css" /><script type="text/javascript" src="highlight.js"></script></head><body><pre>{-# LANGUAGE TypeApplications #-}

2+<a name="line-2"></a>{-# LANGUAGE DataKinds #-}

3+<a name="line-3"></a>{-# LANGUAGE FlexibleInstances #-}

4+<a name="line-4"></a>{-# LANGUAGE GeneralizedNewtypeDeriving #-}

5+<a name="line-5"></a>{-# LANGUAGE KindSignatures #-}

6+<a name="line-6"></a>{-# LANGUAGE ScopedTypeVariables #-}

7+<a name="line-7"></a>

8+<a name="line-8"></a>module Utils.Internal

9+<a name="line-9"></a> ( -- | This is an internal module and it is not meant to be imported.

10+<a name="line-10"></a> --

11+<a name="line-11"></a> -- Utility module that provides the 'Natural' data type.

12+<a name="line-12"></a> -- The semantic associated with this data type is that

13+<a name="line-13"></a> -- it's meant to be a restricted 'Int' value. For example

14+<a name="line-14"></a> -- the type @Natural 6@ can only be instanciated with @Nat n@

15+<a name="line-15"></a> -- where @0 <= n <= 6@. Why, You might ask, because with normal

16+<a name="line-16"></a> -- 'Int's it is not possible to have a decent @Enum (Int, Int)@

17+<a name="line-17"></a> -- instance. See the following probabilistic programming model as and

18+<a name="line-18"></a> -- example:

19+<a name="line-19"></a> --

20+<a name="line-20"></a> -- We want to calculate the probability of the sum of two dice throws.

21+<a name="line-21"></a> -- To do this we start by defining the sample space:

22+<a name="line-22"></a> --

23+<a name="line-23"></a> -- @

24+<a name="line-24"></a> -- type SampleSpace = Int -- We think 'Int' are enough

25+<a name="line-25"></a> --

26+<a name="line-26"></a> -- die :: Dist Int 6

27+<a name="line-27"></a> -- die = unifrom [1..6]

28+<a name="line-28"></a> --

29+<a name="line-29"></a> -- -- Promote 'Int' addition to a matrix

30+<a name="line-30"></a> -- addM = fromF (uncurry (+)) -- Impossible

31+<a name="line-31"></a> -- @

32+<a name="line-32"></a> --

33+<a name="line-33"></a> -- The last line is impossible because @(Int, Int)@ does not have

34+<a name="line-34"></a> -- a good 'Enum' instance: @[(0, 1), (0, 2), .. (0, maxBound), (1, 0),

35+<a name="line-35"></a> -- ..]@. And we'd like the addition matrix to be of 36 columns by 12

36+<a name="line-36"></a> -- rows but limited to integers up to @6@!

37+<a name="line-37"></a> --

38+<a name="line-38"></a> -- One way to solve this issue is by defining and auxilary data type to

39+<a name="line-39"></a> -- represent the sample space:

40+<a name="line-40"></a> --

41+<a name="line-41"></a> -- @

42+<a name="line-42"></a> -- data SampleSpace = S1 | S2 | S3 | S4 | S5 | S6

43+<a name="line-43"></a> -- deriving (Show, Eq, Enum, Bounded) -- Enum and Bounded are

44+<a name="line-44"></a> -- important

45+<a name="line-45"></a> -- @

46+<a name="line-46"></a> --

47+<a name="line-47"></a> -- And write the sample space addition function:

48+<a name="line-48"></a> --

49+<a name="line-49"></a> -- @

50+<a name="line-50"></a> -- ssAdd :: SampleSpace -> SampleSpace -> Int

51+<a name="line-51"></a> -- ssAdd a b = (fromEnum a + 1) + (fromEnum b + 1)

52+<a name="line-52"></a> -- @

53+<a name="line-53"></a> --

54+<a name="line-54"></a> -- And then promote that function to matrix and everything is alright:

55+<a name="line-55"></a> --

56+<a name="line-56"></a> -- @

57+<a name="line-57"></a> -- ssAddM = fromF' (uncurry ssAdd)

58+<a name="line-58"></a> --

59+<a name="line-59"></a> -- dieSumProb = ssAddM `comp` (khatri die die)

60+<a name="line-60"></a> -- @

61+<a name="line-61"></a> --

62+<a name="line-62"></a> -- This is a nice solution for small sample spaces. But for larger ones

63+<a name="line-63"></a> -- it is not feasible to write a data type with hundreds of constructors

64+<a name="line-64"></a> -- and then write manipulation functions that need to deal with them.

65+<a name="line-65"></a> -- To mitigate this limitation the 'Natural' type comes a long way and

66+<a name="line-66"></a> -- allows one to model the sample in an easier way. See for instance:

67+<a name="line-67"></a> --

68+<a name="line-68"></a> -- @

69+<a name="line-69"></a> -- ssAdd :: Natural 6 -> Natural 6 -> Natural 12

70+<a name="line-70"></a> -- ssAdd = coerceNat (+)

71+<a name="line-71"></a> --

72+<a name="line-72"></a> -- ssAddM = fromF' (uncurry sumSS)

73+<a name="line-73"></a> --

74+<a name="line-74"></a> -- die :: Dist (Natural 6) 6

75+<a name="line-75"></a> -- die = uniform [nat @6 1 .. nat 6]

76+<a name="line-76"></a> --

77+<a name="line-77"></a> -- dieSumProb = ssAddM `comp` (khatri die die)

78+<a name="line-78"></a> -- @

79+<a name="line-79"></a> --

80+<a name="line-80"></a> -- * 'Natural' data type

81+<a name="line-81"></a> <a href="Utils.Internal.html#Natural">Natural</a>,

82+<a name="line-82"></a> <a href="Utils.Internal.html#nat">nat</a>,

83+<a name="line-83"></a>

84+<a name="line-84"></a> -- * Coerce auxiliar functions to help promote 'Int' typed functions to

85+<a name="line-85"></a> -- 'Natural' typed functions.

86+<a name="line-86"></a> <a href="Utils.Internal.html#coerceNat">coerceNat</a>,

87+<a name="line-87"></a> <a href="Utils.Internal.html#coerceNat2">coerceNat2</a>,

88+<a name="line-88"></a> <a href="Utils.Internal.html#coerceNat3">coerceNat3</a>,

89+<a name="line-89"></a> )

90+<a name="line-90"></a>where

91+<a name="line-91"></a>

92+<a name="line-92"></a>import Data.Coerce

93+<a name="line-93"></a>import Data.Proxy

94+<a name="line-94"></a>import GHC.TypeLits

95+<a name="line-95"></a>import Control.DeepSeq

96+<a name="line-96"></a>

97+<a name="line-97"></a>-- | Wrapper around 'Int's that have a restrictive semantic associated.

98+<a name="line-98"></a>-- A value of type @'Natural' n m@ can only be instanciated with some 'Int'

99+<a name="line-99"></a>-- @i@ that's @n <= i <= m@.

100+<a name="line-100"></a>newtype <a name="Natural"><a href="Utils.Internal.html#Natural">Natural</a></a> (<a name="local-6989586621679023463"><a href="#local-6989586621679023463">start</a></a> :: Nat) (<a name="local-6989586621679023464"><a href="#local-6989586621679023464">end</a></a> :: Nat) = <a name="Nat"><a href="Utils.Internal.html#Nat">Nat</a></a> Int

101+<a name="line-101"></a> deriving (Show, Read, Eq, Ord, NFData)

102+<a name="line-102"></a>

103+<a name="line-103"></a>-- | Throws a runtime error if any of the operations overflows or

104+<a name="line-104"></a>-- underflows.

105+<a name="line-105"></a>instance (KnownNat <a href="#local-6989586621679031022">n</a>, KnownNat <a href="#local-6989586621679031023">m</a>) => Num (<a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031022">n</a> <a href="#local-6989586621679031023">m</a>) where

106+<a name="line-106"></a> (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031024"><a href="#local-6989586621679031024">a</a></a>) <a name="local-8214565720323790403">+</a> (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031025"><a href="#local-6989586621679031025">b</a></a>) = <a href="Utils.Internal.html#nat">nat</a> @<a href="#local-6989586621679031022">n</a> @<a href="#local-6989586621679031023">m</a> (<a href="#local-6989586621679031024">a</a> + <a href="#local-6989586621679031025">b</a>)

107+<a name="line-107"></a> (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031026"><a href="#local-6989586621679031026">a</a></a>) - (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031027"><a href="#local-6989586621679031027">b</a></a>) = <a href="Utils.Internal.html#nat">nat</a> @<a href="#local-6989586621679031022">n</a> @<a href="#local-6989586621679031023">m</a> (<a href="#local-6989586621679031026">a</a> - <a href="#local-6989586621679031027">b</a>)

108+<a name="line-108"></a> (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031028"><a href="#local-6989586621679031028">a</a></a>) <a name="local-8214565720323790402">*</a> (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031029"><a href="#local-6989586621679031029">b</a></a>) = <a href="Utils.Internal.html#nat">nat</a> @<a href="#local-6989586621679031022">n</a> @<a href="#local-6989586621679031023">m</a> (<a href="#local-6989586621679031028">a</a> * <a href="#local-6989586621679031029">b</a>)

109+<a name="line-109"></a> <a name="local-8214565720323790401">abs</a> (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031030"><a href="#local-6989586621679031030">a</a></a>) = <a href="Utils.Internal.html#nat">nat</a> @<a href="#local-6989586621679031022">n</a> @<a href="#local-6989586621679031023">m</a> (abs <a href="#local-6989586621679031030">a</a>)

110+<a name="line-110"></a> <a name="local-8214565720323790400">signum</a> (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031031"><a href="#local-6989586621679031031">a</a></a>) = <a href="Utils.Internal.html#nat">nat</a> @<a href="#local-6989586621679031022">n</a> @<a href="#local-6989586621679031023">m</a> (signum <a href="#local-6989586621679031031">a</a>)

111+<a name="line-111"></a> <a name="local-3458764513820541088">fromInteger</a> <a name="local-6989586621679031032"><a href="#local-6989586621679031032">i</a></a> = <a href="Utils.Internal.html#nat">nat</a> @<a href="#local-6989586621679031022">n</a> @<a href="#local-6989586621679031023">m</a> (fromInteger <a href="#local-6989586621679031032">i</a>)

112+<a name="line-112"></a>

113+<a name="line-113"></a>-- | Natural constructor function. Throws a runtime error if the 'Int'

114+<a name="line-114"></a>-- value is greater than the corresponding @m@ or lower than @n@ in the @'Natural' n m@ type.

115+<a name="line-115"></a>nat :: forall <a name="local-6989586621679031052"><a href="#local-6989586621679031052">n</a></a> <a name="local-6989586621679031053"><a href="#local-6989586621679031053">m</a></a> . (KnownNat <a href="#local-6989586621679031052">n</a>, KnownNat <a href="#local-6989586621679031053">m</a>) => Int -> <a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031052">n</a> <a href="#local-6989586621679031053">m</a>

116+<a name="line-116"></a><a name="nat"><a href="Utils.Internal.html#nat">nat</a></a> <a name="local-6989586621679031054"><a href="#local-6989586621679031054">i</a></a> =

117+<a name="line-117"></a> let <a name="local-6989586621679031055"><a href="#local-6989586621679031055">start</a></a> = fromInteger (natVal (Proxy :: Proxy <a href="#local-6989586621679031052">n</a>))

118+<a name="line-118"></a> <a name="local-6989586621679031056"><a href="#local-6989586621679031056">end</a></a> = fromInteger (natVal (Proxy :: Proxy <a href="#local-6989586621679031053">m</a>))

119+<a name="line-119"></a> in if <a href="#local-6989586621679031055">start</a> <= <a href="#local-6989586621679031054">i</a> && <a href="#local-6989586621679031054">i</a> <= <a href="#local-6989586621679031056">end</a>

120+<a name="line-120"></a> then <a href="Utils.Internal.html#Nat">Nat</a> <a href="#local-6989586621679031054">i</a>

121+<a name="line-121"></a> else error "Off limits"

122+<a name="line-122"></a>

123+<a name="line-123"></a>-- | Auxiliary function that promotes binary 'Int' functions to 'Natural'

124+<a name="line-124"></a>-- binary functions.

125+<a name="line-125"></a>coerceNat :: (Int -> Int -> Int) -> (<a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031046">a</a> <a href="#local-6989586621679031047">a'</a> -> <a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031048">b</a> <a href="#local-6989586621679031049">b'</a> -> <a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031050">c</a> <a href="#local-6989586621679031051">c'</a>)

126+<a name="line-126"></a><a name="coerceNat"><a href="Utils.Internal.html#coerceNat">coerceNat</a></a> = coerce

127+<a name="line-127"></a>

128+<a name="line-128"></a>-- | Auxiliary function that promotes ternary (binary) 'Int' functions to 'Natural'

129+<a name="line-129"></a>-- functions.

130+<a name="line-130"></a>coerceNat2 :: ((Int, Int) -> Int -> Int) -> ((<a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031038">a</a> <a href="#local-6989586621679031039">a'</a>, <a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031040">b</a> <a href="#local-6989586621679031041">b'</a>) -> <a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031042">c</a> <a href="#local-6989586621679031043">c'</a> -> <a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031044">d</a> <a href="#local-6989586621679031045">d'</a>)

131+<a name="line-131"></a><a name="coerceNat2"><a href="Utils.Internal.html#coerceNat2">coerceNat2</a></a> = coerce

132+<a name="line-132"></a>

133+<a name="line-133"></a>-- | Auxiliary function that promotes ternary (binary) 'Int' functions to 'Natural'

134+<a name="line-134"></a>-- functions.

135+<a name="line-135"></a>coerceNat3 :: (Int -> Int -> <a href="#local-6989586621679031033">a</a>) -> (<a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031034">b</a> <a href="#local-6989586621679031035">b'</a> -> <a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031036">c</a> <a href="#local-6989586621679031037">c'</a> -> <a href="#local-6989586621679031033">a</a>)

136+<a name="line-136"></a><a name="coerceNat3"><a href="Utils.Internal.html#coerceNat3">coerceNat3</a></a> = coerce

137+<a name="line-137"></a>

138+<a name="line-138"></a>instance (KnownNat <a href="#local-6989586621679031020">n</a>, KnownNat <a href="#local-6989586621679031021">m</a>) => Bounded (<a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679031020">n</a> <a href="#local-6989586621679031021">m</a>) where

139+<a name="line-139"></a> <a name="local-8214565720323790309">minBound</a> = <a href="Utils.Internal.html#Nat">Nat</a> $ fromInteger (natVal (Proxy :: Proxy <a href="#local-6989586621679031020">n</a>))

140+<a name="line-140"></a> <a name="local-8214565720323790308">maxBound</a> = <a href="Utils.Internal.html#Nat">Nat</a> $ fromInteger (natVal (Proxy :: Proxy <a href="#local-6989586621679031021">m</a>))

141+<a name="line-141"></a>

142+<a name="line-142"></a>instance (KnownNat <a href="#local-6989586621679030849">n</a>, KnownNat <a href="#local-6989586621679030850">m</a>) => Enum (<a href="Utils.Internal.html#Natural">Natural</a> <a href="#local-6989586621679030849">n</a> <a href="#local-6989586621679030850">m</a>) where

143+<a name="line-143"></a> <a name="local-8214565720323790311">toEnum</a> <a name="local-6989586621679031001"><a href="#local-6989586621679031001">i</a></a> =

144+<a name="line-144"></a> let <a name="local-6989586621679031002"><a href="#local-6989586621679031002">start</a></a> = fromInteger (natVal (Proxy :: Proxy <a href="#local-6989586621679030849">n</a>))

145+<a name="line-145"></a> in <a href="Utils.Internal.html#nat">nat</a> (<a href="#local-6989586621679031002">start</a> + <a href="#local-6989586621679031001">i</a>)

146+<a name="line-146"></a> -- | Throws a runtime error if the value is off limits

147+<a name="line-147"></a> <a name="local-8214565720323790310">fromEnum</a> (<a href="Utils.Internal.html#Nat">Nat</a> <a name="local-6989586621679031003"><a href="#local-6989586621679031003">nat</a></a>) =

148+<a name="line-148"></a> let <a name="local-6989586621679031004"><a href="#local-6989586621679031004">start</a></a> = fromInteger (natVal (Proxy :: Proxy <a href="#local-6989586621679030849">n</a>))

149+<a name="line-149"></a> <a name="local-6989586621679031005"><a href="#local-6989586621679031005">end</a></a> = fromInteger (natVal (Proxy :: Proxy <a href="#local-6989586621679030850">m</a>))

150+<a name="line-150"></a> in if <a href="#local-6989586621679031004">start</a> <= <a href="#local-6989586621679031003">nat</a> && <a href="#local-6989586621679031003">nat</a> <= <a href="#local-6989586621679031005">end</a>

151+<a name="line-151"></a> then <a href="#local-6989586621679031003">nat</a> - <a href="#local-6989586621679031004">start</a>

152+<a name="line-152"></a> else error "Off limits"

153+<a name="line-153"></a>

154+<a name="line-154"></a>-- | Optimized 'Enum' instance for tuples that comply with the given

155+<a name="line-155"></a>-- constraints.

156+<a name="line-156"></a>instance

157+<a name="line-157"></a> ( Enum <a href="#local-6989586621679029190">a</a>,

158+<a name="line-158"></a> Enum <a href="#local-6989586621679029191">b</a>,

159+<a name="line-159"></a> Bounded <a href="#local-6989586621679029191">b</a>

160+<a name="line-160"></a> ) =>

161+<a name="line-161"></a> Enum (<a href="#local-6989586621679029190">a</a>, <a href="#local-6989586621679029191">b</a>)

162+<a name="line-162"></a> where

163+<a name="line-163"></a>

164+<a name="line-164"></a> <a name="local-8214565720323790311">toEnum</a> <a name="local-6989586621679029192"><a href="#local-6989586621679029192">i</a></a> =

165+<a name="line-165"></a> let (<a name="local-6989586621679029193"><a href="#local-6989586621679029193">listB</a></a> :: [<a href="#local-6989586621679029191">b</a>]) = [minBound .. maxBound]

166+<a name="line-166"></a> <a name="local-6989586621679029194"><a href="#local-6989586621679029194">lengthB</a></a> = length <a href="#local-6989586621679029193">listB</a>

167+<a name="line-167"></a> <a name="local-6989586621679029195"><a href="#local-6989586621679029195">fstI</a></a> = div <a href="#local-6989586621679029192">i</a> <a href="#local-6989586621679029194">lengthB</a>

168+<a name="line-168"></a> <a name="local-6989586621679029196"><a href="#local-6989586621679029196">sndI</a></a> = mod <a href="#local-6989586621679029192">i</a> <a href="#local-6989586621679029194">lengthB</a>

169+<a name="line-169"></a> in (toEnum <a href="#local-6989586621679029195">fstI</a>, toEnum <a href="#local-6989586621679029196">sndI</a>)

170+<a name="line-170"></a>

171+<a name="line-171"></a> <a name="local-8214565720323790310">fromEnum</a> (<a name="local-6989586621679030843"><a href="#local-6989586621679030843">a</a></a>, <a name="local-6989586621679030844"><a href="#local-6989586621679030844">b</a></a>) =

172+<a name="line-172"></a> let (<a name="local-6989586621679030845"><a href="#local-6989586621679030845">listB</a></a> :: [<a href="#local-6989586621679029191">b</a>]) = [minBound .. maxBound]

173+<a name="line-173"></a> <a name="local-6989586621679030846"><a href="#local-6989586621679030846">lengthB</a></a> = length <a href="#local-6989586621679030845">listB</a>

174+<a name="line-174"></a> <a name="local-6989586621679030847"><a href="#local-6989586621679030847">fstI</a></a> = fromEnum <a href="#local-6989586621679030843">a</a>

175+<a name="line-175"></a> <a name="local-6989586621679030848"><a href="#local-6989586621679030848">sndI</a></a> = fromEnum <a href="#local-6989586621679030844">b</a>

176+<a name="line-176"></a> in <a href="#local-6989586621679030847">fstI</a> * <a href="#local-6989586621679030846">lengthB</a> + <a href="#local-6989586621679030848">sndI</a>

177+<a name="line-177"></a></pre></body></html>

build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/doc/html/laop-0.1.0.0-docs/src/Utils.htmlnew file+101

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1+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><link rel="stylesheet" type="text/css" href="style.css" /><script type="text/javascript" src="highlight.js"></script></head><body><pre>-----------------------------------------------------------------------------

2+<a name="line-2"></a>-- |

3+<a name="line-3"></a>-- Module : Utils

4+<a name="line-4"></a>-- Copyright : (c) Armando Santos 2019-2020

5+<a name="line-5"></a>-- Maintainer : armandoifsantos@gmail.com

6+<a name="line-6"></a>-- Stability : experimental

7+<a name="line-7"></a>--

8+<a name="line-8"></a>-- __LAoP__ is a library for algebraic (inductive) construction and manipulation of matrices

9+<a name="line-9"></a>-- in Haskell. See <https://github.com/bolt12/master-thesis my Msc Thesis> for the

10+<a name="line-10"></a>-- motivation behind the library, the underlying theory, and implementation details.

11+<a name="line-11"></a>--

12+<a name="line-12"></a>-- This module provides the 'Natural' data type.

13+<a name="line-13"></a>-- The semantic associated with this data type is that

14+<a name="line-14"></a>-- it's meant to be a restricted 'Int' value.

15+<a name="line-15"></a>--

16+<a name="line-16"></a>-----------------------------------------------------------------------------

17+<a name="line-17"></a>

18+<a name="line-18"></a>module Utils

19+<a name="line-19"></a> ( -- | Utility module that provides the 'Natural' data type.

20+<a name="line-20"></a> -- The semantic associated with this data type is that

21+<a name="line-21"></a> -- it's meant to be a restricted 'Int' value. For example

22+<a name="line-22"></a> -- the type @Natural 1 6@ can only be instanciated with @nat n@

23+<a name="line-23"></a> -- where @1 <= n <= 6@. Why, You might ask, because with normal

24+<a name="line-24"></a> -- 'Int's it is not possible to have a decent @Enum (Int, Int)@

25+<a name="line-25"></a> -- instance. See the following probabilistic programming model as and

26+<a name="line-26"></a> -- example:

27+<a name="line-27"></a> --

28+<a name="line-28"></a> -- We want to calculate the probability of the sum of two dice throws.

29+<a name="line-29"></a> -- To do this we start by defining the sample space:

30+<a name="line-30"></a> --

31+<a name="line-31"></a> -- @

32+<a name="line-32"></a> -- type SampleSpace = Int -- We think 'Int' are enough

33+<a name="line-33"></a> --

34+<a name="line-34"></a> -- die :: Dist Int 6

35+<a name="line-35"></a> -- die = unifrom [1..6]

36+<a name="line-36"></a> --

37+<a name="line-37"></a> -- -- Promote 'Int' addition to a matrix

38+<a name="line-38"></a> -- addM = fromF (uncurry (+)) -- Impossible

39+<a name="line-39"></a> -- @

40+<a name="line-40"></a> --

41+<a name="line-41"></a> -- The last line is impossible because @(Int, Int)@ does not have

42+<a name="line-42"></a> -- a good 'Enum' instance: @[(0, 1), (0, 2), .. (0, maxBound), (1, 0),

43+<a name="line-43"></a> -- ..]@. And we'd like the addition matrix to be of 36 columns by 12

44+<a name="line-44"></a> -- rows but limited to integers up to @6@!

45+<a name="line-45"></a> --

46+<a name="line-46"></a> -- One way to solve this issue is by defining and auxilary data type to

47+<a name="line-47"></a> -- represent the sample space:

48+<a name="line-48"></a> --

49+<a name="line-49"></a> -- @

50+<a name="line-50"></a> -- data SampleSpace = S1 | S2 | S3 | S4 | S5 | S6

51+<a name="line-51"></a> -- deriving (Show, Eq, Enum, Bounded) -- Enum and Bounded are

52+<a name="line-52"></a> -- important

53+<a name="line-53"></a> -- @

54+<a name="line-54"></a> --

55+<a name="line-55"></a> -- And write the sample space addition function:

56+<a name="line-56"></a> --

57+<a name="line-57"></a> -- @

58+<a name="line-58"></a> -- ssAdd :: SampleSpace -> SampleSpace -> Int

59+<a name="line-59"></a> -- ssAdd a b = (fromEnum a + 1) + (fromEnum b + 1)

60+<a name="line-60"></a> -- @

61+<a name="line-61"></a> --

62+<a name="line-62"></a> -- And then promote that function to matrix and everything is alright:

63+<a name="line-63"></a> --

64+<a name="line-64"></a> -- @

65+<a name="line-65"></a> -- ssAddM = fromF' (uncurry ssAdd)

66+<a name="line-66"></a> --

67+<a name="line-67"></a> -- dieSumProb = ssAddM `comp` (khatri die die)

68+<a name="line-68"></a> -- @

69+<a name="line-69"></a> --

70+<a name="line-70"></a> -- This is a nice solution for small sample spaces. But for larger ones

71+<a name="line-71"></a> -- it is not feasible to write a data type with hundreds of constructors

72+<a name="line-72"></a> -- and then write manipulation functions that need to deal with them.

73+<a name="line-73"></a> -- To mitigate this limitation the 'Natural' type comes a long way and

74+<a name="line-74"></a> -- allows one to model the sample in an easier way. See for instance:

75+<a name="line-75"></a> --

76+<a name="line-76"></a> -- @

77+<a name="line-77"></a> -- ssAdd :: Natural 1 6 -> Natural 1 6 -> Natural 1 12

78+<a name="line-78"></a> -- ssAdd = coerceNat (+)

79+<a name="line-79"></a> --

80+<a name="line-80"></a> -- ssAddM = fromF' (uncurry sumSS)

81+<a name="line-81"></a> --

82+<a name="line-82"></a> -- die :: Dist (Natural 1 6) 6

83+<a name="line-83"></a> -- die = uniform [nat @1 @6 1 .. nat 6]

84+<a name="line-84"></a> --

85+<a name="line-85"></a> -- dieSumProb = ssAddM `comp` (khatri die die)

86+<a name="line-86"></a> -- @

87+<a name="line-87"></a> --

88+<a name="line-88"></a> -- * 'Natural' data type

89+<a name="line-89"></a> <a href="Utils.Internal.html#Natural">Natural</a>,

90+<a name="line-90"></a> <a href="Utils.Internal.html#nat">nat</a>,

91+<a name="line-91"></a>

92+<a name="line-92"></a> -- * Coerce auxiliar functions to help promote 'Int' typed functions to

93+<a name="line-93"></a> -- 'Natural' typed functions.

94+<a name="line-94"></a> <a href="Utils.Internal.html#coerceNat">coerceNat</a>,

95+<a name="line-95"></a> <a href="Utils.Internal.html#coerceNat2">coerceNat2</a>,

96+<a name="line-96"></a> <a href="Utils.Internal.html#coerceNat3">coerceNat3</a>,

97+<a name="line-97"></a> )

98+<a name="line-98"></a>where

99+<a name="line-99"></a>

100+<a name="line-100"></a>import <a href="Utils.Internal.html">Utils.Internal</a>

101+<a name="line-101"></a></pre></body></html>

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1+{-# LANGUAGE CPP #-}

2+{-# LANGUAGE NoRebindableSyntax #-}

3+{-# OPTIONS_GHC -fno-warn-missing-import-lists #-}

4+module Paths_fake_package (

5+ version,

6+ getBinDir, getLibDir, getDynLibDir, getDataDir, getLibexecDir,

7+ getDataFileName, getSysconfDir

8+ ) where

10+import qualified Control.Exception as Exception

11+import Data.Version (Version(..))

12+import System.Environment (getEnv)

13+import Prelude

14+

15+#if defined(VERSION_base)

16+

17+#if MIN_VERSION_base(4,0,0)

18+catchIO :: IO a -> (Exception.IOException -> IO a) -> IO a

19+#else

20+catchIO :: IO a -> (Exception.Exception -> IO a) -> IO a

21+#endif

22+

23+#else

24+catchIO :: IO a -> (Exception.IOException -> IO a) -> IO a

25+#endif

26+catchIO = Exception.catch

27+

28+version :: Version

29+version = Version [0] []

30+bindir, libdir, dynlibdir, datadir, libexecdir, sysconfdir :: FilePath

31+

32+bindir = "/home/bolt/.cabal/bin"

33+libdir = "/home/bolt/.cabal/lib/x86_64-linux-ghc-8.6.5/fake-package-0-inplace-script"

34+dynlibdir = "/home/bolt/.cabal/lib/x86_64-linux-ghc-8.6.5"

35+datadir = "/home/bolt/.cabal/share/x86_64-linux-ghc-8.6.5/fake-package-0"

36+libexecdir = "/home/bolt/.cabal/libexec/x86_64-linux-ghc-8.6.5/fake-package-0"

37+sysconfdir = "/home/bolt/.cabal/etc"

38+

39+getBinDir, getLibDir, getDynLibDir, getDataDir, getLibexecDir, getSysconfDir :: IO FilePath

40+getBinDir = catchIO (getEnv "fake_package_bindir") (\_ -> return bindir)

41+getLibDir = catchIO (getEnv "fake_package_libdir") (\_ -> return libdir)

42+getDynLibDir = catchIO (getEnv "fake_package_dynlibdir") (\_ -> return dynlibdir)

43+getDataDir = catchIO (getEnv "fake_package_datadir") (\_ -> return datadir)

44+getLibexecDir = catchIO (getEnv "fake_package_libexecdir") (\_ -> return libexecdir)

45+getSysconfDir = catchIO (getEnv "fake_package_sysconfdir") (\_ -> return sysconfdir)

46+

47+getDataFileName :: FilePath -> IO FilePath

48+getDataFileName name = do

49+ dir <- getDataDir

50+ return (dir ++ "/" ++ name)

dist-newstyle/build/x86_64-linux/ghc-8.6.5/fake-package-0/x/script/build/script/autogen/cabal_macros.hnew file+118

@@ -0,0 +1,118 @@

1+/* DO NOT EDIT: This file is automatically generated by Cabal */

3+/* package fake-package-0 */

4+#ifndef VERSION_fake_package

5+#define VERSION_fake_package "0"

6+#endif /* VERSION_fake_package */

7+#ifndef MIN_VERSION_fake_package

8+#define MIN_VERSION_fake_package(major1,major2,minor) (\

9+ (major1) < 0 || \

10+ (major1) == 0 && (major2) < 0 || \

11+ (major1) == 0 && (major2) == 0 && (minor) <= 0)

12+#endif /* MIN_VERSION_fake_package */

13+

14+/* tool gcc-9.2.0 */

15+#ifndef TOOL_VERSION_gcc

16+#define TOOL_VERSION_gcc "9.2.0"

17+#endif /* TOOL_VERSION_gcc */

18+#ifndef MIN_TOOL_VERSION_gcc

19+#define MIN_TOOL_VERSION_gcc(major1,major2,minor) (\

20+ (major1) < 9 || \

21+ (major1) == 9 && (major2) < 2 || \

22+ (major1) == 9 && (major2) == 2 && (minor) <= 0)

23+#endif /* MIN_TOOL_VERSION_gcc */

24+

25+/* tool ghc-8.6.5 */

26+#ifndef TOOL_VERSION_ghc

27+#define TOOL_VERSION_ghc "8.6.5"

28+#endif /* TOOL_VERSION_ghc */

29+#ifndef MIN_TOOL_VERSION_ghc

30+#define MIN_TOOL_VERSION_ghc(major1,major2,minor) (\

31+ (major1) < 8 || \

32+ (major1) == 8 && (major2) < 6 || \

33+ (major1) == 8 && (major2) == 6 && (minor) <= 5)

34+#endif /* MIN_TOOL_VERSION_ghc */

35+

36+/* tool ghc-pkg-8.6.5 */

37+#ifndef TOOL_VERSION_ghc_pkg

38+#define TOOL_VERSION_ghc_pkg "8.6.5"

39+#endif /* TOOL_VERSION_ghc_pkg */

40+#ifndef MIN_TOOL_VERSION_ghc_pkg

41+#define MIN_TOOL_VERSION_ghc_pkg(major1,major2,minor) (\

42+ (major1) < 8 || \

43+ (major1) == 8 && (major2) < 6 || \

44+ (major1) == 8 && (major2) == 6 && (minor) <= 5)

45+#endif /* MIN_TOOL_VERSION_ghc_pkg */

46+

47+/* tool haddock-2.22.0 */

48+#ifndef TOOL_VERSION_haddock

49+#define TOOL_VERSION_haddock "2.22.0"

50+#endif /* TOOL_VERSION_haddock */

51+#ifndef MIN_TOOL_VERSION_haddock

52+#define MIN_TOOL_VERSION_haddock(major1,major2,minor) (\

53+ (major1) < 2 || \

54+ (major1) == 2 && (major2) < 22 || \

55+ (major1) == 2 && (major2) == 22 && (minor) <= 0)

56+#endif /* MIN_TOOL_VERSION_haddock */

57+

58+/* tool hpc-0.67 */

59+#ifndef TOOL_VERSION_hpc

60+#define TOOL_VERSION_hpc "0.67"

61+#endif /* TOOL_VERSION_hpc */

62+#ifndef MIN_TOOL_VERSION_hpc

63+#define MIN_TOOL_VERSION_hpc(major1,major2,minor) (\

64+ (major1) < 0 || \

65+ (major1) == 0 && (major2) < 67 || \

66+ (major1) == 0 && (major2) == 67 && (minor) <= 0)

67+#endif /* MIN_TOOL_VERSION_hpc */

68+

69+/* tool hsc2hs-0.68.5 */

70+#ifndef TOOL_VERSION_hsc2hs

71+#define TOOL_VERSION_hsc2hs "0.68.5"

72+#endif /* TOOL_VERSION_hsc2hs */

73+#ifndef MIN_TOOL_VERSION_hsc2hs

74+#define MIN_TOOL_VERSION_hsc2hs(major1,major2,minor) (\

75+ (major1) < 0 || \

76+ (major1) == 0 && (major2) < 68 || \

77+ (major1) == 0 && (major2) == 68 && (minor) <= 5)

78+#endif /* MIN_TOOL_VERSION_hsc2hs */

79+

80+/* tool pkg-config-1.6.3 */

81+#ifndef TOOL_VERSION_pkg_config

82+#define TOOL_VERSION_pkg_config "1.6.3"

83+#endif /* TOOL_VERSION_pkg_config */

84+#ifndef MIN_TOOL_VERSION_pkg_config

85+#define MIN_TOOL_VERSION_pkg_config(major1,major2,minor) (\

86+ (major1) < 1 || \

87+ (major1) == 1 && (major2) < 6 || \

88+ (major1) == 1 && (major2) == 6 && (minor) <= 3)

89+#endif /* MIN_TOOL_VERSION_pkg_config */

90+

91+/* tool runghc-8.6.5 */

92+#ifndef TOOL_VERSION_runghc

93+#define TOOL_VERSION_runghc "8.6.5"

94+#endif /* TOOL_VERSION_runghc */

95+#ifndef MIN_TOOL_VERSION_runghc

96+#define MIN_TOOL_VERSION_runghc(major1,major2,minor) (\

97+ (major1) < 8 || \

98+ (major1) == 8 && (major2) < 6 || \

99+ (major1) == 8 && (major2) == 6 && (minor) <= 5)

100+#endif /* MIN_TOOL_VERSION_runghc */

101+

102+/* tool strip-2.33 */

103+#ifndef TOOL_VERSION_strip

104+#define TOOL_VERSION_strip "2.33"

105+#endif /* TOOL_VERSION_strip */

106+#ifndef MIN_TOOL_VERSION_strip

107+#define MIN_TOOL_VERSION_strip(major1,major2,minor) (\

108+ (major1) < 2 || \

109+ (major1) == 2 && (major2) < 33 || \

110+ (major1) == 2 && (major2) == 33 && (minor) <= 0)

111+#endif /* MIN_TOOL_VERSION_strip */

112+

113+#ifndef CURRENT_COMPONENT_ID

114+#define CURRENT_COMPONENT_ID "fake-package-0-inplace-script"

115+#endif /* CURRENT_COMPONENT_ID */

116+#ifndef CURRENT_PACKAGE_VERSION

117+#define CURRENT_PACKAGE_VERSION "0"

118+#endif /* CURRENT_PACKAGE_VERSION */

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dist-newstyle/cache/plan.jsonnew file+1

@@ -0,0 +1 @@

1+{"cabal-version":"2.4.1.0","cabal-lib-version":"2.4.1.0","compiler-id":"ghc-8.6.5","os":"linux","arch":"x86_64","install-plan":[{"type":"pre-existing","id":"array-0.5.3.0","pkg-name":"array","pkg-version":"0.5.3.0","depends":["base-4.12.0.0"]},{"type":"pre-existing","id":"base-4.12.0.0","pkg-name":"base","pkg-version":"4.12.0.0","depends":["ghc-prim-0.5.3","integer-gmp-1.0.2.0","rts"]},{"type":"pre-existing","id":"deepseq-1.4.4.0","pkg-name":"deepseq","pkg-version":"1.4.4.0","depends":["array-0.5.3.0","base-4.12.0.0"]},{"type":"configured","id":"fake-package-0-inplace-script","pkg-name":"fake-package","pkg-version":"0","flags":{},"style":"local","pkg-src":{"type":"local","path":"/tmp/cabal-repl.-15730"},"dist-dir":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/dist-newstyle/build/x86_64-linux/ghc-8.6.5/fake-package-0/x/script","depends":[],"exe-depends":[],"component-name":"exe:script","bin-file":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/dist-newstyle/build/x86_64-linux/ghc-8.6.5/fake-package-0/x/script/build/script/script"},{"type":"pre-existing","id":"ghc-prim-0.5.3","pkg-name":"ghc-prim","pkg-version":"0.5.3","depends":["rts"]},{"type":"pre-existing","id":"integer-gmp-1.0.2.0","pkg-name":"integer-gmp","pkg-version":"1.0.2.0","depends":["ghc-prim-0.5.3"]},{"type":"configured","id":"laop-0.1.0.0-inplace","pkg-name":"laop","pkg-version":"0.1.0.0","flags":{},"style":"local","pkg-src":{"type":"local","path":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/."},"dist-dir":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/dist-newstyle/build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0","depends":["base-4.12.0.0","deepseq-1.4.4.0"],"exe-depends":[],"component-name":"lib"},{"type":"configured","id":"laop-0.1.0.0-inplace-laop-exe","pkg-name":"laop","pkg-version":"0.1.0.0","flags":{},"style":"local","pkg-src":{"type":"local","path":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/."},"dist-dir":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/dist-newstyle/build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/x/laop-exe","depends":["base-4.12.0.0","deepseq-1.4.4.0","laop-0.1.0.0-inplace"],"exe-depends":[],"component-name":"exe:laop-exe","bin-file":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/dist-newstyle/build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/x/laop-exe/build/laop-exe/laop-exe"},{"type":"configured","id":"laop-0.1.0.0-inplace-laop-test","pkg-name":"laop","pkg-version":"0.1.0.0","flags":{},"style":"local","pkg-src":{"type":"local","path":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/."},"dist-dir":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/dist-newstyle/build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/t/laop-test","depends":["base-4.12.0.0","laop-0.1.0.0-inplace"],"exe-depends":[],"component-name":"test:laop-test","bin-file":"/home/bolt/Desktop/Bolt/Playground/Haskell/laop/dist-newstyle/build/x86_64-linux/ghc-8.6.5/laop-0.1.0.0/t/laop-test/build/laop-test/laop-test"},{"type":"pre-existing","id":"rts","pkg-name":"rts","pkg-version":"1.0","depends":[]}]}

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hackage.shnew file+10

@@ -0,0 +1,10 @@

1+#!/bin/sh

2+set -e

4+dir=$(mktemp -d dist-docs.XXXXXX)

5+trap 'rm -r "$dir"' EXIT

7+# assumes cabal 2.4 or later

8+cabal v2-haddock --builddir="$dir" --haddock-for-hackage --enable-doc

10+cabal upload -d $dir/*-docs.tar.gz

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src/LAoP/Relation/Internal.hs+96−1

@@ -97,6 +97,8 @@ module LAoP.Relation.Internal

9797 divR,

9898 divL,

9999 divS,

100+ shrunkBy,

101+ overriddenBy,

100102

101103 -- * Relational pairing

102104 splitR,

@@ -132,8 +134,13 @@ module LAoP.Relation.Internal

132134 equivalence,

133135 partialEquivalence,

134136

137+ -- * Conditionals

138+ equalizer,

139+

135140 -- ** McCarthy's Conditional

136− -- cond,

141+ predR,

142+ guard,

143+ cond,

137144

138145 -- * Relational composition and lifting

139146 identity,

@@ -143,6 +150,7 @@ module LAoP.Relation.Internal

143150

144151 -- ** Relational application

145152 pointAp,

153+ pointApBool,

146154

147155 -- * Matrix printing

148156 pretty,

@@ -387,6 +395,30 @@ divL (R x) (R y) = R (I.divL x y)

387395divS :: Relation c a -> Relation b a -> Relation c b

388396divS (R x) (R y) = R (I.divS x y)

389397

398+-- | Relational shrinking.

399+--

400+-- @r `'shrunkBy'` s@ is the largest part of @r@ such that,

401+-- if it yields an output for an input @x@, it must be a maximum,

402+-- with respect to @s@, among all possible outputs of @x@ by @r@.

403+shrunkBy :: Relation b a -> Relation a a -> Relation b a

404+shrunkBy r s = r `intersection` divR s (conv r)

405+

406+-- | Relational overriding.

407+--

408+-- @r `'overriddenBy'` s@ yields the relation which contains the

409+-- whole of @s@ and that part of @r@ where @s@ is undefined.

410+--

411+-- @

412+-- 'zeros' `'overriddenBy'` s == s

413+-- r `'overriddenBy'` 'zeros' == r

414+-- r `'overriddenBy'` r == r

415+-- @

416+overriddenBy ::

417+ ( I.FromLists Boolean (I.Normalize b) (I.Normalize b),

418+ KnownNat (I.Count (I.Normalize b))

419+ ) => Relation a b -> Relation a b -> Relation a b

420+overriddenBy r s = s `union` r `intersection` divR zeros (conv s)

421+

390422-- | Relational application

391423pointAp ::

392424 ( Bounded a,

@@ -402,6 +434,21 @@ pointAp ::

402434 ) => a -> b -> Relation a b -> Relation One One

403435pointAp a b r = conv (point b) `comp` r `comp` point a

404436

437+-- | Relational application

438+pointApBool ::

439+ ( Bounded a,

440+ Bounded b,

441+ Enum a,

442+ Enum b,

443+ Eq a,

444+ Eq b,

445+ KnownNat (I.Count (I.Normalize a)),

446+ KnownNat (I.Count (I.Normalize b)),

447+ I.FromLists Boolean (I.Normalize a) One,

448+ I.FromLists Boolean (I.Normalize b) One

449+ ) => a -> b -> Relation a b -> Bool

450+pointApBool a b r = toBool $ conv (point b) `comp` r `comp` point a

451+

405452-- | Relational converse

406453conv :: Relation a b -> Relation b a

407454conv (R a) = R (I.tr a)

@@ -733,6 +780,54 @@ untrans ::

733780 => Relation a (c, b) -> Relation (a, b) c

734781untrans s = p1 `comp` conv (splitR (conv s) p2)

735782

783+-- | Transforms predicate @p@ into a correflexive relation.

784+predR ::

785+ ( Bounded a,

786+ Enum a,

787+ KnownNat (I.Count (I.Normalize a)),

788+ I.FromLists Boolean (I.Normalize a) (I.Normalize a),

789+ I.FromLists Boolean (I.Normalize Bool) (I.Normalize a)

790+ )

791+ => (a -> Bool) -> Relation a a

792+predR p = identity `intersection` divisionF (fromF' (const True)) (fromF' p)

793+

794+-- | Equalizes functions @f@ and @g@.

795+-- That is, @'equalizer' f g@ is the largest coreflexive

796+-- that restricts @g@ so that @f@ and @g@ yield the same outputs.

797+equalizer ::

798+ ( KnownNat (I.Count (I.Normalize a)),

799+ I.FromLists Boolean (I.Normalize a) (I.Normalize a)

800+ )

801+ => Relation a b -> Relation a b -> Relation a a

802+equalizer f g = identity `intersection` divisionF f g

803+

804+-- | Relational conditional guard.

805+--

806+-- @

807+-- 'guard' p = 'i2' `'overriddenBy'` 'i1' `'comp'` 'predR' p

808+-- @

809+guard ::

810+ ( Bounded b,

811+ Enum b,

812+ KnownNat (I.Count (I.Normalize b)),

813+ I.FromLists Boolean (I.Normalize b) (I.Normalize b),

814+ I.FromLists Boolean (I.Normalize Bool) (I.Normalize b),

815+ I.Normalize (Either b b) ~ Either (I.Normalize b) (I.Normalize b)

816+ ) => (b -> Bool) -> Relation b (Either b b)

817+guard p = conv (eitherR (predR p) (predR (not . p)))

818+

819+-- | Relational McCarthy's conditional.

820+cond ::

821+ ( Bounded b,

822+ Enum b,

823+ KnownNat (I.Count (I.Normalize b)),

824+ I.FromLists Boolean (I.Normalize b) (I.Normalize b),

825+ I.FromLists Boolean (I.Normalize Bool) (I.Normalize b),

826+ I.Normalize (Either b b) ~ Either (I.Normalize b) (I.Normalize b)

827+ )

828+ => (b -> Bool) -> Relation b c -> Relation b c -> Relation b c

829+cond p r s = eitherR r s `comp` guard p

830+

736831-- Relation pretty print

737832

738833-- | Relation pretty printing