master..28f7b16 · laop

git.iko.soy/laop

36 files changed+3619−1527

unifiedsplit

.ghc.environment.x86_64-linux-8.6.5+17 .github/workflows/ci.yml−43 .gitignore+2−54 .travis.yml−47 CHANGELOG.md−17 ChangeLog.md+3 LICENSE+26−17 README.md+30−34 Setup.hs+2 benchmark/Main.hs → app/Benchmarks.hs+18−16 test/Examples/Readme.hs → app/Examples.hs+31−56 app/Main.hs+7 test/Examples/Spreadsheets.hs → app/Spreadsheets.hs+20−9 appveyor.yml−34 hackage.sh+10 laop-0.1.0.0-docs.tar.gz laop.cabal−89 package.yaml+57 report-lazy.html+1169 report-lazy.pdf report-strict.html+1169 report-strict.pdf src/LAoP/Dist.hs+2−2 src/LAoP/Dist/Internal.hs+45−46 src/LAoP/Matrix/Internal.hs+390−371 src/LAoP/Matrix/Nat.hs+124−139 src/LAoP/Matrix/Type.hs+180−224 src/LAoP/Relation.hs+9−8 src/LAoP/Relation/Internal.hs+234−245 src/LAoP/Utils.hs+1−4 src/LAoP/Utils/Internal.hs+2−28 stack-8.8.3.yaml−1 stack.yaml+66−1 stack.yaml.lock+4−4 test/Examples/Quantum.hs−31 test/Spec.hs+1−7

.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

.github/workflows/ci.ymldeleted−43

@@ -1,43 +0,0 @@

1−name: CI

2−

3−# Trigger the workflow on push or pull request, but only for the master branch

4−on:

5− pull_request:

6− push:

7− branches: [master]

8−

9−jobs:

10− build:

11− name: ghc ${{ matrix.ghc }}

12− runs-on: ubuntu-16.04

13− strategy:

14− matrix:

15− cabal: ["3.0"]

16− ghc:

17− - "8.6.5"

18− - "8.8.3"

19−

20− steps:

21− - uses: actions/checkout@v2

22− if: github.event.action == 'opened' || github.event.action == 'synchronize' || github.event.ref == 'refs/heads/master'

23−

24− - uses: actions/setup-haskell@v1

25− name: Setup Haskell

26− with:

27− ghc-version: ${{ matrix.ghc }}

28− cabal-version: ${{ matrix.cabal }}

29−

30− - uses: actions/cache@v1

31− name: Cache ~/.cabal/store

32− with:

33− path: ~/.cabal/store

34− key: ${{ runner.os }}-${{ matrix.ghc }}-cabal

35−

36− - name: Build

37− run: |

38− cabal v2-update

39− cabal v2-build --enable-tests --enable-benchmarks

40−

41− - name: Test

42− run: |

43− cabal v2-test --enable-tests

.gitignore+2−54

@@ -1,55 +1,3 @@

1−### Haskell

2−dist

3−dist-*

4−cabal-dev

5−*.o

6−*.hi

7−*.chi

8−*.chs.h

9−*.dyn_o

10−*.dyn_hi

11−*.prof

12−*.aux

13−*.hp

14−*.eventlog

15−.virtualenv

16−.hsenv

17−.hpc

18−.cabal-sandbox/

19−cabal.sandbox.config

20−cabal.config

21−cabal.project.local

22−.ghc.environment.*

23−.HTF/

24−# Stack

251.stack-work/

26−stack.yaml.lock

27−

28−### IDE/support

29−# Vim

30−[._]*.s[a-v][a-z]

31−[._]*.sw[a-p]

32−[._]s[a-v][a-z]

33−[._]sw[a-p]

34−*~

35−tags

36−

37−# IntellijIDEA

38−.idea/

39−.ideaHaskellLib/

40−*.iml

41−

42−# Atom

43−.haskell-ghc-mod.json

44−

45−# VS

46−.vscode/

47−

48−# Emacs

49−*#

50−.dir-locals.el

51−TAGS

52−

53−# other

54−.DS_Store

55−hackage.sh

2+laop.cabal

3+*~

.travis.ymldeleted−47

@@ -1,47 +0,0 @@

1−sudo: true

2−language: haskell

3−

4−git:

5− depth: 5

6−

7−cabal: "3.0"

8−

9−cache:

10− directories:

11− - "$HOME/.cabal/store"

12− - "$HOME/.stack"

13− - "$TRAVIS_BUILD_DIR/.stack-work"

14−

15−matrix:

16− include:

17− - ghc: 8.6.5

18− - ghc: 8.8.3

19−

20− - ghc: 8.8.3

21− env: STACK_YAML="$TRAVIS_BUILD_DIR/stack-8.8.3.yaml"

22−

23− - ghc: 8.6.5

24− env: STACK_YAML="$TRAVIS_BUILD_DIR/stack.yaml"

25−

26−

27−install:

28− - |

29− if [ -z "$STACK_YAML" ]; then

30− cabal v2-update

31− cabal v2-build --enable-tests --enable-benchmarks

32− else

33− curl -sSL https://get.haskellstack.org/ | sh

34− stack --version

35− stack build --system-ghc --test --bench --no-run-tests --no-run-benchmarks

36− fi

37−

38−script:

39− - |

40− if [ -z "$STACK_YAML" ]; then

41− cabal v2-test --enable-tests

42− else

43− stack test --system-ghc

44− fi

45−

46−notifications:

47− email: false

CHANGELOG.mddeleted−17

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

1−# Changelog

2−

3−`laop` uses [PVP Versioning][1].

4−The changelog is available [on GitHub][2].

5−

6−## 0.1.1.1

7−

8−* Bump base version to work with cabal

9−

10−## 0.1.1.0

11−

12−* Package is more organized and now has tests and benchmarks separated

13−* Repository is more organized and clean

14−* Added CI

15−

16−[1]: https://pvp.haskell.org

17−[2]: https://github.com/bolt12/laop2/releases

ChangeLog.mdnew file+3

@@ -0,0 +1,3 @@

1+# Changelog for laop

3+## Unreleased changes

LICENSE+26−17

@@ -1,21 +1,30 @@

1−MIT License

5−Permission is hereby granted, free of charge, to any person obtaining a copy

6−of this software and associated documentation files (the "Software"), to deal

7−in the Software without restriction, including without limitation the rights

8−to use, copy, modify, merge, publish, distribute, sublicense, and/or sell

9−copies of the Software, and to permit persons to whom the Software is

10−furnished to do so, subject to the following conditions:

5+Redistribution and use in source and binary forms, with or without

6+modification, are permitted provided that the following conditions are met:

117

12−The above copyright notice and this permission notice shall be included in all

13−copies or substantial portions of the Software.

8+ * Redistributions of source code must retain the above copyright

9+ notice, this list of conditions and the following disclaimer.

1410

15−THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

16−IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

17−FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE

18−AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

19−LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,

20−OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

21−SOFTWARE.

11+ * Redistributions in binary form must reproduce the above

12+ copyright notice, this list of conditions and the following

13+ disclaimer in the documentation and/or other materials provided

14+ with the distribution.

15+

16+ * Neither the name of Armando Santos nor the names of other

17+ contributors may be used to endorse or promote products derived

18+ from this software without specific prior written permission.

19+

20+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS

21+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT

22+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR

23+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT

24+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,

25+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT

26+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,

27+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY

28+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT

29+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE

30+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

README.md+30−34

@@ -1,11 +1,5 @@

11# laop - Linear Algebra of Programming library

3−[![GitHub CI](https://github.com/bolt12/laop/workflows/CI/badge.svg)](https://github.com/bolt12/laop/actions)

4−[![Build status](https://img.shields.io/travis/bolt12/laop.svg?logo=travis)](https://travis-ci.org/bolt12/laop)

5−[![Hackage](https://img.shields.io/hackage/v/laop.svg?logo=haskell)](https://hackage.haskell.org/package/laop)

6−[![Stackage Lts](http://stackage.org/package/laop/badge/lts)](http://stackage.org/lts/package/laop)

7−[![Stackage Nightly](http://stackage.org/package/laop/badge/nightly)](http://stackage.org/nightly/package/laop)

8−

93The LAoP discipline generalises relations and functions treating them as

104Boolean matrices and in turn consider these as arrows.

115

@@ -16,38 +10,40 @@ motivation behind the library, the underlying theory, and implementation details

1610This module offers many of the combinators mentioned in the work of

1711[Macedo (2012)](https://repositorium.sdum.uminho.pt/handle/1822/22894) and [Oliveira (2012)](https://pdfs.semanticscholar.org/ccf5/27fa9179081223bffe8067edd81948644fc0.pdf).

1812

19−See the package in hackage [here](https://hackage.haskell.org/package/laop-0.1.1.0)

20−

21−A Functional Pearl has been written and can be regarded as the [reference document](https://github.com/bolt12/tymfgg-pearl) for this library.

22−

23−## Features

24−

25−This library offers 3 main matrix programming modules:

13+See the package in hackage [here](https://hackage.haskell.org/package/laop-0.1.0.5)

2614

27−- One in which matrices are typed with type level natural numbers;

28−- One in which matrices are typed with arbitrary generic data types;

29−- One in which matrices are regarded as relations, i.e. boolean matrices;

15+There are a couple of repos with a WIP of benchmarks comparing [matrix composition](https://github.com/bolt12/laop-benchmarks) and a real use case of [data analytics](https://github.com/bolt12/laop-analytics).

3016

31−There's also an experimental module that uses matrices to represent probability

32−distributions.

17+A Functional Pearl is also on its way, hopefully will be the reference document for this library.

3318

34−The most interesting feature is that matrices are represented as an inductive data type.

35−Given this formulation, matrix algorithms can be expressed in a much more elegant and

36−calculational style than the traditional vector of vectors representation. This data type

37−guarantees that a matrix will always have valid dimensions. It can also express block matrix

38−computations naturally, which leads to total, efficient and statically typed manipulation

39−and transformation functions.

40−

41−Like matrix multiplication, other common operations, such as matrix transposition, benefit from a block-oriented structure that leads to a simple and natural divide-and-conquer algorithmic solution. Performance wise, this means that without much effort we can obtain optimal cache-oblivious algorithms.

42−

43−Given this, this new matrix formulation compared to other libraries:

44−

45−- Is more compositional and polymorphic and does not have partial matrix manipulation functions (hence less chances for usage errors);

46−- Our implementation of matrices enables simple manipulation of submatrices, making it particularly suitable for formal verification and equation reasoning, using the mathematical framework defined by the linear algebra of programming. Furthermore, the data type constructors ensure that the matrices of this kind are sound, i.e. malformed matrices with incorrect dimensions of the sort, can not be constructed.

47−

48−## Known issues

19+## Features

4920

50−Unfortunately, due to the use of type-level programming features, this approach sometimes requires type dimensions to be constrainted, in some way, impossible to write idiomatic Arrow instances, for example. Type inference isn't perfect, when it comes to infer the types of matrices which dimensions are computed using type level naturals multiplication, the compiler needs type annotations in order to succeed. And not all kinds of programs can be modeled using matrices, namely programs that deal with arbitrary infinite data types such as lists or integers (although there are some workarounds).

21+This library offers:

22+

23+- An internal module representation that uses normal datatypes (`Void`, `()`, `Either`) for matrix dimensions and two

24+ type families `FromNat` and `Count` to make it easier to work with these type of matrices.

25+- An interfacing module that uses generalised types for the dimensions and is just a newtype wrapper

26+ around the internal matrix data type.

27+- An interfacing module that uses type level naturals for the dimensions and is just a newtype wrapper

28+ around the internal matrix data type.

29+- An interfacing module that restricts the matrix contents to being only 0's or 1's (True

30+ and False). This module is called 'Relation' and offers many of the combinators seen in

31+ AoP and Relational Calculus/Algebra.

32+- A very simple Probabilistic Programming module and several functions and data types to

33+ make it easier to deal with sample space.

34+

35+Given this, this new matrix formulation compared to other libraries one has much more advantages, such as:

36+

37+- Has an inductive definition enabling writing matrix manipulation functions in a much more elegant and calculational way;

38+- Statically typed dimensions;

39+- Polymorphic data type dimensions;

40+- Polymorphic matrix content;

41+- Awesome dimension type inference;

42+- Fast type natural conversion via `FromNat` type family;

43+- Matrix `Junc` and `Split`-ing in O(1);

44+- Matrix composition takes advantage of divide-and-conquer and fusion laws.

45+

46+Unfortunately, this approach does not solve the issue of type dimensions being in some way constrainted making it impossible to write Arrow instances, for example. Type inference isn't perfect, when it comes to infer the types of matrices which dimensions are computed using type level naturals multiplication, the compiler needs type annotations in order to succeed.

5147

5248## Notes

5349

Setup.hsnew file+2

@@ -0,0 +1,2 @@

1+import Distribution.Simple

2+main = defaultMain

benchmark/Main.hs → app/Benchmarks.hsrenamed+18−16

@@ -8,36 +8,38 @@

88{-# LANGUAGE AllowAmbiguousTypes #-}

99{-# LANGUAGE ScopedTypeVariables #-}

1010

11−module Main (main) where

11+module Benchmarks

12+ ( benchmark

13+ )

14+ where

1215

1316import LAoP.Dist.Internal

1417import LAoP.Utils

15−import LAoP.Matrix.Type hiding (CountableN, Countable, FLN)

16−import qualified LAoP.Matrix.Type as T (FLN)

18+import LAoP.Matrix.Type hiding (CountableN, Countable, FromListsN)

19+import qualified LAoP.Matrix.Type as T (FromListsN)

1720import Criterion.Main

1821import Control.DeepSeq

1922import Test.QuickCheck

2023import GHC.TypeLits

2124import Data.Proxy

22−import Prelude hiding (id, (.))

2325

2426selectM2 ::

2527 ( Num e,

26− T.FLN b b,

28+ T.FromListsN e b b,

2729 CountableN b

2830 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b

29−selectM2 m y = join y iden `comp` m

31+selectM2 m y = junc y identity `comp` m

3032

3133selectD2 ::

32− ( FLN b b,

34+ ( FromListsN b b,

3335 CountableN b

3436 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b

35−selectD2 (D d) m = D (join m iden `comp` d)

37+selectD2 (D d) m = D (junc m identity `comp` d)

3638

37−-- Composition with iden

38−compId m = comp iden m

39+-- Composition with identity

40+compId m = comp identity m

3941

40−randomDist :: forall a . (Countable a, FLN () a) => Gen (Dist a)

42+randomDist :: forall a . (Countable a, FromListsN () a) => Gen (Dist a)

4143randomDist = do

4244 let size = fromInteger (natVal (Proxy :: Proxy (Count a)))

4345 l <- vectorOf size (arbitrary :: Gen Prob)

@@ -46,7 +48,7 @@ randomDist = do

4648 m = fromLists lr

4749 return (D m)

4850

49−randomMatrix :: forall a b . (CountableDims a b, FLN a b) => Gen (Matrix Prob a b)

51+randomMatrix :: forall a b . (CountableDimensions a b, FromListsN a b) => Gen (Matrix Prob a b)

5052randomMatrix = do

5153 let cols = fromInteger (natVal (Proxy :: Proxy (Count a)))

5254 rows = fromInteger (natVal (Proxy :: Proxy (Count b)))

@@ -105,7 +107,7 @@ normalize3 as l = let s = sum l

105107 probs = map (/ s) l

106108 in zip as probs

107109

108−randomDistF :: forall a b . (CountableDims a b, CoArbitrary a, Arbitrary b) => Gen (Dist' (a -> b))

110+randomDistF :: forall a b . (CountableDimensions a b, CoArbitrary a, Arbitrary b) => Gen (Dist' (a -> b))

109111randomDistF = do

110112 let a = fromInteger (natVal (Proxy :: Proxy (Count a)))

111113 b = fromInteger (natVal (Proxy :: Proxy (Count b)))

@@ -144,8 +146,8 @@ setupEnv2 = do

144146 distList2 <- generate (resize 1 (randomDistF @(Natural 0 100) @(Natural 0 100)))

145147 return (m21, m40, dist, dist2, distList1, distList2)

146148

147−main :: IO ()

148−main = defaultMain [

149+benchmark :: IO ()

150+benchmark = defaultMain [

149151 env setupEnv $ \ ~(m11, m12, m21, m22, m31, m32) -> bgroup "Matrix Composition" [

150152 bgroup "10x10" [

151153 bench "WHNF - 10x10" $ whnf (comp m11) m12

@@ -160,7 +162,7 @@ main = defaultMain [

160162 , bench "NF - 200x200" $ nf (comp m31) m32

161163 ],

162164 bgroup "200x200 - RULES" [

163− bench "No rules - 200x200" $ nf (comp m21) iden

165+ bench "No rules - 200x200" $ nf (comp m21) identity

164166 , bench "Rules - 200x200" $ nf compId m21

165167 ] ],

166168 env setupEnv2 $ \ ~(m21, m40, dist, dist2, dl1, dl2) -> bgroup "Matrix vs List - `select`" [

test/Examples/Readme.hs → app/Examples.hsrenamed+31−56

@@ -1,10 +1,10 @@

1−{-# LANGUAGE GADTs #-}

21{-# LANGUAGE DeriveGeneric #-}

32{-# LANGUAGE FlexibleContexts #-}

3+{-# LANGUAGE TypeOperators #-}

44{-# LANGUAGE TypeApplications #-}

55{-# LANGUAGE DataKinds #-}

7−module Examples.Readme

7+module Examples

88 ( exec

99 )

1010 where

@@ -15,12 +15,13 @@ import LAoP.Utils

1515import LAoP.Dist

1616import GHC.TypeLits

1717import Data.Coerce

18−import qualified GHC.Generics as G

19−import Prelude hiding (id, (.))

18+import GHC.Generics

19+import Control.Category hiding (id)

20+import Prelude hiding ((.))

2021

2122-- Monty Hall Problem

2223data Outcome = Win | Lose

23− deriving (Bounded, Enum, Eq, Show, G.Generic)

24+ deriving (Bounded, Enum, Eq, Show, Generic)

2425

2526switch :: Outcome -> Outcome

2627switch Win = Lose

@@ -30,7 +31,7 @@ firstChoice :: Matrix Double () Outcome

3031firstChoice = col [1/3, 2/3]

3132

3233secondChoice :: Matrix Double Outcome Outcome

33−secondChoice = fromF switch

34+secondChoice = fromF' switch

3435

3536-- Dice sum

3637

@@ -39,7 +40,7 @@ type SS = Natural 1 6 -- Sample Space

3940sumSS :: SS -> SS -> Natural 2 12

4041sumSS = coerceNat (+)

4142

42−sumSSM = fromF (uncurry sumSS)

43+sumSSM = fromF' (uncurry sumSS)

4344

4445condition :: (Int, Int) -> Int -> Int

4546condition (fst, snd) thrd = if fst == snd

@@ -49,64 +50,38 @@ condition (fst, snd) thrd = if fst == snd

4950conditionSS :: (SS, SS) -> SS -> Natural 3 18

5051conditionSS = coerceNat2 condition

5152

52−conditionalThrows = fromF (uncurry conditionSS) . kr (kr die die) die

53+conditionalThrows = fromF' (uncurry conditionSS) . khatri (khatri die die) die

5354

5455die :: Matrix Double () SS

5556die = col $ map (const (1/6)) [nat @1 @6 1 .. nat 6]

5657

5758-- Sprinkler

58−data G = Dry | Wet

59− deriving (Bounded, Enum, Eq, Show, G.Generic)

6059

61−data S = Off | On

62− deriving (Bounded, Enum, Eq, Show, G.Generic)

60+rain :: Matrix Double () Bool

61+rain = col [0.8, 0.2]

6362

64−data R = No | Yes

65− deriving (Bounded, Enum, Eq, Show, G.Generic)

63+sprinkler :: Matrix Double Bool Bool

64+sprinkler = fromLists [[0.6, 0.99], [0.4, 0.01]]

6665

67−rain :: Matrix Double () R

68−rain = matrixBuilder gen

69− where

70− gen (_, No) = 0.8

71− gen (_, Yes) = 0.2

72−

73−sprinkler :: Matrix Double R S

74−sprinkler = matrixBuilder gen

75− where

76− gen (No, Off) = 0.6

77− gen (No, On) = 0.4

78− gen (Yes, Off) = 0.99

79− gen (Yes, On) = 0.01

80−

81−grass :: Matrix Double (S, R) G

82−grass = matrixBuilder gen

83− where

84− gen ((Off, No), Dry) = 1

85− gen ((Off, Yes), Dry) = 0.2

86− gen ((On, No), Dry) = 0.1

87− gen ((On, Yes), Dry) = 0.01

88− gen ((Off, No), Wet) = 0

89− gen ((Off, Yes), Wet) = 0.8

90− gen ((On, No), Wet) = 0.9

91− gen ((On, Yes), Wet) = 0.99

92−

93−tag f = kr f id

66+grass :: Matrix Double (Bool, Bool) Bool

67+grass = fromLists [[1, 0.2, 0.1, 0.01], [0, 0.8, 0.9, 0.99]]

9468

95−state g s r = tag g . tag s . r

69+state :: Matrix Double () (Bool, (Bool, Bool))

70+state = khatri grass identity . khatri sprinkler identity . rain

9671

97−grass_wet :: Matrix Double () (G, (S, R)) -> Matrix Double One One

98−grass_wet state = row [0,1] . fstM . state

72+grass_wet :: Matrix Double (Bool, (Bool, Bool)) One

73+grass_wet = row [0,1] . kp1

9974

100−rainning :: Matrix Double (G, (S, R)) One

101−rainning = row [0,1] . sndM . sndM

75+rainning :: Matrix Double (Bool, (Bool, Bool)) One

76+rainning = row [0,1] . kp2 . kp2

10277

10378-- Alcuin Puzzle

10479

10580data Being = Farmer | Fox | Goose | Beans

106− deriving (Bounded, Enum, Eq, Show, G.Generic)

81+ deriving (Bounded, Enum, Eq, Show, Generic)

10782

10883data Bank = LeftB | RightB

109− deriving (Bounded, Enum, Eq, Show, G.Generic)

84+ deriving (Bounded, Enum, Eq, Show, Generic)

11085

11186eats :: Being -> Being -> Bool

11287eats Fox Goose = True

@@ -121,21 +96,21 @@ cross LeftB = RightB

12196cross RightB = LeftB

12297

12398crossR :: R.Relation Bank Bank

124−crossR = R.fromF cross

99+crossR = R.fromF' cross

125100

126101-- | Initial state, everyone in the left bank

127102locationLeft :: Being -> Bank

128103locationLeft _ = LeftB

129104

130105locationLeftR :: R.Relation Being Bank

131−locationLeftR = R.fromF locationLeft

106+locationLeftR = R.fromF' locationLeft

132107

133108-- | Initial state, everyone in the right bank

134109locationRight :: Being -> Bank

135110locationRight _ = RightB

136111

137112locationRightR :: R.Relation Being Bank

138−locationRightR = R.fromF locationRight

113+locationRightR = R.fromF' locationRight

139114

140115-- Properties

141116

@@ -152,7 +127,7 @@ inv :: R.Relation Being Bank -> Bool

152127inv w = (w `R.comp` canEat w) `R.sse` (w `R.comp` farmer)

153128 where

154129 farmer :: R.Relation Being Being

155− farmer = R.fromF (const Farmer)

130+ farmer = R.fromF' (const Farmer)

156131

157132-- Arbitrary state

158133bankState :: Being -> Bank -> Bool

@@ -171,14 +146,14 @@ exec = do

171146 putStrLn "Monty Hall Problem solution:"

172147 prettyPrint (secondChoice . firstChoice)

173148 putStrLn "\n Sum of dices probability:"

174− prettyPrint (sumSSM . kr die die)

149+ prettyPrint (sumSSM `comp` khatri die die)

175150 putStrLn "\n Conditional dice throw:"

176151 prettyPrint conditionalThrows

177152 putStrLn "\n Checking that the last result is indeed a distribution: "

178− prettyPrint (bang . sumSSM . kr die die)

153+ prettyPrint (bang . sumSSM . khatri die die)

179154 putStrLn "\n Probability of grass being wet:"

180− prettyPrint (grass_wet (state grass sprinkler rain))

155+ prettyPrint (grass_wet . state)

181156 putStrLn "\n Probability of rain:"

182− prettyPrint (rainning . state grass sprinkler rain)

157+ prettyPrint (rainning . state)

183158 putStrLn "\n Is the arbitrary state a valid state? (Alcuin Puzzle)"

184159 print (inv bankStateR)

app/Main.hsnew file+7

@@ -0,0 +1,7 @@

1+module Main where

3+import Examples

4+import Benchmarks

6+main :: IO ()

7+main = benchmark

test/Examples/Spreadsheets.hs → app/Spreadsheets.hsrenamed+20−9

@@ -1,11 +1,14 @@

1+{-# LANGUAGE DataKinds #-}

2+{-# LANGUAGE GADTs #-}

3+{-# LANGUAGE FlexibleContexts #-}

14{-# LANGUAGE DeriveGeneric #-}

3−module Examples.Spreadsheets

6+module Spreadsheets

7+ where

5−import LAoP.Utils

69import LAoP.Matrix.Type

10+import qualified LAoP.Matrix.Internal as I

711import GHC.Generics

8−import Prelude hiding (id, (.))

912

1013data Student = Student1 | Student2 | Student3 | Student4

1114 deriving (Eq, Show, Enum, Bounded, Generic)

@@ -35,13 +38,21 @@ xls :: Matrix Float Question One

3538 -> Matrix Float Question Student

3639 -> Matrix Float Student One

3740 -> Matrix Float (Either Question Results) (Either One Student)

38−xls w m t = join (fork w m) (fork zeros r)

41+xls w m t = junc (split w m) (split zeros r)

3942 where

40− rExam = m . tr w

43+ rExam = m `comp` tr w

4144 rTest = tr t

42− rFinal = rTest `maxPW` rExam

43− r = (rExam . tr exam) + (rTest . tr test) + (rFinal . tr final)

45+ rFinal = rTest `maxPP` rExam

46+ r = (rExam `comp` tr exam) + (rTest `comp` tr test) + (rFinal `comp` tr final)

4447

4548-- | Overloaded, point-wise 'max' function

46−maxPW :: Ord e => Matrix e a b -> Matrix e a b -> Matrix e a b

47−maxPW = zipWithM max

49+maxPP_ :: Ord e => I.Matrix e a b -> I.Matrix e a b -> I.Matrix e a b

50+maxPP_ I.Empty I.Empty = I.Empty

51+maxPP_ (I.One a) (I.One b) = I.One (a `max` b)

52+maxPP_ (I.Junc a b) (I.Junc c d) = I.Junc (maxPP_ a c) (maxPP_ b d)

53+maxPP_ (I.Split a b) (I.Split c d) = I.Split (maxPP_ a c) (maxPP_ b d)

54+maxPP_ x@(I.Split _ _) y@(I.Junc _ _) = maxPP_ x (I.abideJS y)

55+maxPP_ x@(I.Junc _ _) y@(I.Split _ _) = maxPP_ (I.abideJS x) y

56+

57+maxPP :: Ord e => Matrix e a b -> Matrix e a b -> Matrix e a b

58+maxPP (M a) (M b) = M (maxPP_ a b)

appveyor.ymldeleted−34

@@ -1,34 +0,0 @@

1−clone_folder: "c:\\WORK"

2−clone_depth: 5

3−

4−# Do not build feature branch with open Pull Requests

5−skip_branch_with_pr: true

6−

7−platform:

8− - x86_64

9−

10−cache:

11− - "C:\\SR"

12− - dist-newstyle

13−

14−environment:

15− global:

16− CABOPTS: --store-dir=C:\\SR

17−

18− matrix:

19− - GHCVER: 8.6.5

20−

21−install:

22− - choco source add -n mistuke -s https://www.myget.org/F/mistuke/api/v2

23− - choco install -y cabal --version 2.4.1.0

24− - choco install -y ghc --version 8.6.3

25− - refreshenv

26−

27−before_build:

28− - cabal --version

29− - ghc --version

30− - cabal %CABOPTS% v2-update

31−

32−build_script:

33− - cabal %CABOPTS% v2-build --enable-tests

34− - cabal %CABOPTS% v2-test --enable-tests

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 --publish

laop-0.1.0.0-docs.tar.gznew file

Binary file not shown.

laop.cabaldeleted−89

@@ -1,89 +0,0 @@

1−cabal-version: 2.4

2−name: laop

3−version: 0.1.1.1

4−synopsis: Matrix programming library

5−description: Matrix programming library that uses a type-safe inductive definition

6− inspired by the Linear Algebra of Programming

7−homepage: https://github.com/bolt12/laop

8−bug-reports: https://github.com/bolt12/laop/issues

9−license: MIT

10−license-file: LICENSE

11−author: Armando Santos

12−maintainer: Armando Santos <armandoifsantos@gmail.com>

13−copyright: 2020 Armando Santos

14−category: Data

15−build-type: Simple

16−extra-doc-files: README.md

17− CHANGELOG.md

18−tested-with: GHC == 8.6.5

19− GHC == 8.8.3

20−

21−source-repository head

22− type: git

23− location: https://github.com/bolt12/laop.git

24−

25−common common-options

26− build-depends: base >= 4.12.0.0 && < 5,

27− deepseq

28−

29− ghc-options: -Wall

30− -Wcompat

31− -Widentities

32− -Wincomplete-uni-patterns

33− -Wincomplete-record-updates

34− if impl(ghc >= 8.0)

35− ghc-options: -Wredundant-constraints

36− if impl(ghc >= 8.2)

37− ghc-options: -fhide-source-paths

38− if impl(ghc >= 8.4)

39− ghc-options: -Wmissing-export-lists

40− -Wpartial-fields

41− if impl(ghc >= 8.8)

42− ghc-options: -Wmissing-deriving-strategies

43−

44− default-language: Haskell2010

45−

46−library

47− import: common-options

48− hs-source-dirs: src

49− exposed-modules: LAoP.Dist

50− LAoP.Dist.Internal

51− LAoP.Matrix.Internal

52− LAoP.Matrix.Nat

53− LAoP.Matrix.Type

54− LAoP.Relation

55− LAoP.Relation.Internal

56− LAoP.Utils

57− LAoP.Utils.Internal

58−

59−test-suite laop-test

60− import: common-options

61− type: exitcode-stdio-1.0

62− hs-source-dirs: test

63− other-modules: Examples.Readme

64− main-is: Spec.hs

65− build-depends: laop

66− ghc-options: -threaded

67− -rtsopts

68− -with-rtsopts=-N

69− -funfolding-use-threshold=16

70− -fexcess-precision

71− -optc-O3

72− -optc-ffast-math

73−

74−benchmark laop-benchmark

75− import: common-options

76− type: exitcode-stdio-1.0

77− hs-source-dirs: benchmark

78− main-is: Main.hs

79− build-depends: criterion

80− , QuickCheck

81− , deepseq

82− , laop

83− ghc-options: -threaded

84− -rtsopts

85− -with-rtsopts=-N

86− -funfolding-use-threshold=16

87− -fexcess-precision

88− -optc-O3

89− -optc-ffast-math

package.yamlnew file+57

@@ -0,0 +1,57 @@

1+name: laop

2+version: 0.1.0.5

3+github: "bolt12/laop"

4+license: BSD3

5+author: "Armando Santos"

6+maintainer: "armandoifsantos@gmail.com"

7+copyright: "MIT"

9+extra-source-files:

10+- README.md

11+- ChangeLog.md

12+

13+# Metadata used when publishing your package

14+# synopsis: Short description of your package

15+category: Data

16+

17+# To avoid duplicated efforts in documentation and dealing with the

18+# complications of embedding Haddock markup inside cabal files, it is

19+# common to point users to the README.md file.

20+description: Please see the README on GitHub at <https://github.com/bolt12/laop#readme>

21+

22+dependencies:

23+- base >= 4.7 && < 5

24+- deepseq

25+

26+library:

27+ source-dirs: src

28+

29+executables:

30+ laop-exe:

31+ main: Main.hs

32+ source-dirs: app

33+ ghc-options:

34+ - -threaded

35+ - -rtsopts

36+ - -with-rtsopts=-N

37+ - -funfolding-use-threshold=16

38+ - -fexcess-precision # Good for doubles

39+ - -optc-O3 # Good for doubles

40+ - -optc-ffast-math # Good for doubles

41+ - -O2

42+ dependencies:

43+ - laop

44+ - criterion

45+ - deepseq

46+ - QuickCheck

47+

48+tests:

49+ laop-test:

50+ main: Spec.hs

51+ source-dirs: test

52+ ghc-options:

53+ - -threaded

54+ - -rtsopts

55+ - -with-rtsopts=-N

56+ dependencies:

57+ - laop

report-lazy.htmlnew file+1169

@@ -0,0 +1,1169 @@

1+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">

2+<html>

3+ <head>

4+ <meta http-equiv="Content-Type" content="text/html; charset=utf-8">

5+ <title>criterion report</title>

6+ <script language="javascript" type="text/javascript">

7+ /*! jQuery v3.3.1 | (c) JS Foundation and other contributors | jquery.org/license */

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xmin=topSentry,ymin=topSentry,xmax=bottomSentry,ymax=bottomSentry;for(j=0;j<points.length;j+=ps){if(points[j]==null)continue;for(m=0;m<ps;++m){val=points[j+m];f=format[m];if(!f||f.autoscale===false||val==fakeInfinity||val==-fakeInfinity)continue;if(f.x){if(val<xmin)xmin=val;if(val>xmax)xmax=val}if(f.y){if(val<ymin)ymin=val;if(val>ymax)ymax=val}}}if(s.bars.show){var delta;switch(s.bars.align){case"left":delta=0;break;case"right":delta=-s.bars.barWidth;break;default:delta=-s.bars.barWidth/2}if(s.bars.horizontal){ymin+=delta;ymax+=delta+s.bars.barWidth}else{xmin+=delta;xmax+=delta+s.bars.barWidth}}updateAxis(s.xaxis,xmin,xmax);updateAxis(s.yaxis,ymin,ymax)}$.each(allAxes(),function(_,axis){if(axis.datamin==topSentry)axis.datamin=null;if(axis.datamax==bottomSentry)axis.datamax=null})}function setupCanvases(){placeholder.css("padding",0).children().filter(function(){return!$(this).hasClass("flot-overlay")&&!$(this).hasClass("flot-base")}).remove();if(placeholder.css("position")=="static")placeholder.css("position","relative");surface=new Canvas("flot-base",placeholder);overlay=new Canvas("flot-overlay",placeholder);ctx=surface.context;octx=overlay.context;eventHolder=$(overlay.element).unbind();var existing=placeholder.data("plot");if(existing){existing.shutdown();overlay.clear()}placeholder.data("plot",plot)}function bindEvents(){if(options.grid.hoverable){eventHolder.mousemove(onMouseMove);eventHolder.bind("mouseleave",onMouseLeave)}if(options.grid.clickable)eventHolder.click(onClick);executeHooks(hooks.bindEvents,[eventHolder])}function shutdown(){if(redrawTimeout)clearTimeout(redrawTimeout);eventHolder.unbind("mousemove",onMouseMove);eventHolder.unbind("mouseleave",onMouseLeave);eventHolder.unbind("click",onClick);executeHooks(hooks.shutdown,[eventHolder])}function setTransformationHelpers(axis){function identity(x){return x}var s,m,t=axis.options.transform||identity,it=axis.options.inverseTransform;if(axis.direction=="x"){s=axis.scale=plotWidth/Math.abs(t(axis.max)-t(axis.min));m=Math.min(t(axis.max),t(axis.min))}else{s=axis.scale=plotHeight/Math.abs(t(axis.max)-t(axis.min));s=-s;m=Math.max(t(axis.max),t(axis.min))}if(t==identity)axis.p2c=function(p){return(p-m)*s};else axis.p2c=function(p){return(t(p)-m)*s};if(!it)axis.c2p=function(c){return m+c/s};else axis.c2p=function(c){return it(m+c/s)}}function measureTickLabels(axis){var opts=axis.options,ticks=axis.ticks||[],labelWidth=opts.labelWidth||0,labelHeight=opts.labelHeight||0,maxWidth=labelWidth||(axis.direction=="x"?Math.floor(surface.width/(ticks.length||1)):null),legacyStyles=axis.direction+"Axis "+axis.direction+axis.n+"Axis",layer="flot-"+axis.direction+"-axis flot-"+axis.direction+axis.n+"-axis "+legacyStyles,font=opts.font||"flot-tick-label tickLabel";for(var i=0;i<ticks.length;++i){var t=ticks[i];if(!t.label)continue;var info=surface.getTextInfo(layer,t.label,font,null,maxWidth);labelWidth=Math.max(labelWidth,info.width);labelHeight=Math.max(labelHeight,info.height)}axis.labelWidth=opts.labelWidth||labelWidth;axis.labelHeight=opts.labelHeight||labelHeight}function allocateAxisBoxFirstPhase(axis){var lw=axis.labelWidth,lh=axis.labelHeight,pos=axis.options.position,isXAxis=axis.direction==="x",tickLength=axis.options.tickLength,axisMargin=options.grid.axisMargin,padding=options.grid.labelMargin,innermost=true,outermost=true,first=true,found=false;$.each(isXAxis?xaxes:yaxes,function(i,a){if(a&&(a.show||a.reserveSpace)){if(a===axis){found=true}else if(a.options.position===pos){if(found){outermost=false}else{innermost=false}}if(!found){first=false}}});if(outermost){axisMargin=0}if(tickLength==null){tickLength=first?"full":5}if(!isNaN(+tickLength))padding+=+tickLength;if(isXAxis){lh+=padding;if(pos=="bottom"){plotOffset.bottom+=lh+axisMargin;axis.box={top:surface.height-plotOffset.bottom,height:lh}}else{axis.box={top:plotOffset.top+axisMargin,height:lh};plotOffset.top+=lh+axisMargin}}else{lw+=padding;if(pos=="left"){axis.box={left:plotOffset.left+axisMargin,width:lw};plotOffset.left+=lw+axisMargin}else{plotOffset.right+=lw+axisMargin;axis.box={left:surface.width-plotOffset.right,width:lw}}}axis.position=pos;axis.tickLength=tickLength;axis.box.padding=padding;axis.innermost=innermost}function allocateAxisBoxSecondPhase(axis){if(axis.direction=="x"){axis.box.left=plotOffset.left-axis.labelWidth/2;axis.box.width=surface.width-plotOffset.left-plotOffset.right+axis.labelWidth}else{axis.box.top=plotOffset.top-axis.labelHeight/2;axis.box.height=surface.height-plotOffset.bottom-plotOffset.top+axis.labelHeight}}function adjustLayoutForThingsStickingOut(){var minMargin=options.grid.minBorderMargin,axis,i;if(minMargin==null){minMargin=0;for(i=0;i<series.length;++i)minMargin=Math.max(minMargin,2*(series[i].points.radius+series[i].points.lineWidth/2))}var margins={left:minMargin,right:minMargin,top:minMargin,bottom:minMargin};$.each(allAxes(),function(_,axis){if(axis.reserveSpace&&axis.ticks&&axis.ticks.length){if(axis.direction==="x"){margins.left=Math.max(margins.left,axis.labelWidth/2);margins.right=Math.max(margins.right,axis.labelWidth/2)}else{margins.bottom=Math.max(margins.bottom,axis.labelHeight/2);margins.top=Math.max(margins.top,axis.labelHeight/2)}}});plotOffset.left=Math.ceil(Math.max(margins.left,plotOffset.left));plotOffset.right=Math.ceil(Math.max(margins.right,plotOffset.right));plotOffset.top=Math.ceil(Math.max(margins.top,plotOffset.top));plotOffset.bottom=Math.ceil(Math.max(margins.bottom,plotOffset.bottom))}function setupGrid(){var i,axes=allAxes(),showGrid=options.grid.show;for(var a in plotOffset){var margin=options.grid.margin||0;plotOffset[a]=typeof margin=="number"?margin:margin[a]||0}executeHooks(hooks.processOffset,[plotOffset]);for(var a in plotOffset){if(typeof options.grid.borderWidth=="object"){plotOffset[a]+=showGrid?options.grid.borderWidth[a]:0}else{plotOffset[a]+=showGrid?options.grid.borderWidth:0}}$.each(axes,function(_,axis){var axisOpts=axis.options;axis.show=axisOpts.show==null?axis.used:axisOpts.show;axis.reserveSpace=axisOpts.reserveSpace==null?axis.show:axisOpts.reserveSpace;setRange(axis)});if(showGrid){var allocatedAxes=$.grep(axes,function(axis){return axis.show||axis.reserveSpace});$.each(allocatedAxes,function(_,axis){setupTickGeneration(axis);setTicks(axis);snapRangeToTicks(axis,axis.ticks);measureTickLabels(axis)});for(i=allocatedAxes.length-1;i>=0;--i)allocateAxisBoxFirstPhase(allocatedAxes[i]);adjustLayoutForThingsStickingOut();$.each(allocatedAxes,function(_,axis){allocateAxisBoxSecondPhase(axis)})}plotWidth=surface.width-plotOffset.left-plotOffset.right;plotHeight=surface.height-plotOffset.bottom-plotOffset.top;$.each(axes,function(_,axis){setTransformationHelpers(axis)});if(showGrid){drawAxisLabels()}insertLegend()}function setRange(axis){var opts=axis.options,min=+(opts.min!=null?opts.min:axis.datamin),max=+(opts.max!=null?opts.max:axis.datamax),delta=max-min;if(delta==0){var widen=max==0?1:.01;if(opts.min==null)min-=widen;if(opts.max==null||opts.min!=null)max+=widen}else{var margin=opts.autoscaleMargin;if(margin!=null){if(opts.min==null){min-=delta*margin;if(min<0&&axis.datamin!=null&&axis.datamin>=0)min=0}if(opts.max==null){max+=delta*margin;if(max>0&&axis.datamax!=null&&axis.datamax<=0)max=0}}}axis.min=min;axis.max=max}function setupTickGeneration(axis){var opts=axis.options;var noTicks;if(typeof opts.ticks=="number"&&opts.ticks>0)noTicks=opts.ticks;else noTicks=.3*Math.sqrt(axis.direction=="x"?surface.width:surface.height);var delta=(axis.max-axis.min)/noTicks,dec=-Math.floor(Math.log(delta)/Math.LN10),maxDec=opts.tickDecimals;if(maxDec!=null&&dec>maxDec){dec=maxDec}var magn=Math.pow(10,-dec),norm=delta/magn,size;if(norm<1.5){size=1}else if(norm<3){size=2;if(norm>2.25&&(maxDec==null||dec+1<=maxDec)){size=2.5;++dec}}else if(norm<7.5){size=5}else{size=10}size*=magn;if(opts.minTickSize!=null&&size<opts.minTickSize){size=opts.minTickSize}axis.delta=delta;axis.tickDecimals=Math.max(0,maxDec!=null?maxDec:dec);axis.tickSize=opts.tickSize||size;if(opts.mode=="time"&&!axis.tickGenerator){throw new Error("Time mode requires the flot.time plugin.")}if(!axis.tickGenerator){axis.tickGenerator=function(axis){var ticks=[],start=floorInBase(axis.min,axis.tickSize),i=0,v=Number.NaN,prev;do{prev=v;v=start+i*axis.tickSize;ticks.push(v);++i}while(v<axis.max&&v!=prev);return ticks};axis.tickFormatter=function(value,axis){var factor=axis.tickDecimals?Math.pow(10,axis.tickDecimals):1;var formatted=""+Math.round(value*factor)/factor;if(axis.tickDecimals!=null){var decimal=formatted.indexOf(".");var precision=decimal==-1?0:formatted.length-decimal-1;if(precision<axis.tickDecimals){return(precision?formatted:formatted+".")+(""+factor).substr(1,axis.tickDecimals-precision)}}return formatted}}if($.isFunction(opts.tickFormatter))axis.tickFormatter=function(v,axis){return""+opts.tickFormatter(v,axis)};if(opts.alignTicksWithAxis!=null){var otherAxis=(axis.direction=="x"?xaxes:yaxes)[opts.alignTicksWithAxis-1];if(otherAxis&&otherAxis.used&&otherAxis!=axis){var niceTicks=axis.tickGenerator(axis);if(niceTicks.length>0){if(opts.min==null)axis.min=Math.min(axis.min,niceTicks[0]);if(opts.max==null&&niceTicks.length>1)axis.max=Math.max(axis.max,niceTicks[niceTicks.length-1])}axis.tickGenerator=function(axis){var ticks=[],v,i;for(i=0;i<otherAxis.ticks.length;++i){v=(otherAxis.ticks[i].v-otherAxis.min)/(otherAxis.max-otherAxis.min);v=axis.min+v*(axis.max-axis.min);ticks.push(v)}return ticks};if(!axis.mode&&opts.tickDecimals==null){var extraDec=Math.max(0,-Math.floor(Math.log(axis.delta)/Math.LN10)+1),ts=axis.tickGenerator(axis);if(!(ts.length>1&&/\..*0$/.test((ts[1]-ts[0]).toFixed(extraDec))))axis.tickDecimals=extraDec}}}}function setTicks(axis){var oticks=axis.options.ticks,ticks=[];if(oticks==null||typeof oticks=="number"&&oticks>0)ticks=axis.tickGenerator(axis);else if(oticks){if($.isFunction(oticks))ticks=oticks(axis);else ticks=oticks}var i,v;axis.ticks=[];for(i=0;i<ticks.length;++i){var label=null;var t=ticks[i];if(typeof t=="object"){v=+t[0];if(t.length>1)label=t[1]}else v=+t;if(label==null)label=axis.tickFormatter(v,axis);if(!isNaN(v))axis.ticks.push({v:v,label:label})}}function snapRangeToTicks(axis,ticks){if(axis.options.autoscaleMargin&&ticks.length>0){if(axis.options.min==null)axis.min=Math.min(axis.min,ticks[0].v);if(axis.options.max==null&&ticks.length>1)axis.max=Math.max(axis.max,ticks[ticks.length-1].v)}}function draw(){surface.clear();executeHooks(hooks.drawBackground,[ctx]);var grid=options.grid;if(grid.show&&grid.backgroundColor)drawBackground();if(grid.show&&!grid.aboveData){drawGrid()}for(var i=0;i<series.length;++i){executeHooks(hooks.drawSeries,[ctx,series[i]]);drawSeries(series[i])}executeHooks(hooks.draw,[ctx]);if(grid.show&&grid.aboveData){drawGrid()}surface.render();triggerRedrawOverlay()}function extractRange(ranges,coord){var axis,from,to,key,axes=allAxes();for(var i=0;i<axes.length;++i){axis=axes[i];if(axis.direction==coord){key=coord+axis.n+"axis";if(!ranges[key]&&axis.n==1)key=coord+"axis";if(ranges[key]){from=ranges[key].from;to=ranges[key].to;break}}}if(!ranges[key]){axis=coord=="x"?xaxes[0]:yaxes[0];from=ranges[coord+"1"];to=ranges[coord+"2"]}if(from!=null&&to!=null&&from>to){var tmp=from;from=to;to=tmp}return{from:from,to:to,axis:axis}}function drawBackground(){ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.fillStyle=getColorOrGradient(options.grid.backgroundColor,plotHeight,0,"rgba(255, 255, 255, 0)");ctx.fillRect(0,0,plotWidth,plotHeight);ctx.restore()}function drawGrid(){var i,axes,bw,bc;ctx.save();ctx.translate(plotOffset.left,plotOffset.top);var markings=options.grid.markings;if(markings){if($.isFunction(markings)){axes=plot.getAxes();axes.xmin=axes.xaxis.min;axes.xmax=axes.xaxis.max;axes.ymin=axes.yaxis.min;axes.ymax=axes.yaxis.max;markings=markings(axes)}for(i=0;i<markings.length;++i){var m=markings[i],xrange=extractRange(m,"x"),yrange=extractRange(m,"y");if(xrange.from==null)xrange.from=xrange.axis.min;if(xrange.to==null)xrange.to=xrange.axis.max;

19+if(yrange.from==null)yrange.from=yrange.axis.min;if(yrange.to==null)yrange.to=yrange.axis.max;if(xrange.to<xrange.axis.min||xrange.from>xrange.axis.max||yrange.to<yrange.axis.min||yrange.from>yrange.axis.max)continue;xrange.from=Math.max(xrange.from,xrange.axis.min);xrange.to=Math.min(xrange.to,xrange.axis.max);yrange.from=Math.max(yrange.from,yrange.axis.min);yrange.to=Math.min(yrange.to,yrange.axis.max);var xequal=xrange.from===xrange.to,yequal=yrange.from===yrange.to;if(xequal&&yequal){continue}xrange.from=Math.floor(xrange.axis.p2c(xrange.from));xrange.to=Math.floor(xrange.axis.p2c(xrange.to));yrange.from=Math.floor(yrange.axis.p2c(yrange.from));yrange.to=Math.floor(yrange.axis.p2c(yrange.to));if(xequal||yequal){var lineWidth=m.lineWidth||options.grid.markingsLineWidth,subPixel=lineWidth%2?.5:0;ctx.beginPath();ctx.strokeStyle=m.color||options.grid.markingsColor;ctx.lineWidth=lineWidth;if(xequal){ctx.moveTo(xrange.to+subPixel,yrange.from);ctx.lineTo(xrange.to+subPixel,yrange.to)}else{ctx.moveTo(xrange.from,yrange.to+subPixel);ctx.lineTo(xrange.to,yrange.to+subPixel)}ctx.stroke()}else{ctx.fillStyle=m.color||options.grid.markingsColor;ctx.fillRect(xrange.from,yrange.to,xrange.to-xrange.from,yrange.from-yrange.to)}}}axes=allAxes();bw=options.grid.borderWidth;for(var j=0;j<axes.length;++j){var axis=axes[j],box=axis.box,t=axis.tickLength,x,y,xoff,yoff;if(!axis.show||axis.ticks.length==0)continue;ctx.lineWidth=1;if(axis.direction=="x"){x=0;if(t=="full")y=axis.position=="top"?0:plotHeight;else y=box.top-plotOffset.top+(axis.position=="top"?box.height:0)}else{y=0;if(t=="full")x=axis.position=="left"?0:plotWidth;else x=box.left-plotOffset.left+(axis.position=="left"?box.width:0)}if(!axis.innermost){ctx.strokeStyle=axis.options.color;ctx.beginPath();xoff=yoff=0;if(axis.direction=="x")xoff=plotWidth+1;else yoff=plotHeight+1;if(ctx.lineWidth==1){if(axis.direction=="x"){y=Math.floor(y)+.5}else{x=Math.floor(x)+.5}}ctx.moveTo(x,y);ctx.lineTo(x+xoff,y+yoff);ctx.stroke()}ctx.strokeStyle=axis.options.tickColor;ctx.beginPath();for(i=0;i<axis.ticks.length;++i){var v=axis.ticks[i].v;xoff=yoff=0;if(isNaN(v)||v<axis.min||v>axis.max||t=="full"&&(typeof bw=="object"&&bw[axis.position]>0||bw>0)&&(v==axis.min||v==axis.max))continue;if(axis.direction=="x"){x=axis.p2c(v);yoff=t=="full"?-plotHeight:t;if(axis.position=="top")yoff=-yoff}else{y=axis.p2c(v);xoff=t=="full"?-plotWidth:t;if(axis.position=="left")xoff=-xoff}if(ctx.lineWidth==1){if(axis.direction=="x")x=Math.floor(x)+.5;else y=Math.floor(y)+.5}ctx.moveTo(x,y);ctx.lineTo(x+xoff,y+yoff)}ctx.stroke()}if(bw){bc=options.grid.borderColor;if(typeof bw=="object"||typeof bc=="object"){if(typeof bw!=="object"){bw={top:bw,right:bw,bottom:bw,left:bw}}if(typeof bc!=="object"){bc={top:bc,right:bc,bottom:bc,left:bc}}if(bw.top>0){ctx.strokeStyle=bc.top;ctx.lineWidth=bw.top;ctx.beginPath();ctx.moveTo(0-bw.left,0-bw.top/2);ctx.lineTo(plotWidth,0-bw.top/2);ctx.stroke()}if(bw.right>0){ctx.strokeStyle=bc.right;ctx.lineWidth=bw.right;ctx.beginPath();ctx.moveTo(plotWidth+bw.right/2,0-bw.top);ctx.lineTo(plotWidth+bw.right/2,plotHeight);ctx.stroke()}if(bw.bottom>0){ctx.strokeStyle=bc.bottom;ctx.lineWidth=bw.bottom;ctx.beginPath();ctx.moveTo(plotWidth+bw.right,plotHeight+bw.bottom/2);ctx.lineTo(0,plotHeight+bw.bottom/2);ctx.stroke()}if(bw.left>0){ctx.strokeStyle=bc.left;ctx.lineWidth=bw.left;ctx.beginPath();ctx.moveTo(0-bw.left/2,plotHeight+bw.bottom);ctx.lineTo(0-bw.left/2,0);ctx.stroke()}}else{ctx.lineWidth=bw;ctx.strokeStyle=options.grid.borderColor;ctx.strokeRect(-bw/2,-bw/2,plotWidth+bw,plotHeight+bw)}}ctx.restore()}function drawAxisLabels(){$.each(allAxes(),function(_,axis){var box=axis.box,legacyStyles=axis.direction+"Axis "+axis.direction+axis.n+"Axis",layer="flot-"+axis.direction+"-axis flot-"+axis.direction+axis.n+"-axis "+legacyStyles,font=axis.options.font||"flot-tick-label tickLabel",tick,x,y,halign,valign;surface.removeText(layer);if(!axis.show||axis.ticks.length==0)return;for(var i=0;i<axis.ticks.length;++i){tick=axis.ticks[i];if(!tick.label||tick.v<axis.min||tick.v>axis.max)continue;if(axis.direction=="x"){halign="center";x=plotOffset.left+axis.p2c(tick.v);if(axis.position=="bottom"){y=box.top+box.padding}else{y=box.top+box.height-box.padding;valign="bottom"}}else{valign="middle";y=plotOffset.top+axis.p2c(tick.v);if(axis.position=="left"){x=box.left+box.width-box.padding;halign="right"}else{x=box.left+box.padding}}surface.addText(layer,x,y,tick.label,font,null,null,halign,valign)}})}function drawSeries(series){if(series.lines.show)drawSeriesLines(series);if(series.bars.show)drawSeriesBars(series);if(series.points.show)drawSeriesPoints(series)}function drawSeriesLines(series){function plotLine(datapoints,xoffset,yoffset,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize,prevx=null,prevy=null;ctx.beginPath();for(var i=ps;i<points.length;i+=ps){var x1=points[i-ps],y1=points[i-ps+1],x2=points[i],y2=points[i+1];if(x1==null||x2==null)continue;if(y1<=y2&&y1<axisy.min){if(y2<axisy.min)continue;x1=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.min}else if(y2<=y1&&y2<axisy.min){if(y1<axisy.min)continue;x2=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.min}if(y1>=y2&&y1>axisy.max){if(y2>axisy.max)continue;x1=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.max}else if(y2>=y1&&y2>axisy.max){if(y1>axisy.max)continue;x2=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.max}if(x1<=x2&&x1<axisx.min){if(x2<axisx.min)continue;y1=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.min}else if(x2<=x1&&x2<axisx.min){if(x1<axisx.min)continue;y2=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.min}if(x1>=x2&&x1>axisx.max){if(x2>axisx.max)continue;y1=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.max}else if(x2>=x1&&x2>axisx.max){if(x1>axisx.max)continue;y2=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.max}if(x1!=prevx||y1!=prevy)ctx.moveTo(axisx.p2c(x1)+xoffset,axisy.p2c(y1)+yoffset);prevx=x2;prevy=y2;ctx.lineTo(axisx.p2c(x2)+xoffset,axisy.p2c(y2)+yoffset)}ctx.stroke()}function plotLineArea(datapoints,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize,bottom=Math.min(Math.max(0,axisy.min),axisy.max),i=0,top,areaOpen=false,ypos=1,segmentStart=0,segmentEnd=0;while(true){if(ps>0&&i>points.length+ps)break;i+=ps;var x1=points[i-ps],y1=points[i-ps+ypos],x2=points[i],y2=points[i+ypos];if(areaOpen){if(ps>0&&x1!=null&&x2==null){segmentEnd=i;ps=-ps;ypos=2;continue}if(ps<0&&i==segmentStart+ps){ctx.fill();areaOpen=false;ps=-ps;ypos=1;i=segmentStart=segmentEnd+ps;continue}}if(x1==null||x2==null)continue;if(x1<=x2&&x1<axisx.min){if(x2<axisx.min)continue;y1=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.min}else if(x2<=x1&&x2<axisx.min){if(x1<axisx.min)continue;y2=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.min}if(x1>=x2&&x1>axisx.max){if(x2>axisx.max)continue;y1=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.max}else if(x2>=x1&&x2>axisx.max){if(x1>axisx.max)continue;y2=(axisx.max-x1)/(x2-x1)*(y2-y1)+y1;x2=axisx.max}if(!areaOpen){ctx.beginPath();ctx.moveTo(axisx.p2c(x1),axisy.p2c(bottom));areaOpen=true}if(y1>=axisy.max&&y2>=axisy.max){ctx.lineTo(axisx.p2c(x1),axisy.p2c(axisy.max));ctx.lineTo(axisx.p2c(x2),axisy.p2c(axisy.max));continue}else if(y1<=axisy.min&&y2<=axisy.min){ctx.lineTo(axisx.p2c(x1),axisy.p2c(axisy.min));ctx.lineTo(axisx.p2c(x2),axisy.p2c(axisy.min));continue}var x1old=x1,x2old=x2;if(y1<=y2&&y1<axisy.min&&y2>=axisy.min){x1=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.min}else if(y2<=y1&&y2<axisy.min&&y1>=axisy.min){x2=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.min}if(y1>=y2&&y1>axisy.max&&y2<=axisy.max){x1=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.max}else if(y2>=y1&&y2>axisy.max&&y1<=axisy.max){x2=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.max}if(x1!=x1old){ctx.lineTo(axisx.p2c(x1old),axisy.p2c(y1))}ctx.lineTo(axisx.p2c(x1),axisy.p2c(y1));ctx.lineTo(axisx.p2c(x2),axisy.p2c(y2));if(x2!=x2old){ctx.lineTo(axisx.p2c(x2),axisy.p2c(y2));ctx.lineTo(axisx.p2c(x2old),axisy.p2c(y2))}}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.lineJoin="round";var lw=series.lines.lineWidth,sw=series.shadowSize;if(lw>0&&sw>0){ctx.lineWidth=sw;ctx.strokeStyle="rgba(0,0,0,0.1)";var angle=Math.PI/18;plotLine(series.datapoints,Math.sin(angle)*(lw/2+sw/2),Math.cos(angle)*(lw/2+sw/2),series.xaxis,series.yaxis);ctx.lineWidth=sw/2;plotLine(series.datapoints,Math.sin(angle)*(lw/2+sw/4),Math.cos(angle)*(lw/2+sw/4),series.xaxis,series.yaxis)}ctx.lineWidth=lw;ctx.strokeStyle=series.color;var fillStyle=getFillStyle(series.lines,series.color,0,plotHeight);if(fillStyle){ctx.fillStyle=fillStyle;plotLineArea(series.datapoints,series.xaxis,series.yaxis)}if(lw>0)plotLine(series.datapoints,0,0,series.xaxis,series.yaxis);ctx.restore()}function drawSeriesPoints(series){function plotPoints(datapoints,radius,fillStyle,offset,shadow,axisx,axisy,symbol){var points=datapoints.points,ps=datapoints.pointsize;for(var i=0;i<points.length;i+=ps){var x=points[i],y=points[i+1];if(x==null||x<axisx.min||x>axisx.max||y<axisy.min||y>axisy.max)continue;ctx.beginPath();x=axisx.p2c(x);y=axisy.p2c(y)+offset;if(symbol=="circle")ctx.arc(x,y,radius,0,shadow?Math.PI:Math.PI*2,false);else symbol(ctx,x,y,radius,shadow);ctx.closePath();if(fillStyle){ctx.fillStyle=fillStyle;ctx.fill()}ctx.stroke()}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);var lw=series.points.lineWidth,sw=series.shadowSize,radius=series.points.radius,symbol=series.points.symbol;if(lw==0)lw=1e-4;if(lw>0&&sw>0){var w=sw/2;ctx.lineWidth=w;ctx.strokeStyle="rgba(0,0,0,0.1)";plotPoints(series.datapoints,radius,null,w+w/2,true,series.xaxis,series.yaxis,symbol);ctx.strokeStyle="rgba(0,0,0,0.2)";plotPoints(series.datapoints,radius,null,w/2,true,series.xaxis,series.yaxis,symbol)}ctx.lineWidth=lw;ctx.strokeStyle=series.color;plotPoints(series.datapoints,radius,getFillStyle(series.points,series.color),0,false,series.xaxis,series.yaxis,symbol);ctx.restore()}function drawBar(x,y,b,barLeft,barRight,fillStyleCallback,axisx,axisy,c,horizontal,lineWidth){var left,right,bottom,top,drawLeft,drawRight,drawTop,drawBottom,tmp;if(horizontal){drawBottom=drawRight=drawTop=true;drawLeft=false;left=b;right=x;top=y+barLeft;bottom=y+barRight;if(right<left){tmp=right;right=left;left=tmp;drawLeft=true;drawRight=false}}else{drawLeft=drawRight=drawTop=true;drawBottom=false;left=x+barLeft;right=x+barRight;bottom=b;top=y;if(top<bottom){tmp=top;top=bottom;bottom=tmp;drawBottom=true;drawTop=false}}if(right<axisx.min||left>axisx.max||top<axisy.min||bottom>axisy.max)return;if(left<axisx.min){left=axisx.min;drawLeft=false}if(right>axisx.max){right=axisx.max;drawRight=false}if(bottom<axisy.min){bottom=axisy.min;drawBottom=false}if(top>axisy.max){top=axisy.max;drawTop=false}left=axisx.p2c(left);bottom=axisy.p2c(bottom);right=axisx.p2c(right);top=axisy.p2c(top);if(fillStyleCallback){c.fillStyle=fillStyleCallback(bottom,top);c.fillRect(left,top,right-left,bottom-top)}if(lineWidth>0&&(drawLeft||drawRight||drawTop||drawBottom)){c.beginPath();c.moveTo(left,bottom);if(drawLeft)c.lineTo(left,top);else c.moveTo(left,top);if(drawTop)c.lineTo(right,top);else c.moveTo(right,top);if(drawRight)c.lineTo(right,bottom);else c.moveTo(right,bottom);if(drawBottom)c.lineTo(left,bottom);else c.moveTo(left,bottom);c.stroke()}}function drawSeriesBars(series){function plotBars(datapoints,barLeft,barRight,fillStyleCallback,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize;for(var i=0;i<points.length;i+=ps){if(points[i]==null)continue;drawBar(points[i],points[i+1],points[i+2],barLeft,barRight,fillStyleCallback,axisx,axisy,ctx,series.bars.horizontal,series.bars.lineWidth)}}ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.lineWidth=series.bars.lineWidth;ctx.strokeStyle=series.color;var barLeft;switch(series.bars.align){case"left":barLeft=0;break;case"right":barLeft=-series.bars.barWidth;break;default:barLeft=-series.bars.barWidth/2}var fillStyleCallback=series.bars.fill?function(bottom,top){return getFillStyle(series.bars,series.color,bottom,top)}:null;plotBars(series.datapoints,barLeft,barLeft+series.bars.barWidth,fillStyleCallback,series.xaxis,series.yaxis);ctx.restore()}function getFillStyle(filloptions,seriesColor,bottom,top){var fill=filloptions.fill;if(!fill)return null;if(filloptions.fillColor)return getColorOrGradient(filloptions.fillColor,bottom,top,seriesColor);var c=$.color.parse(seriesColor);c.a=typeof fill=="number"?fill:.4;c.normalize();return c.toString()}function insertLegend(){if(options.legend.container!=null){$(options.legend.container).html("")}else{placeholder.find(".legend").remove()}if(!options.legend.show){return}var fragments=[],entries=[],rowStarted=false,lf=options.legend.labelFormatter,s,label;for(var i=0;i<series.length;++i){s=series[i];if(s.label){label=lf?lf(s.label,s):s.label;if(label){entries.push({label:label,color:s.color})}}}if(options.legend.sorted){if($.isFunction(options.legend.sorted)){entries.sort(options.legend.sorted)}else if(options.legend.sorted=="reverse"){entries.reverse()}else{var ascending=options.legend.sorted!="descending";entries.sort(function(a,b){return a.label==b.label?0:a.label<b.label!=ascending?1:-1})}}for(var i=0;i<entries.length;++i){var entry=entries[i];if(i%options.legend.noColumns==0){if(rowStarted)fragments.push("</tr>");fragments.push("<tr>");rowStarted=true}fragments.push('<td class="legendColorBox"><div style="border:1px solid '+options.legend.labelBoxBorderColor+';padding:1px"><div style="width:4px;height:0;border:5px solid '+entry.color+';overflow:hidden"></div></div></td>'+'<td class="legendLabel">'+entry.label+"</td>")}if(rowStarted)fragments.push("</tr>");if(fragments.length==0)return;var table='<table style="font-size:smaller;color:'+options.grid.color+'">'+fragments.join("")+"</table>";if(options.legend.container!=null)$(options.legend.container).html(table);else{var pos="",p=options.legend.position,m=options.legend.margin;if(m[0]==null)m=[m,m];if(p.charAt(0)=="n")pos+="top:"+(m[1]+plotOffset.top)+"px;";else if(p.charAt(0)=="s")pos+="bottom:"+(m[1]+plotOffset.bottom)+"px;";if(p.charAt(1)=="e")pos+="right:"+(m[0]+plotOffset.right)+"px;";else if(p.charAt(1)=="w")pos+="left:"+(m[0]+plotOffset.left)+"px;";var legend=$('<div class="legend">'+table.replace('style="','style="position:absolute;'+pos+";")+"</div>").appendTo(placeholder);if(options.legend.backgroundOpacity!=0){var c=options.legend.backgroundColor;if(c==null){c=options.grid.backgroundColor;if(c&&typeof c=="string")c=$.color.parse(c);else c=$.color.extract(legend,"background-color");c.a=1;c=c.toString()}var div=legend.children();$('<div style="position:absolute;width:'+div.width()+"px;height:"+div.height()+"px;"+pos+"background-color:"+c+';"> </div>').prependTo(legend).css("opacity",options.legend.backgroundOpacity)}}}var highlights=[],redrawTimeout=null;function findNearbyItem(mouseX,mouseY,seriesFilter){var maxDistance=options.grid.mouseActiveRadius,smallestDistance=maxDistance*maxDistance+1,item=null,foundPoint=false,i,j,ps;for(i=series.length-1;i>=0;--i){if(!seriesFilter(series[i]))continue;var s=series[i],axisx=s.xaxis,axisy=s.yaxis,points=s.datapoints.points,mx=axisx.c2p(mouseX),my=axisy.c2p(mouseY),maxx=maxDistance/axisx.scale,maxy=maxDistance/axisy.scale;ps=s.datapoints.pointsize;if(axisx.options.inverseTransform)maxx=Number.MAX_VALUE;if(axisy.options.inverseTransform)maxy=Number.MAX_VALUE;if(s.lines.show||s.points.show){for(j=0;j<points.length;j+=ps){var x=points[j],y=points[j+1];if(x==null)continue;if(x-mx>maxx||x-mx<-maxx||y-my>maxy||y-my<-maxy)continue;var dx=Math.abs(axisx.p2c(x)-mouseX),dy=Math.abs(axisy.p2c(y)-mouseY),dist=dx*dx+dy*dy;if(dist<smallestDistance){smallestDistance=dist;item=[i,j/ps]}}}if(s.bars.show&&!item){var barLeft,barRight;switch(s.bars.align){case"left":barLeft=0;break;case"right":barLeft=-s.bars.barWidth;break;default:barLeft=-s.bars.barWidth/2}barRight=barLeft+s.bars.barWidth;for(j=0;j<points.length;j+=ps){var x=points[j],y=points[j+1],b=points[j+2];if(x==null)continue;if(series[i].bars.horizontal?mx<=Math.max(b,x)&&mx>=Math.min(b,x)&&my>=y+barLeft&&my<=y+barRight:mx>=x+barLeft&&mx<=x+barRight&&my>=Math.min(b,y)&&my<=Math.max(b,y))item=[i,j/ps]}}}if(item){i=item[0];j=item[1];ps=series[i].datapoints.pointsize;return{datapoint:series[i].datapoints.points.slice(j*ps,(j+1)*ps),dataIndex:j,series:series[i],seriesIndex:i}}return null}function onMouseMove(e){if(options.grid.hoverable)triggerClickHoverEvent("plothover",e,function(s){return s["hoverable"]!=false})}function onMouseLeave(e){if(options.grid.hoverable)triggerClickHoverEvent("plothover",e,function(s){return false})}function onClick(e){triggerClickHoverEvent("plotclick",e,function(s){return s["clickable"]!=false})}function triggerClickHoverEvent(eventname,event,seriesFilter){var offset=eventHolder.offset(),canvasX=event.pageX-offset.left-plotOffset.left,canvasY=event.pageY-offset.top-plotOffset.top,pos=canvasToAxisCoords({left:canvasX,top:canvasY});pos.pageX=event.pageX;pos.pageY=event.pageY;var item=findNearbyItem(canvasX,canvasY,seriesFilter);if(item){item.pageX=parseInt(item.series.xaxis.p2c(item.datapoint[0])+offset.left+plotOffset.left,10);item.pageY=parseInt(item.series.yaxis.p2c(item.datapoint[1])+offset.top+plotOffset.top,10)}if(options.grid.autoHighlight){for(var i=0;i<highlights.length;++i){var h=highlights[i];if(h.auto==eventname&&!(item&&h.series==item.series&&h.point[0]==item.datapoint[0]&&h.point[1]==item.datapoint[1]))unhighlight(h.series,h.point)}if(item)highlight(item.series,item.datapoint,eventname)}placeholder.trigger(eventname,[pos,item])}function triggerRedrawOverlay(){var t=options.interaction.redrawOverlayInterval;if(t==-1){drawOverlay();return}if(!redrawTimeout)redrawTimeout=setTimeout(drawOverlay,t)}function drawOverlay(){redrawTimeout=null;octx.save();overlay.clear();octx.translate(plotOffset.left,plotOffset.top);var i,hi;for(i=0;i<highlights.length;++i){hi=highlights[i];if(hi.series.bars.show)drawBarHighlight(hi.series,hi.point);else drawPointHighlight(hi.series,hi.point)}octx.restore();executeHooks(hooks.drawOverlay,[octx])}function highlight(s,point,auto){if(typeof s=="number")s=series[s];if(typeof point=="number"){var ps=s.datapoints.pointsize;point=s.datapoints.points.slice(ps*point,ps*(point+1))}var i=indexOfHighlight(s,point);if(i==-1){highlights.push({series:s,point:point,auto:auto});triggerRedrawOverlay()}else if(!auto)highlights[i].auto=false}function unhighlight(s,point){if(s==null&&point==null){highlights=[];triggerRedrawOverlay();return}if(typeof s=="number")s=series[s];if(typeof point=="number"){var ps=s.datapoints.pointsize;point=s.datapoints.points.slice(ps*point,ps*(point+1))}var i=indexOfHighlight(s,point);if(i!=-1){highlights.splice(i,1);triggerRedrawOverlay()}}function indexOfHighlight(s,p){for(var i=0;i<highlights.length;++i){var h=highlights[i];if(h.series==s&&h.point[0]==p[0]&&h.point[1]==p[1])return i}return-1}function drawPointHighlight(series,point){var x=point[0],y=point[1],axisx=series.xaxis,axisy=series.yaxis,highlightColor=typeof series.highlightColor==="string"?series.highlightColor:$.color.parse(series.color).scale("a",.5).toString();if(x<axisx.min||x>axisx.max||y<axisy.min||y>axisy.max)return;var pointRadius=series.points.radius+series.points.lineWidth/2;octx.lineWidth=pointRadius;octx.strokeStyle=highlightColor;var radius=1.5*pointRadius;x=axisx.p2c(x);y=axisy.p2c(y);octx.beginPath();if(series.points.symbol=="circle")octx.arc(x,y,radius,0,2*Math.PI,false);else series.points.symbol(octx,x,y,radius,false);octx.closePath();octx.stroke()}function drawBarHighlight(series,point){var highlightColor=typeof series.highlightColor==="string"?series.highlightColor:$.color.parse(series.color).scale("a",.5).toString(),fillStyle=highlightColor,barLeft;switch(series.bars.align){case"left":barLeft=0;break;case"right":barLeft=-series.bars.barWidth;break;default:barLeft=-series.bars.barWidth/2}octx.lineWidth=series.bars.lineWidth;octx.strokeStyle=highlightColor;drawBar(point[0],point[1],point[2]||0,barLeft,barLeft+series.bars.barWidth,function(){return fillStyle},series.xaxis,series.yaxis,octx,series.bars.horizontal,series.bars.lineWidth)}function getColorOrGradient(spec,bottom,top,defaultColor){if(typeof spec=="string")return spec;else{var gradient=ctx.createLinearGradient(0,top,0,bottom);for(var i=0,l=spec.colors.length;i<l;++i){var c=spec.colors[i];if(typeof c!="string"){var co=$.color.parse(defaultColor);if(c.brightness!=null)co=co.scale("rgb",c.brightness);if(c.opacity!=null)co.a*=c.opacity;c=co.toString()}gradient.addColorStop(i/(l-1),c)}return gradient}}}$.plot=function(placeholder,data,options){var plot=new Plot($(placeholder),data,options,$.plot.plugins);return plot};$.plot.version="0.8.3";$.plot.plugins=[];$.fn.plot=function(data,options){return this.each(function(){$.plot(this,data,options)})};function floorInBase(n,base){return base*Math.floor(n/base)}})(jQuery);

20+ </script>

21+ <script language="javascript" type="text/javascript">

22+ /* Javascript plotting library for jQuery, version 0.8.3.

23+

25+Licensed under the MIT license.

26+

27+*/

28+(function($){var options={series:{points:{errorbars:null,xerr:{err:"x",show:null,asymmetric:null,upperCap:null,lowerCap:null,color:null,radius:null},yerr:{err:"y",show:null,asymmetric:null,upperCap:null,lowerCap:null,color:null,radius:null}}}};function processRawData(plot,series,data,datapoints){if(!series.points.errorbars)return;var format=[{x:true,number:true,required:true},{y:true,number:true,required:true}];var errors=series.points.errorbars;if(errors=="x"||errors=="xy"){if(series.points.xerr.asymmetric){format.push({x:true,number:true,required:true});format.push({x:true,number:true,required:true})}else format.push({x:true,number:true,required:true})}if(errors=="y"||errors=="xy"){if(series.points.yerr.asymmetric){format.push({y:true,number:true,required:true});format.push({y:true,number:true,required:true})}else format.push({y:true,number:true,required:true})}datapoints.format=format}function parseErrors(series,i){var points=series.datapoints.points;var exl=null,exu=null,eyl=null,eyu=null;var xerr=series.points.xerr,yerr=series.points.yerr;var eb=series.points.errorbars;if(eb=="x"||eb=="xy"){if(xerr.asymmetric){exl=points[i+2];exu=points[i+3];if(eb=="xy")if(yerr.asymmetric){eyl=points[i+4];eyu=points[i+5]}else eyl=points[i+4]}else{exl=points[i+2];if(eb=="xy")if(yerr.asymmetric){eyl=points[i+3];eyu=points[i+4]}else eyl=points[i+3]}}else if(eb=="y")if(yerr.asymmetric){eyl=points[i+2];eyu=points[i+3]}else eyl=points[i+2];if(exu==null)exu=exl;if(eyu==null)eyu=eyl;var errRanges=[exl,exu,eyl,eyu];if(!xerr.show){errRanges[0]=null;errRanges[1]=null}if(!yerr.show){errRanges[2]=null;errRanges[3]=null}return errRanges}function drawSeriesErrors(plot,ctx,s){var points=s.datapoints.points,ps=s.datapoints.pointsize,ax=[s.xaxis,s.yaxis],radius=s.points.radius,err=[s.points.xerr,s.points.yerr];var invertX=false;if(ax[0].p2c(ax[0].max)<ax[0].p2c(ax[0].min)){invertX=true;var tmp=err[0].lowerCap;err[0].lowerCap=err[0].upperCap;err[0].upperCap=tmp}var 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229+.confinterval {

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233+h1 {

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253+ <!--[if !IE 7]>

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256+ </style>

257+ <![endif]-->

258+ </head>

259+ <body>

260+ <div id="wrap">

261+ <div id="main" class="body">

262+ <h1>criterion performance measurements</h1>

263+

264+<h2>overview</h2>

265+

266+<p><a href="#grokularation">want to understand this report?</a></p>

267+

268+<div id="overview" class="ovchart" style="width:900px;height:100px;"></div>

269+

270+<h2><a name="b0">Matrix Composition/10x10/WHNF - 10x10</a></h2>

271+ <table width="100%">

272+ <tbody>

273+ <tr>

274+ <td><div id="kde0" class="kdechart"

275+ style="width:450px;height:278px;"></div></td>

276+ <td><div id="time0" class="timechart"

277+ style="width:450px;height:278px;"></div></td>

278+<!--

279+ <td><div id="cycle0" class="cyclechart"

280+ style="width:300px;height:278px;"></div></td>

281+-->

282+ </tr>

283+ </tbody>

284+ </table>

285+

286+ <table>

287+ <thead class="analysis">

288+ <th></th>

289+ <th class="cibound"

290+ title="0.95 confidence level">lower bound</th>

291+ <th>estimate</th>

292+ <th class="cibound"

293+ title="0.95 confidence level">upper bound</th>

294+ </thead>

295+ <tbody>

296+ <tr>

297+ <td>OLS regression</td>

298+ <td><span class="confinterval olstimelb0">xxx</span></td>

299+ <td><span class="olstimept0">xxx</span></td>

300+ <td><span class="confinterval olstimeub0">xxx</span></td>

301+ </tr>

302+ <tr>

303+ <td>R² goodness-of-fit</td>

304+ <td><span class="confinterval olsr2lb0">xxx</span></td>

305+ <td><span class="olsr2pt0">xxx</span></td>

306+ <td><span class="confinterval olsr2ub0">xxx</span></td>

307+ </tr>

308+ <tr>

309+ <td>Mean execution time</td>

310+ <td><span class="confinterval citime">2.429905310206746e-8</span></td>

311+ <td><span class="time">2.4514866756029205e-8</span></td>

312+ <td><span class="confinterval citime">2.48855951010762e-8</span></td>

313+ </tr>

314+ <tr>

315+ <td>Standard deviation</td>

316+ <td><span class="confinterval citime">6.998202238158643e-10</span></td>

317+ <td><span class="time">9.647785488002723e-10</span></td>

318+ <td><span class="confinterval citime">1.4224955576371737e-9</span></td>

319+ </tr>

320+ </tbody>

321+ </table>

322+

323+ <span class="outliers">

324+ <p>Outlying measurements have severe

325+ (<span class="percent">0.6233390798012226</span>%)

326+ effect on estimated standard deviation.</p>

327+ </span>

328+<h2><a name="b1">Matrix Composition/10x10/NF - 10x10</a></h2>

329+ <table width="100%">

330+ <tbody>

331+ <tr>

332+ <td><div id="kde1" class="kdechart"

333+ style="width:450px;height:278px;"></div></td>

334+ <td><div id="time1" class="timechart"

335+ style="width:450px;height:278px;"></div></td>

336+<!--

337+ <td><div id="cycle1" class="cyclechart"

338+ style="width:300px;height:278px;"></div></td>

339+-->

340+ </tr>

341+ </tbody>

342+ </table>

343+

344+ <table>

345+ <thead class="analysis">

346+ <th></th>

347+ <th class="cibound"

348+ title="0.95 confidence level">lower bound</th>

349+ <th>estimate</th>

350+ <th class="cibound"

351+ title="0.95 confidence level">upper bound</th>

352+ </thead>

353+ <tbody>

354+ <tr>

355+ <td>OLS regression</td>

356+ <td><span class="confinterval olstimelb1">xxx</span></td>

357+ <td><span class="olstimept1">xxx</span></td>

358+ <td><span class="confinterval olstimeub1">xxx</span></td>

359+ </tr>

360+ <tr>

361+ <td>R² goodness-of-fit</td>

362+ <td><span class="confinterval olsr2lb1">xxx</span></td>

363+ <td><span class="olsr2pt1">xxx</span></td>

364+ <td><span class="confinterval olsr2ub1">xxx</span></td>

365+ </tr>

366+ <tr>

367+ <td>Mean execution time</td>

368+ <td><span class="confinterval citime">2.0370099798754226e-4</span></td>

369+ <td><span class="time">2.0678688880349948e-4</span></td>

370+ <td><span class="confinterval citime">2.120795744857106e-4</span></td>

371+ </tr>

372+ <tr>

373+ <td>Standard deviation</td>

374+ <td><span class="confinterval citime">9.393316405757422e-6</span></td>

375+ <td><span class="time">1.2679488723877765e-5</span></td>

376+ <td><span class="confinterval citime">1.685081532022437e-5</span></td>

377+ </tr>

378+ </tbody>

379+ </table>

380+

381+ <span class="outliers">

382+ <p>Outlying measurements have severe

383+ (<span class="percent">0.5927893628180484</span>%)

384+ effect on estimated standard deviation.</p>

385+ </span>

386+<h2><a name="b2">Matrix Composition/100x100/WHNF - 100x100</a></h2>

387+ <table width="100%">

388+ <tbody>

389+ <tr>

390+ <td><div id="kde2" class="kdechart"

391+ style="width:450px;height:278px;"></div></td>

392+ <td><div id="time2" class="timechart"

393+ style="width:450px;height:278px;"></div></td>

394+<!--

395+ <td><div id="cycle2" class="cyclechart"

396+ style="width:300px;height:278px;"></div></td>

397+-->

398+ </tr>

399+ </tbody>

400+ </table>

401+

402+ <table>

403+ <thead class="analysis">

404+ <th></th>

405+ <th class="cibound"

406+ title="0.95 confidence level">lower bound</th>

407+ <th>estimate</th>

408+ <th class="cibound"

409+ title="0.95 confidence level">upper bound</th>

410+ </thead>

411+ <tbody>

412+ <tr>

413+ <td>OLS regression</td>

414+ <td><span class="confinterval olstimelb2">xxx</span></td>

415+ <td><span class="olstimept2">xxx</span></td>

416+ <td><span class="confinterval olstimeub2">xxx</span></td>

417+ </tr>

418+ <tr>

419+ <td>R² goodness-of-fit</td>

420+ <td><span class="confinterval olsr2lb2">xxx</span></td>

421+ <td><span class="olsr2pt2">xxx</span></td>

422+ <td><span class="confinterval olsr2ub2">xxx</span></td>

423+ </tr>

424+ <tr>

425+ <td>Mean execution time</td>

426+ <td><span class="confinterval citime">2.0050477013786835e-8</span></td>

427+ <td><span class="time">2.032500748180748e-8</span></td>

428+ <td><span class="confinterval citime">2.076846088643864e-8</span></td>

429+ </tr>

430+ <tr>

431+ <td>Standard deviation</td>

432+ <td><span class="confinterval citime">8.13204445187969e-10</span></td>

433+ <td><span class="time">1.1748079988373767e-9</span></td>

434+ <td><span class="confinterval citime">1.9440744217217704e-9</span></td>

435+ </tr>

436+ </tbody>

437+ </table>

438+

439+ <span class="outliers">

440+ <p>Outlying measurements have severe

441+ (<span class="percent">0.783687156722499</span>%)

442+ effect on estimated standard deviation.</p>

443+ </span>

444+<h2><a name="b3">Matrix Composition/100x100/NF - 100x100</a></h2>

445+ <table width="100%">

446+ <tbody>

447+ <tr>

448+ <td><div id="kde3" class="kdechart"

449+ style="width:450px;height:278px;"></div></td>

450+ <td><div id="time3" class="timechart"

451+ style="width:450px;height:278px;"></div></td>

452+<!--

453+ <td><div id="cycle3" class="cyclechart"

454+ style="width:300px;height:278px;"></div></td>

455+-->

456+ </tr>

457+ </tbody>

458+ </table>

459+

460+ <table>

461+ <thead class="analysis">

462+ <th></th>

463+ <th class="cibound"

464+ title="0.95 confidence level">lower bound</th>

465+ <th>estimate</th>

466+ <th class="cibound"

467+ title="0.95 confidence level">upper bound</th>

468+ </thead>

469+ <tbody>

470+ <tr>

471+ <td>OLS regression</td>

472+ <td><span class="confinterval olstimelb3">xxx</span></td>

473+ <td><span class="olstimept3">xxx</span></td>

474+ <td><span class="confinterval olstimeub3">xxx</span></td>

475+ </tr>

476+ <tr>

477+ <td>R² goodness-of-fit</td>

478+ <td><span class="confinterval olsr2lb3">xxx</span></td>

479+ <td><span class="olsr2pt3">xxx</span></td>

480+ <td><span class="confinterval olsr2ub3">xxx</span></td>

481+ </tr>

482+ <tr>

483+ <td>Mean execution time</td>

484+ <td><span class="confinterval citime">0.3498868480000965</span></td>

485+ <td><span class="time">0.3562973993334708</span></td>

486+ <td><span class="confinterval citime">0.36268595299998196</span></td>

487+ </tr>

488+ <tr>

489+ <td>Standard deviation</td>

490+ <td><span class="confinterval citime">3.523610261477639e-3</span></td>

491+ <td><span class="time">7.81042655007339e-3</span></td>

492+ <td><span class="confinterval citime">9.18947292446396e-3</span></td>

493+ </tr>

494+ </tbody>

495+ </table>

496+

497+ <span class="outliers">

498+ <p>Outlying measurements have moderate

499+ (<span class="percent">0.1875</span>%)

500+ effect on estimated standard deviation.</p>

501+ </span>

502+<h2><a name="b4">Matrix Composition/200x200/WHNF - 200x200</a></h2>

503+ <table width="100%">

504+ <tbody>

505+ <tr>

506+ <td><div id="kde4" class="kdechart"

507+ style="width:450px;height:278px;"></div></td>

508+ <td><div id="time4" class="timechart"

509+ style="width:450px;height:278px;"></div></td>

510+<!--

511+ <td><div id="cycle4" class="cyclechart"

512+ style="width:300px;height:278px;"></div></td>

513+-->

514+ </tr>

515+ </tbody>

516+ </table>

517+

518+ <table>

519+ <thead class="analysis">

520+ <th></th>

521+ <th class="cibound"

522+ title="0.95 confidence level">lower bound</th>

523+ <th>estimate</th>

524+ <th class="cibound"

525+ title="0.95 confidence level">upper bound</th>

526+ </thead>

527+ <tbody>

528+ <tr>

529+ <td>OLS regression</td>

530+ <td><span class="confinterval olstimelb4">xxx</span></td>

531+ <td><span class="olstimept4">xxx</span></td>

532+ <td><span class="confinterval olstimeub4">xxx</span></td>

533+ </tr>

534+ <tr>

535+ <td>R² goodness-of-fit</td>

536+ <td><span class="confinterval olsr2lb4">xxx</span></td>

537+ <td><span class="olsr2pt4">xxx</span></td>

538+ <td><span class="confinterval olsr2ub4">xxx</span></td>

539+ </tr>

540+ <tr>

541+ <td>Mean execution time</td>

542+ <td><span class="confinterval citime">2.0235240565823596e-8</span></td>

543+ <td><span class="time">2.0667543937993357e-8</span></td>

544+ <td><span class="confinterval citime">2.143971075518602e-8</span></td>

545+ </tr>

546+ <tr>

547+ <td>Standard deviation</td>

548+ <td><span class="confinterval citime">1.1209286317154773e-9</span></td>

549+ <td><span class="time">1.8602778611455406e-9</span></td>

550+ <td><span class="confinterval citime">2.8888629297529752e-9</span></td>

551+ </tr>

552+ </tbody>

553+ </table>

554+

555+ <span class="outliers">

556+ <p>Outlying measurements have severe

557+ (<span class="percent">0.8983666121212811</span>%)

558+ effect on estimated standard deviation.</p>

559+ </span>

560+<h2><a name="b5">Matrix Composition/200x200/NF - 200x200</a></h2>

561+ <table width="100%">

562+ <tbody>

563+ <tr>

564+ <td><div id="kde5" class="kdechart"

565+ style="width:450px;height:278px;"></div></td>

566+ <td><div id="time5" class="timechart"

567+ style="width:450px;height:278px;"></div></td>

568+<!--

569+ <td><div id="cycle5" class="cyclechart"

570+ style="width:300px;height:278px;"></div></td>

571+-->

572+ </tr>

573+ </tbody>

574+ </table>

575+

576+ <table>

577+ <thead class="analysis">

578+ <th></th>

579+ <th class="cibound"

580+ title="0.95 confidence level">lower bound</th>

581+ <th>estimate</th>

582+ <th class="cibound"

583+ title="0.95 confidence level">upper bound</th>

584+ </thead>

585+ <tbody>

586+ <tr>

587+ <td>OLS regression</td>

588+ <td><span class="confinterval olstimelb5">xxx</span></td>

589+ <td><span class="olstimept5">xxx</span></td>

590+ <td><span class="confinterval olstimeub5">xxx</span></td>

591+ </tr>

592+ <tr>

593+ <td>R² goodness-of-fit</td>

594+ <td><span class="confinterval olsr2lb5">xxx</span></td>

595+ <td><span class="olsr2pt5">xxx</span></td>

596+ <td><span class="confinterval olsr2ub5">xxx</span></td>

597+ </tr>

598+ <tr>

599+ <td>Mean execution time</td>

600+ <td><span class="confinterval citime">4.562200145314364</span></td>

601+ <td><span class="time">4.623436544688502</span></td>

602+ <td><span class="confinterval citime">4.66968996875039</span></td>

603+ </tr>

604+ <tr>

605+ <td>Standard deviation</td>

606+ <td><span class="confinterval citime">3.460169931915702e-2</span></td>

607+ <td><span class="time">6.412809734921064e-2</span></td>

608+ <td><span class="confinterval citime">8.889305315202672e-2</span></td>

609+ </tr>

610+ </tbody>

611+ </table>

612+

613+ <span class="outliers">

614+ <p>Outlying measurements have moderate

615+ (<span class="percent">0.18749999999999997</span>%)

616+ effect on estimated standard deviation.</p>

617+ </span>

618+<h2><a name="b6">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version</a></h2>

619+ <table width="100%">

620+ <tbody>

621+ <tr>

622+ <td><div id="kde6" class="kdechart"

623+ style="width:450px;height:278px;"></div></td>

624+ <td><div id="time6" class="timechart"

625+ style="width:450px;height:278px;"></div></td>

626+<!--

627+ <td><div id="cycle6" class="cyclechart"

628+ style="width:300px;height:278px;"></div></td>

629+-->

630+ </tr>

631+ </tbody>

632+ </table>

633+

634+ <table>

635+ <thead class="analysis">

636+ <th></th>

637+ <th class="cibound"

638+ title="0.95 confidence level">lower bound</th>

639+ <th>estimate</th>

640+ <th class="cibound"

641+ title="0.95 confidence level">upper bound</th>

642+ </thead>

643+ <tbody>

644+ <tr>

645+ <td>OLS regression</td>

646+ <td><span class="confinterval olstimelb6">xxx</span></td>

647+ <td><span class="olstimept6">xxx</span></td>

648+ <td><span class="confinterval olstimeub6">xxx</span></td>

649+ </tr>

650+ <tr>

651+ <td>R² goodness-of-fit</td>

652+ <td><span class="confinterval olsr2lb6">xxx</span></td>

653+ <td><span class="olsr2pt6">xxx</span></td>

654+ <td><span class="confinterval olsr2ub6">xxx</span></td>

655+ </tr>

656+ <tr>

657+ <td>Mean execution time</td>

658+ <td><span class="confinterval citime">2.2228158466256596</span></td>

659+ <td><span class="time">2.3105826970010335</span></td>

660+ <td><span class="confinterval citime">2.477541572751458</span></td>

661+ </tr>

662+ <tr>

663+ <td>Standard deviation</td>

664+ <td><span class="confinterval citime">1.668510235695031e-3</span></td>

665+ <td><span class="time">0.16563995052316</span></td>

666+ <td><span class="confinterval citime">0.19608795539767002</span></td>

667+ </tr>

668+ </tbody>

669+ </table>

670+

671+ <span class="outliers">

672+ <p>Outlying measurements have moderate

673+ (<span class="percent">0.2024935146554294</span>%)

674+ effect on estimated standard deviation.</p>

675+ </span>

676+<h2><a name="b7">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version</a></h2>

677+ <table width="100%">

678+ <tbody>

679+ <tr>

680+ <td><div id="kde7" class="kdechart"

681+ style="width:450px;height:278px;"></div></td>

682+ <td><div id="time7" class="timechart"

683+ style="width:450px;height:278px;"></div></td>

684+<!--

685+ <td><div id="cycle7" class="cyclechart"

686+ style="width:300px;height:278px;"></div></td>

687+-->

688+ </tr>

689+ </tbody>

690+ </table>

691+

692+ <table>

693+ <thead class="analysis">

694+ <th></th>

695+ <th class="cibound"

696+ title="0.95 confidence level">lower bound</th>

697+ <th>estimate</th>

698+ <th class="cibound"

699+ title="0.95 confidence level">upper bound</th>

700+ </thead>

701+ <tbody>

702+ <tr>

703+ <td>OLS regression</td>

704+ <td><span class="confinterval olstimelb7">xxx</span></td>

705+ <td><span class="olstimept7">xxx</span></td>

706+ <td><span class="confinterval olstimeub7">xxx</span></td>

707+ </tr>

708+ <tr>

709+ <td>R² goodness-of-fit</td>

710+ <td><span class="confinterval olsr2lb7">xxx</span></td>

711+ <td><span class="olsr2pt7">xxx</span></td>

712+ <td><span class="confinterval olsr2ub7">xxx</span></td>

713+ </tr>

714+ <tr>

715+ <td>Mean execution time</td>

716+ <td><span class="confinterval citime">2.4757740044307665e-3</span></td>

717+ <td><span class="time">2.672449312433179e-3</span></td>

718+ <td><span class="confinterval citime">3.145392355479385e-3</span></td>

719+ </tr>

720+ <tr>

721+ <td>Standard deviation</td>

722+ <td><span class="confinterval citime">4.61354238444537e-4</span></td>

723+ <td><span class="time">9.064184723100453e-4</span></td>

724+ <td><span class="confinterval citime">1.692293726555292e-3</span></td>

725+ </tr>

726+ </tbody>

727+ </table>

728+

729+ <span class="outliers">

730+ <p>Outlying measurements have severe

731+ (<span class="percent">0.9598911701243743</span>%)

732+ effect on estimated standard deviation.</p>

733+ </span>

734+<h2><a name="b8">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version</a></h2>

735+ <table width="100%">

736+ <tbody>

737+ <tr>

738+ <td><div id="kde8" class="kdechart"

739+ style="width:450px;height:278px;"></div></td>

740+ <td><div id="time8" class="timechart"

741+ style="width:450px;height:278px;"></div></td>

742+<!--

743+ <td><div id="cycle8" class="cyclechart"

744+ style="width:300px;height:278px;"></div></td>

745+-->

746+ </tr>

747+ </tbody>

748+ </table>

749+

750+ <table>

751+ <thead class="analysis">

752+ <th></th>

753+ <th class="cibound"

754+ title="0.95 confidence level">lower bound</th>

755+ <th>estimate</th>

756+ <th class="cibound"

757+ title="0.95 confidence level">upper bound</th>

758+ </thead>

759+ <tbody>

760+ <tr>

761+ <td>OLS regression</td>

762+ <td><span class="confinterval olstimelb8">xxx</span></td>

763+ <td><span class="olstimept8">xxx</span></td>

764+ <td><span class="confinterval olstimeub8">xxx</span></td>

765+ </tr>

766+ <tr>

767+ <td>R² goodness-of-fit</td>

768+ <td><span class="confinterval olsr2lb8">xxx</span></td>

769+ <td><span class="olsr2pt8">xxx</span></td>

770+ <td><span class="confinterval olsr2ub8">xxx</span></td>

771+ </tr>

772+ <tr>

773+ <td>Mean execution time</td>

774+ <td><span class="confinterval citime">1.0094556598949091e-3</span></td>

775+ <td><span class="time">1.0459672120901292e-3</span></td>

776+ <td><span class="confinterval citime">1.1900093977774448e-3</span></td>

777+ </tr>

778+ <tr>

779+ <td>Standard deviation</td>

780+ <td><span class="confinterval citime">4.936441129145525e-5</span></td>

781+ <td><span class="time">2.169293235834326e-4</span></td>

782+ <td><span class="confinterval citime">4.929920714921142e-4</span></td>

783+ </tr>

784+ </tbody>

785+ </table>

786+

787+ <span class="outliers">

788+ <p>Outlying measurements have severe

789+ (<span class="percent">0.9240968489851639</span>%)

790+ effect on estimated standard deviation.</p>

791+ </span>

792+<h2><a name="b9">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version</a></h2>

793+ <table width="100%">

794+ <tbody>

795+ <tr>

796+ <td><div id="kde9" class="kdechart"

797+ style="width:450px;height:278px;"></div></td>

798+ <td><div id="time9" class="timechart"

799+ style="width:450px;height:278px;"></div></td>

800+<!--

801+ <td><div id="cycle9" class="cyclechart"

802+ style="width:300px;height:278px;"></div></td>

803+-->

804+ </tr>

805+ </tbody>

806+ </table>

807+

808+ <table>

809+ <thead class="analysis">

810+ <th></th>

811+ <th class="cibound"

812+ title="0.95 confidence level">lower bound</th>

813+ <th>estimate</th>

814+ <th class="cibound"

815+ title="0.95 confidence level">upper bound</th>

816+ </thead>

817+ <tbody>

818+ <tr>

819+ <td>OLS regression</td>

820+ <td><span class="confinterval olstimelb9">xxx</span></td>

821+ <td><span class="olstimept9">xxx</span></td>

822+ <td><span class="confinterval olstimeub9">xxx</span></td>

823+ </tr>

824+ <tr>

825+ <td>R² goodness-of-fit</td>

826+ <td><span class="confinterval olsr2lb9">xxx</span></td>

827+ <td><span class="olsr2pt9">xxx</span></td>

828+ <td><span class="confinterval olsr2ub9">xxx</span></td>

829+ </tr>

830+ <tr>

831+ <td>Mean execution time</td>

832+ <td><span class="confinterval citime">1.1142126609993284</span></td>

833+ <td><span class="time">1.1506916786456713</span></td>

834+ <td><span class="confinterval citime">1.1642280000833125</span></td>

835+ </tr>

836+ <tr>

837+ <td>Standard deviation</td>

838+ <td><span class="confinterval citime">3.115381125098793e-3</span></td>

839+ <td><span class="time">2.468474748870533e-2</span></td>

840+ <td><span class="confinterval citime">3.126079530343771e-2</span></td>

841+ </tr>

842+ </tbody>

843+ </table>

844+

845+ <span class="outliers">

846+ <p>Outlying measurements have moderate

847+ (<span class="percent">0.1875</span>%)

848+ effect on estimated standard deviation.</p>

849+ </span>

850+<h2><a name="b10">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version</a></h2>

851+ <table width="100%">

852+ <tbody>

853+ <tr>

854+ <td><div id="kde10" class="kdechart"

855+ style="width:450px;height:278px;"></div></td>

856+ <td><div id="time10" class="timechart"

857+ style="width:450px;height:278px;"></div></td>

858+<!--

859+ <td><div id="cycle10" class="cyclechart"

860+ style="width:300px;height:278px;"></div></td>

861+-->

862+ </tr>

863+ </tbody>

864+ </table>

865+

866+ <table>

867+ <thead class="analysis">

868+ <th></th>

869+ <th class="cibound"

870+ title="0.95 confidence level">lower bound</th>

871+ <th>estimate</th>

872+ <th class="cibound"

873+ title="0.95 confidence level">upper bound</th>

874+ </thead>

875+ <tbody>

876+ <tr>

877+ <td>OLS regression</td>

878+ <td><span class="confinterval olstimelb10">xxx</span></td>

879+ <td><span class="olstimept10">xxx</span></td>

880+ <td><span class="confinterval olstimeub10">xxx</span></td>

881+ </tr>

882+ <tr>

883+ <td>R² goodness-of-fit</td>

884+ <td><span class="confinterval olsr2lb10">xxx</span></td>

885+ <td><span class="olsr2pt10">xxx</span></td>

886+ <td><span class="confinterval olsr2ub10">xxx</span></td>

887+ </tr>

888+ <tr>

889+ <td>Mean execution time</td>

890+ <td><span class="confinterval citime">0.530786815458517</span></td>

891+ <td><span class="time">0.5400133454575856</span></td>

892+ <td><span class="confinterval citime">0.5473636064980383</span></td>

893+ </tr>

894+ <tr>

895+ <td>Standard deviation</td>

896+ <td><span class="confinterval citime">4.333057553316104e-3</span></td>

897+ <td><span class="time">9.71574644699696e-3</span></td>

898+ <td><span class="confinterval citime">1.3200731985635176e-2</span></td>

899+ </tr>

900+ </tbody>

901+ </table>

902+

903+ <span class="outliers">

904+ <p>Outlying measurements have moderate

905+ (<span class="percent">0.18749999999999997</span>%)

906+ effect on estimated standard deviation.</p>

907+ </span>

908+

909+ <h2><a name="grokularation">understanding this report</a></h2>

910+

911+ <p>In this report, each function benchmarked by criterion is assigned

912+ a section of its own. The charts in each section are active; if

913+ you hover your mouse over data points and annotations, you will see

914+ more details.</p>

915+

916+ <ul>

917+ <li>The chart on the left is a

918+ <a href="http://en.wikipedia.org/wiki/Kernel_density_estimation">kernel

919+ density estimate</a> (also known as a KDE) of time

920+ measurements. This graphs the probability of any given time

921+ measurement occurring. A spike indicates that a measurement of a

922+ particular time occurred; its height indicates how often that

923+ measurement was repeated.</li>

924+

925+ <li>The chart on the right is the raw data from which the kernel

926+ density estimate is built. The <i>x</i> axis indicates the

927+ number of loop iterations, while the <i>y</i> axis shows measured

928+ execution time for the given number of loop iterations. The

929+ line behind the values is the linear regression prediction of

930+ execution time for a given number of iterations. Ideally, all

931+ measurements will be on (or very near) this line.</li>

932+ </ul>

933+

934+ <p>Under the charts is a small table.

935+ The first two rows are the results of a linear regression run

936+ on the measurements displayed in the right-hand chart.</p>

937+

938+ <ul>

939+ <li><i>OLS regression</i> indicates the

940+ time estimated for a single loop iteration using an ordinary

941+ least-squares regression model. This number is more accurate

942+ than the <i>mean</i> estimate below it, as it more effectively

943+ eliminates measurement overhead and other constant factors.</li>

944+ <li><i>R² goodness-of-fit</i> is a measure of how

945+ accurately the linear regression model fits the observed

946+ measurements. If the measurements are not too noisy, R²

947+ should lie between 0.99 and 1, indicating an excellent fit. If

948+ the number is below 0.99, something is confounding the accuracy

949+ of the linear model.</li>

950+ <li><i>Mean execution time</i> and <i>standard deviation</i> are

951+ statistics calculated from execution time

952+ divided by number of iterations.</li>

953+ </ul>

954+

955+ <p>We use a statistical technique called

956+ the <a href="http://en.wikipedia.org/wiki/Bootstrapping_(statistics)">bootstrap</a>

957+ to provide confidence intervals on our estimates. The

958+ bootstrap-derived upper and lower bounds on estimates let you see

959+ how accurate we believe those estimates to be. (Hover the mouse

960+ over the table headers to see the confidence levels.)</p>

961+

962+ <p>A noisy benchmarking environment can cause some or many

963+ measurements to fall far from the mean. These outlying

964+ measurements can have a significant inflationary effect on the

965+ estimate of the standard deviation. We calculate and display an

966+ estimate of the extent to which the standard deviation has been

967+ inflated by outliers.</p>

968+

969+<script type="text/javascript">

970+$(function () {

971+ function mangulate(rpt) {

972+ var measured = function(key) {

973+ var idx = rpt.reportKeys.indexOf(key);

974+ return rpt.reportMeasured.map(function(r) { return r[idx]; });

975+ };

976+ var lowerBound = function(est) {

977+ return est.estPoint - est.estError.confIntLDX;

978+ };

979+ var upperBound = function(est) {

980+ return est.estPoint + est.estError.confIntUDX;

981+ };

982+ var number = rpt.reportNumber;

983+ var name = rpt.reportName;

984+ var mean = rpt.reportAnalysis.anMean.estPoint;

985+ var iters = measured("iters");

986+ var times = measured("time");

987+ var kdetimes = rpt.reportKDEs[0].kdeValues;

988+ var kdepdf = rpt.reportKDEs[0].kdePDF;

989+

990+ var meanSecs = mean;

991+ var units = $.timeUnits(mean);

992+ var rgrs = rpt.reportAnalysis.anRegress[0];

993+ var scale = units[0];

994+ var olsTime = rgrs.regCoeffs.iters;

995+ $(".olstimept" + number).text(function() {

996+ return $.renderTime(olsTime.estPoint);

997+ });

998+ $(".olstimelb" + number).text(function() {

999+ return $.renderTime(lowerBound(olsTime));

1000+ });

1001+ $(".olstimeub" + number).text(function() {

1002+ return $.renderTime(upperBound(olsTime));

1003+ });

1004+ $(".olsr2pt" + number).text(function() {

1005+ return rgrs.regRSquare.estPoint.toFixed(3);

1006+ });

1007+ $(".olsr2lb" + number).text(function() {

1008+ return lowerBound(rgrs.regRSquare).toFixed(3);

1009+ });

1010+ $(".olsr2ub" + number).text(function() {

1011+ return upperBound(rgrs.regRSquare).toFixed(3);

1012+ });

1013+ mean *= scale;

1014+ kdetimes = $.scaleBy(scale, kdetimes);

1015+ var kq = $("#kde" + number);

1016+ var k = $.plot(kq,

1017+ [{ label: name + " time densities",

1018+ data: $.zip(kdetimes, kdepdf),

1019+ }],

1020+ { xaxis: { tickFormatter: $.unitFormatter(scale) },

1021+ yaxis: { ticks: false },

1022+ grid: { borderColor: "#777",

1023+ hoverable: true, markings: [ { color: '#6fd3fb',

1024+ lineWidth: 1.5, xaxis: { from: mean, to: mean } } ] },

1025+ });

1026+ var o = k.pointOffset({ x: mean, y: 0});

1027+ kq.append('<div class="meanlegend" title="' + $.renderTime(meanSecs) +

1028+ '" style="position:absolute;left:' + (o.left + 4) +

1029+ 'px;bottom:139px;">mean</div>');

1030+ $.addTooltip("#kde" + number,

1031+ function(secs) { return $.renderTime(secs / scale); });

1032+ var timepairs = new Array(times.length);

1033+ var lastiter = iters[iters.length-1];

1034+ var olspairs = [[0,0], [lastiter, lastiter * scale * olsTime.estPoint]];

1035+ for (var i = 0; i < times.length; i++)

1036+ timepairs[i] = [iters[i],times[i]*scale];

1037+ iterFormatter = function() {

1038+ var denom = 0;

1039+ return function(iters) {

1040+ if (iters == 0)

1041+ return '';

1042+ if (denom > 0)

1043+ return (iters / denom).toFixed();

1044+ var power;

1045+ if (iters >= 1e9) {

1046+ denom = '1e9'; power = '⁹';

1047+ }

1048+ if (iters >= 1e6) {

1049+ denom = '1e6'; power = '⁶';

1050+ }

1051+ else if (iters >= 1e3) {

1052+ denom = '1e3'; power = '³';

1053+ }

1054+ else denom = 1;

1055+ if (denom > 1) {

1056+ iters = (iters / denom).toFixed();

1057+ iters += '×10' + power + ' iters';

1058+ } else {

1059+ iters += ' iters';

1060+ }

1061+ return iters;

1062+ };

1063+ };

1064+ $.plot($("#time" + number),

1065+ [{ label: "regression", data: olspairs,

1066+ lines: { show: true } },

1067+ { label: name + " times", data: timepairs,

1068+ points: { show: true } }],

1069+ { grid: { borderColor: "#777", hoverable: true },

1070+ xaxis: { tickFormatter: iterFormatter() },

1071+ yaxis: { tickFormatter: $.unitFormatter(scale) } });

1072+ $.addTooltip("#time" + number,

1073+ function(iters,secs) {

1074+ return ($.renderTime(secs / scale) + ' / ' +

1075+ iters.toLocaleString() + ' iters');

1076+ });

1077+ if (0) {

1078+ var cyclepairs = new Array(cycles.length);

1079+ for (var i = 0; i < cycles.length; i++)

1080+ cyclepairs[i] = [cycles[i],i];

1081+ $.plot($("#cycle" + number),

1082+ [{ label: name + " cycles",

1083+ data: cyclepairs }],

1084+ { points: { show: true },

1085+ grid: { borderColor: "#777", hoverable: true },

1086+ xaxis: { tickFormatter:

1087+ function(cycles,axis) { return cycles + ' cycles'; }},

1088+ yaxis: { ticks: false },

1089+ });

1090+ $.addTooltip("#cycles" + number, function(x,y) { return x + ' cycles'; });

1091+ }

1092+ };

1093+ var reports = 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1094+ reports.map(mangulate);

1095+

1096+ var benches = ["Matrix Composition/10x10/WHNF - 10x10","Matrix Composition/10x10/NF - 10x10","Matrix Composition/100x100/WHNF - 100x100","Matrix Composition/100x100/NF - 100x100","Matrix Composition/200x200/WHNF - 200x200","Matrix Composition/200x200/NF - 200x200","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version","Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version","Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version","Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version",];

1097+ var ylabels = [[-0,"<a href=\"#b0\">Matrix Composition/10x10/WHNF - 10x10</a>"],[-1,"<a href=\"#b1\">Matrix Composition/10x10/NF - 10x10</a>"],[-2,"<a href=\"#b2\">Matrix Composition/100x100/WHNF - 100x100</a>"],[-3,"<a href=\"#b3\">Matrix Composition/100x100/NF - 100x100</a>"],[-4,"<a href=\"#b4\">Matrix Composition/200x200/WHNF - 200x200</a>"],[-5,"<a href=\"#b5\">Matrix Composition/200x200/NF - 200x200</a>"],[-6,"<a href=\"#b6\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version</a>"],[-7,"<a href=\"#b7\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version</a>"],[-8,"<a href=\"#b8\">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version</a>"],[-9,"<a href=\"#b9\">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version</a>"],[-10,"<a href=\"#b10\">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version</a>"],];

1098+ var means = $.scaleTimes([2.4514866756029205e-8,2.0678688880349948e-4,2.032500748180748e-8,0.3562973993334708,2.0667543937993357e-8,4.623436544688502,2.3105826970010335,2.672449312433179e-3,1.0459672120901292e-3,1.1506916786456713,0.5400133454575856,]);

1099+ var stddevs = [9.647785488002723e-10,1.2679488723877765e-5,1.1748079988373767e-9,7.81042655007339e-3,1.8602778611455406e-9,6.412809734921064e-2,0.16563995052316,9.064184723100453e-4,2.169293235834326e-4,2.468474748870533e-2,9.71574644699696e-3,];

1100+ stddevs = $.scaleBy(means[1], stddevs);

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1122+ xs[xs.length - 1].data.push([means[0][i], -i, stddevs[i]]);

1123+ }

1124+ max_time = Math.max(max_time, means[0][i] + stddevs[i]);

1125+ }

1126+ var oq = $("#overview");

1127+ var max_x = max_time * 1.02;

1128+ o = $.plot(oq, xs, { grid: { borderColor: "#777", hoverable: true },

1129+ legend: { show: xs.length > 1 },

1130+ xaxis: { max: max_x, zoomRange: [false, max_x], panRange: [0, max_x] },

1131+ yaxis: { ticks: ylabels, tickColor: '#ffffff', zoomRange: false, panRange: false },

1132+ zoom: { interactive: true, amount: 1.05 },

1133+ pan: { interactive: true } });

1134+ if (benches.length > 3)

1135+ o.getPlaceholder().height(28*benches.length);

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1139+ $.addTooltip("#overview", function(x,y) { return $.renderTime(x / means[1]); });

1140+});

1141+$(document).ready(function () {

1142+ $(".time").text(function(_, text) {

1143+ return $.renderTime(text);

1144+ });

1145+ $(".citime").text(function(_, text) {

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1148+ $(".percent").text(function(_, text) {

1149+ return (text*100).toFixed(1);

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1152+</script>

1153+

1154+ </div>

1155+ </div>

1156+ <div id="footer">

1157+ <div class="body">

1158+ <div class="footfirst">

1159+ <h2>colophon</h2>

1160+ <p>This report was created using the

1161+ <a href="http://hackage.haskell.org/package/criterion">criterion</a>

1162+ benchmark execution and performance analysis tool.</p>

1163+ <p>Criterion is developed and maintained

1164+ by <a href="http://www.serpentine.com/blog/">Bryan O'Sullivan</a>.</p>

1165+ </div>

1166+ </div>

1167+ </div>

1168+ </body>

1169+</html>

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256+ </style>

257+ <![endif]-->

258+ </head>

259+ <body>

260+ <div id="wrap">

261+ <div id="main" class="body">

262+ <h1>criterion performance measurements</h1>

263+

264+<h2>overview</h2>

265+

266+<p><a href="#grokularation">want to understand this report?</a></p>

267+

268+<div id="overview" class="ovchart" style="width:900px;height:100px;"></div>

269+

270+<h2><a name="b0">Matrix Composition/10x10/WHNF - 10x10</a></h2>

271+ <table width="100%">

272+ <tbody>

273+ <tr>

274+ <td><div id="kde0" class="kdechart"

275+ style="width:450px;height:278px;"></div></td>

276+ <td><div id="time0" class="timechart"

277+ style="width:450px;height:278px;"></div></td>

278+<!--

279+ <td><div id="cycle0" class="cyclechart"

280+ style="width:300px;height:278px;"></div></td>

281+-->

282+ </tr>

283+ </tbody>

284+ </table>

285+

286+ <table>

287+ <thead class="analysis">

288+ <th></th>

289+ <th class="cibound"

290+ title="0.95 confidence level">lower bound</th>

291+ <th>estimate</th>

292+ <th class="cibound"

293+ title="0.95 confidence level">upper bound</th>

294+ </thead>

295+ <tbody>

296+ <tr>

297+ <td>OLS regression</td>

298+ <td><span class="confinterval olstimelb0">xxx</span></td>

299+ <td><span class="olstimept0">xxx</span></td>

300+ <td><span class="confinterval olstimeub0">xxx</span></td>

301+ </tr>

302+ <tr>

303+ <td>R² goodness-of-fit</td>

304+ <td><span class="confinterval olsr2lb0">xxx</span></td>

305+ <td><span class="olsr2pt0">xxx</span></td>

306+ <td><span class="confinterval olsr2ub0">xxx</span></td>

307+ </tr>

308+ <tr>

309+ <td>Mean execution time</td>

310+ <td><span class="confinterval citime">1.2439476132780966e-4</span></td>

311+ <td><span class="time">1.2521282696584778e-4</span></td>

312+ <td><span class="confinterval citime">1.2627361635087712e-4</span></td>

313+ </tr>

314+ <tr>

315+ <td>Standard deviation</td>

316+ <td><span class="confinterval citime">2.3769830641700065e-6</span></td>

317+ <td><span class="time">3.0000227210624054e-6</span></td>

318+ <td><span class="confinterval citime">3.868635052370606e-6</span></td>

319+ </tr>

320+ </tbody>

321+ </table>

322+

323+ <span class="outliers">

324+ <p>Outlying measurements have moderate

325+ (<span class="percent">0.19510840974237945</span>%)

326+ effect on estimated standard deviation.</p>

327+ </span>

328+<h2><a name="b1">Matrix Composition/10x10/NF - 10x10</a></h2>

329+ <table width="100%">

330+ <tbody>

331+ <tr>

332+ <td><div id="kde1" class="kdechart"

333+ style="width:450px;height:278px;"></div></td>

334+ <td><div id="time1" class="timechart"

335+ style="width:450px;height:278px;"></div></td>

336+<!--

337+ <td><div id="cycle1" class="cyclechart"

338+ style="width:300px;height:278px;"></div></td>

339+-->

340+ </tr>

341+ </tbody>

342+ </table>

343+

344+ <table>

345+ <thead class="analysis">

346+ <th></th>

347+ <th class="cibound"

348+ title="0.95 confidence level">lower bound</th>

349+ <th>estimate</th>

350+ <th class="cibound"

351+ title="0.95 confidence level">upper bound</th>

352+ </thead>

353+ <tbody>

354+ <tr>

355+ <td>OLS regression</td>

356+ <td><span class="confinterval olstimelb1">xxx</span></td>

357+ <td><span class="olstimept1">xxx</span></td>

358+ <td><span class="confinterval olstimeub1">xxx</span></td>

359+ </tr>

360+ <tr>

361+ <td>R² goodness-of-fit</td>

362+ <td><span class="confinterval olsr2lb1">xxx</span></td>

363+ <td><span class="olsr2pt1">xxx</span></td>

364+ <td><span class="confinterval olsr2ub1">xxx</span></td>

365+ </tr>

366+ <tr>

367+ <td>Mean execution time</td>

368+ <td><span class="confinterval citime">1.4537321208713184e-4</span></td>

369+ <td><span class="time">1.532024430909428e-4</span></td>

370+ <td><span class="confinterval citime">1.6749129455977834e-4</span></td>

371+ </tr>

372+ <tr>

373+ <td>Standard deviation</td>

374+ <td><span class="confinterval citime">2.365045193527146e-5</span></td>

375+ <td><span class="time">3.649213223188502e-5</span></td>

376+ <td><span class="confinterval citime">5.3596936354843454e-5</span></td>

377+ </tr>

378+ </tbody>

379+ </table>

380+

381+ <span class="outliers">

382+ <p>Outlying measurements have severe

383+ (<span class="percent">0.9609582426012205</span>%)

384+ effect on estimated standard deviation.</p>

385+ </span>

386+<h2><a name="b2">Matrix Composition/100x100/WHNF - 100x100</a></h2>

387+ <table width="100%">

388+ <tbody>

389+ <tr>

390+ <td><div id="kde2" class="kdechart"

391+ style="width:450px;height:278px;"></div></td>

392+ <td><div id="time2" class="timechart"

393+ style="width:450px;height:278px;"></div></td>

394+<!--

395+ <td><div id="cycle2" class="cyclechart"

396+ style="width:300px;height:278px;"></div></td>

397+-->

398+ </tr>

399+ </tbody>

400+ </table>

401+

402+ <table>

403+ <thead class="analysis">

404+ <th></th>

405+ <th class="cibound"

406+ title="0.95 confidence level">lower bound</th>

407+ <th>estimate</th>

408+ <th class="cibound"

409+ title="0.95 confidence level">upper bound</th>

410+ </thead>

411+ <tbody>

412+ <tr>

413+ <td>OLS regression</td>

414+ <td><span class="confinterval olstimelb2">xxx</span></td>

415+ <td><span class="olstimept2">xxx</span></td>

416+ <td><span class="confinterval olstimeub2">xxx</span></td>

417+ </tr>

418+ <tr>

419+ <td>R² goodness-of-fit</td>

420+ <td><span class="confinterval olsr2lb2">xxx</span></td>

421+ <td><span class="olsr2pt2">xxx</span></td>

422+ <td><span class="confinterval olsr2ub2">xxx</span></td>

423+ </tr>

424+ <tr>

425+ <td>Mean execution time</td>

426+ <td><span class="confinterval citime">0.11287564945528825</span></td>

427+ <td><span class="time">0.11922032795600032</span></td>

428+ <td><span class="confinterval citime">0.12600585030653141</span></td>

429+ </tr>

430+ <tr>

431+ <td>Standard deviation</td>

432+ <td><span class="confinterval citime">6.3874541360917384e-3</span></td>

433+ <td><span class="time">9.77563027930971e-3</span></td>

434+ <td><span class="confinterval citime">1.620035460618151e-2</span></td>

435+ </tr>

436+ </tbody>

437+ </table>

438+

439+ <span class="outliers">

440+ <p>Outlying measurements have moderate

441+ (<span class="percent">0.23184395941421526</span>%)

442+ effect on estimated standard deviation.</p>

443+ </span>

444+<h2><a name="b3">Matrix Composition/100x100/NF - 100x100</a></h2>

445+ <table width="100%">

446+ <tbody>

447+ <tr>

448+ <td><div id="kde3" class="kdechart"

449+ style="width:450px;height:278px;"></div></td>

450+ <td><div id="time3" class="timechart"

451+ style="width:450px;height:278px;"></div></td>

452+<!--

453+ <td><div id="cycle3" class="cyclechart"

454+ style="width:300px;height:278px;"></div></td>

455+-->

456+ </tr>

457+ </tbody>

458+ </table>

459+

460+ <table>

461+ <thead class="analysis">

462+ <th></th>

463+ <th class="cibound"

464+ title="0.95 confidence level">lower bound</th>

465+ <th>estimate</th>

466+ <th class="cibound"

467+ title="0.95 confidence level">upper bound</th>

468+ </thead>

469+ <tbody>

470+ <tr>

471+ <td>OLS regression</td>

472+ <td><span class="confinterval olstimelb3">xxx</span></td>

473+ <td><span class="olstimept3">xxx</span></td>

474+ <td><span class="confinterval olstimeub3">xxx</span></td>

475+ </tr>

476+ <tr>

477+ <td>R² goodness-of-fit</td>

478+ <td><span class="confinterval olsr2lb3">xxx</span></td>

479+ <td><span class="olsr2pt3">xxx</span></td>

480+ <td><span class="confinterval olsr2ub3">xxx</span></td>

481+ </tr>

482+ <tr>

483+ <td>Mean execution time</td>

484+ <td><span class="confinterval citime">0.1110982578725974</span></td>

485+ <td><span class="time">0.11758616896428131</span></td>

486+ <td><span class="confinterval citime">0.12249179825349378</span></td>

487+ </tr>

488+ <tr>

489+ <td>Standard deviation</td>

490+ <td><span class="confinterval citime">5.369746750528417e-3</span></td>

491+ <td><span class="time">8.150134548496543e-3</span></td>

492+ <td><span class="confinterval citime">1.1065658668699107e-2</span></td>

493+ </tr>

494+ </tbody>

495+ </table>

496+

497+ <span class="outliers">

498+ <p>Outlying measurements have moderate

499+ (<span class="percent">0.22459068358328985</span>%)

500+ effect on estimated standard deviation.</p>

501+ </span>

502+<h2><a name="b4">Matrix Composition/200x200/WHNF - 200x200</a></h2>

503+ <table width="100%">

504+ <tbody>

505+ <tr>

506+ <td><div id="kde4" class="kdechart"

507+ style="width:450px;height:278px;"></div></td>

508+ <td><div id="time4" class="timechart"

509+ style="width:450px;height:278px;"></div></td>

510+<!--

511+ <td><div id="cycle4" class="cyclechart"

512+ style="width:300px;height:278px;"></div></td>

513+-->

514+ </tr>

515+ </tbody>

516+ </table>

517+

518+ <table>

519+ <thead class="analysis">

520+ <th></th>

521+ <th class="cibound"

522+ title="0.95 confidence level">lower bound</th>

523+ <th>estimate</th>

524+ <th class="cibound"

525+ title="0.95 confidence level">upper bound</th>

526+ </thead>

527+ <tbody>

528+ <tr>

529+ <td>OLS regression</td>

530+ <td><span class="confinterval olstimelb4">xxx</span></td>

531+ <td><span class="olstimept4">xxx</span></td>

532+ <td><span class="confinterval olstimeub4">xxx</span></td>

533+ </tr>

534+ <tr>

535+ <td>R² goodness-of-fit</td>

536+ <td><span class="confinterval olsr2lb4">xxx</span></td>

537+ <td><span class="olsr2pt4">xxx</span></td>

538+ <td><span class="confinterval olsr2ub4">xxx</span></td>

539+ </tr>

540+ <tr>

541+ <td>Mean execution time</td>

542+ <td><span class="confinterval citime">0.9781591890205164</span></td>

543+ <td><span class="time">1.0404128327718354</span></td>

544+ <td><span class="confinterval citime">1.0852378857525764</span></td>

545+ </tr>

546+ <tr>

547+ <td>Standard deviation</td>

548+ <td><span class="confinterval citime">2.2371087252395228e-2</span></td>

549+ <td><span class="time">6.182803786470918e-2</span></td>

550+ <td><span class="confinterval citime">8.480026920295321e-2</span></td>

551+ </tr>

552+ </tbody>

553+ </table>

554+

555+ <span class="outliers">

556+ <p>Outlying measurements have moderate

557+ (<span class="percent">0.18749999999999994</span>%)

558+ effect on estimated standard deviation.</p>

559+ </span>

560+<h2><a name="b5">Matrix Composition/200x200/NF - 200x200</a></h2>

561+ <table width="100%">

562+ <tbody>

563+ <tr>

564+ <td><div id="kde5" class="kdechart"

565+ style="width:450px;height:278px;"></div></td>

566+ <td><div id="time5" class="timechart"

567+ style="width:450px;height:278px;"></div></td>

568+<!--

569+ <td><div id="cycle5" class="cyclechart"

570+ style="width:300px;height:278px;"></div></td>

571+-->

572+ </tr>

573+ </tbody>

574+ </table>

575+

576+ <table>

577+ <thead class="analysis">

578+ <th></th>

579+ <th class="cibound"

580+ title="0.95 confidence level">lower bound</th>

581+ <th>estimate</th>

582+ <th class="cibound"

583+ title="0.95 confidence level">upper bound</th>

584+ </thead>

585+ <tbody>

586+ <tr>

587+ <td>OLS regression</td>

588+ <td><span class="confinterval olstimelb5">xxx</span></td>

589+ <td><span class="olstimept5">xxx</span></td>

590+ <td><span class="confinterval olstimeub5">xxx</span></td>

591+ </tr>

592+ <tr>

593+ <td>R² goodness-of-fit</td>

594+ <td><span class="confinterval olsr2lb5">xxx</span></td>

595+ <td><span class="olsr2pt5">xxx</span></td>

596+ <td><span class="confinterval olsr2ub5">xxx</span></td>

597+ </tr>

598+ <tr>

599+ <td>Mean execution time</td>

600+ <td><span class="confinterval citime">1.1011682298167216</span></td>

601+ <td><span class="time">1.1075485033964771</span></td>

602+ <td><span class="confinterval citime">1.1151673705599023</span></td>

603+ </tr>

604+ <tr>

605+ <td>Standard deviation</td>

606+ <td><span class="confinterval citime">2.193747621276998e-3</span></td>

607+ <td><span class="time">7.979551817654461e-3</span></td>

608+ <td><span class="confinterval citime">1.077654356866516e-2</span></td>

609+ </tr>

610+ </tbody>

611+ </table>

612+

613+ <span class="outliers">

614+ <p>Outlying measurements have moderate

615+ (<span class="percent">0.1875</span>%)

616+ effect on estimated standard deviation.</p>

617+ </span>

618+<h2><a name="b6">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/List Distribution - Applicative version</a></h2>

619+ <table width="100%">

620+ <tbody>

621+ <tr>

622+ <td><div id="kde6" class="kdechart"

623+ style="width:450px;height:278px;"></div></td>

624+ <td><div id="time6" class="timechart"

625+ style="width:450px;height:278px;"></div></td>

626+<!--

627+ <td><div id="cycle6" class="cyclechart"

628+ style="width:300px;height:278px;"></div></td>

629+-->

630+ </tr>

631+ </tbody>

632+ </table>

633+

634+ <table>

635+ <thead class="analysis">

636+ <th></th>

637+ <th class="cibound"

638+ title="0.95 confidence level">lower bound</th>

639+ <th>estimate</th>

640+ <th class="cibound"

641+ title="0.95 confidence level">upper bound</th>

642+ </thead>

643+ <tbody>

644+ <tr>

645+ <td>OLS regression</td>

646+ <td><span class="confinterval olstimelb6">xxx</span></td>

647+ <td><span class="olstimept6">xxx</span></td>

648+ <td><span class="confinterval olstimeub6">xxx</span></td>

649+ </tr>

650+ <tr>

651+ <td>R² goodness-of-fit</td>

652+ <td><span class="confinterval olsr2lb6">xxx</span></td>

653+ <td><span class="olsr2pt6">xxx</span></td>

654+ <td><span class="confinterval olsr2ub6">xxx</span></td>

655+ </tr>

656+ <tr>

657+ <td>Mean execution time</td>

658+ <td><span class="confinterval citime">2.338956891665778</span></td>

659+ <td><span class="time">2.3478542657700623</span></td>

660+ <td><span class="confinterval citime">2.359088486582247</span></td>

661+ </tr>

662+ <tr>

663+ <td>Standard deviation</td>

664+ <td><span class="confinterval citime">3.62336445641734e-3</span></td>

665+ <td><span class="time">1.2441745894453989e-2</span></td>

666+ <td><span class="confinterval citime">1.67050971444586e-2</span></td>

667+ </tr>

668+ </tbody>

669+ </table>

670+

671+ <span class="outliers">

672+ <p>Outlying measurements have moderate

673+ (<span class="percent">0.18749999999999997</span>%)

674+ effect on estimated standard deviation.</p>

675+ </span>

676+<h2><a name="b7">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Applicative version</a></h2>

677+ <table width="100%">

678+ <tbody>

679+ <tr>

680+ <td><div id="kde7" class="kdechart"

681+ style="width:450px;height:278px;"></div></td>

682+ <td><div id="time7" class="timechart"

683+ style="width:450px;height:278px;"></div></td>

684+<!--

685+ <td><div id="cycle7" class="cyclechart"

686+ style="width:300px;height:278px;"></div></td>

687+-->

688+ </tr>

689+ </tbody>

690+ </table>

691+

692+ <table>

693+ <thead class="analysis">

694+ <th></th>

695+ <th class="cibound"

696+ title="0.95 confidence level">lower bound</th>

697+ <th>estimate</th>

698+ <th class="cibound"

699+ title="0.95 confidence level">upper bound</th>

700+ </thead>

701+ <tbody>

702+ <tr>

703+ <td>OLS regression</td>

704+ <td><span class="confinterval olstimelb7">xxx</span></td>

705+ <td><span class="olstimept7">xxx</span></td>

706+ <td><span class="confinterval olstimeub7">xxx</span></td>

707+ </tr>

708+ <tr>

709+ <td>R² goodness-of-fit</td>

710+ <td><span class="confinterval olsr2lb7">xxx</span></td>

711+ <td><span class="olsr2pt7">xxx</span></td>

712+ <td><span class="confinterval olsr2ub7">xxx</span></td>

713+ </tr>

714+ <tr>

715+ <td>Mean execution time</td>

716+ <td><span class="confinterval citime">1.6422040204675979e-3</span></td>

717+ <td><span class="time">1.7931655457283859e-3</span></td>

718+ <td><span class="confinterval citime">1.9714955275173672e-3</span></td>

719+ </tr>

720+ <tr>

721+ <td>Standard deviation</td>

722+ <td><span class="confinterval citime">3.9388340187426643e-4</span></td>

723+ <td><span class="time">5.021999918501304e-4</span></td>

724+ <td><span class="confinterval citime">6.587054587998915e-4</span></td>

725+ </tr>

726+ </tbody>

727+ </table>

728+

729+ <span class="outliers">

730+ <p>Outlying measurements have severe

731+ (<span class="percent">0.9470035753933379</span>%)

732+ effect on estimated standard deviation.</p>

733+ </span>

734+<h2><a name="b8">Matrix vs List - `select`/Distribution `select` - 100+100 / 100x100/Matrix Distribution - Selective version</a></h2>

735+ <table width="100%">

736+ <tbody>

737+ <tr>

738+ <td><div id="kde8" class="kdechart"

739+ style="width:450px;height:278px;"></div></td>

740+ <td><div id="time8" class="timechart"

741+ style="width:450px;height:278px;"></div></td>

742+<!--

743+ <td><div id="cycle8" class="cyclechart"

744+ style="width:300px;height:278px;"></div></td>

745+-->

746+ </tr>

747+ </tbody>

748+ </table>

749+

750+ <table>

751+ <thead class="analysis">

752+ <th></th>

753+ <th class="cibound"

754+ title="0.95 confidence level">lower bound</th>

755+ <th>estimate</th>

756+ <th class="cibound"

757+ title="0.95 confidence level">upper bound</th>

758+ </thead>

759+ <tbody>

760+ <tr>

761+ <td>OLS regression</td>

762+ <td><span class="confinterval olstimelb8">xxx</span></td>

763+ <td><span class="olstimept8">xxx</span></td>

764+ <td><span class="confinterval olstimeub8">xxx</span></td>

765+ </tr>

766+ <tr>

767+ <td>R² goodness-of-fit</td>

768+ <td><span class="confinterval olsr2lb8">xxx</span></td>

769+ <td><span class="olsr2pt8">xxx</span></td>

770+ <td><span class="confinterval olsr2ub8">xxx</span></td>

771+ </tr>

772+ <tr>

773+ <td>Mean execution time</td>

774+ <td><span class="confinterval citime">8.252875148785076e-4</span></td>

775+ <td><span class="time">9.038536710022285e-4</span></td>

776+ <td><span class="confinterval citime">1.0137042058789136e-3</span></td>

777+ </tr>

778+ <tr>

779+ <td>Standard deviation</td>

780+ <td><span class="confinterval citime">2.3352589892872938e-4</span></td>

781+ <td><span class="time">3.1773226135504875e-4</span></td>

782+ <td><span class="confinterval citime">4.273324974311236e-4</span></td>

783+ </tr>

784+ </tbody>

785+ </table>

786+

787+ <span class="outliers">

788+ <p>Outlying measurements have severe

789+ (<span class="percent">0.984823670419889</span>%)

790+ effect on estimated standard deviation.</p>

791+ </span>

792+<h2><a name="b9">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Applicative version</a></h2>

793+ <table width="100%">

794+ <tbody>

795+ <tr>

796+ <td><div id="kde9" class="kdechart"

797+ style="width:450px;height:278px;"></div></td>

798+ <td><div id="time9" class="timechart"

799+ style="width:450px;height:278px;"></div></td>

800+<!--

801+ <td><div id="cycle9" class="cyclechart"

802+ style="width:300px;height:278px;"></div></td>

803+-->

804+ </tr>

805+ </tbody>

806+ </table>

807+

808+ <table>

809+ <thead class="analysis">

810+ <th></th>

811+ <th class="cibound"

812+ title="0.95 confidence level">lower bound</th>

813+ <th>estimate</th>

814+ <th class="cibound"

815+ title="0.95 confidence level">upper bound</th>

816+ </thead>

817+ <tbody>

818+ <tr>

819+ <td>OLS regression</td>

820+ <td><span class="confinterval olstimelb9">xxx</span></td>

821+ <td><span class="olstimept9">xxx</span></td>

822+ <td><span class="confinterval olstimeub9">xxx</span></td>

823+ </tr>

824+ <tr>

825+ <td>R² goodness-of-fit</td>

826+ <td><span class="confinterval olsr2lb9">xxx</span></td>

827+ <td><span class="olsr2pt9">xxx</span></td>

828+ <td><span class="confinterval olsr2ub9">xxx</span></td>

829+ </tr>

830+ <tr>

831+ <td>Mean execution time</td>

832+ <td><span class="confinterval citime">0.20685697058300623</span></td>

833+ <td><span class="time">0.20792234497182815</span></td>

834+ <td><span class="confinterval citime">0.20898771936065005</span></td>

835+ </tr>

836+ <tr>

837+ <td>Standard deviation</td>

838+ <td><span class="confinterval citime">1.11631780898578e-3</span></td>

839+ <td><span class="time">1.5104002558460128e-3</span></td>

840+ <td><span class="confinterval citime">1.827809373068682e-3</span></td>

841+ </tr>

842+ </tbody>

843+ </table>

844+

845+ <span class="outliers">

846+ <p>Outlying measurements have moderate

847+ (<span class="percent">0.1388888888888886</span>%)

848+ effect on estimated standard deviation.</p>

849+ </span>

850+<h2><a name="b10">Matrix vs List - `select`/Matrix `select` - 100x(100+100) / 100x100/Selective version</a></h2>

851+ <table width="100%">

852+ <tbody>

853+ <tr>

854+ <td><div id="kde10" class="kdechart"

855+ style="width:450px;height:278px;"></div></td>

856+ <td><div id="time10" class="timechart"

857+ style="width:450px;height:278px;"></div></td>

858+<!--

859+ <td><div id="cycle10" class="cyclechart"

860+ style="width:300px;height:278px;"></div></td>

861+-->

862+ </tr>

863+ </tbody>

864+ </table>

865+

866+ <table>

867+ <thead class="analysis">

868+ <th></th>

869+ <th class="cibound"

870+ title="0.95 confidence level">lower bound</th>

871+ <th>estimate</th>

872+ <th class="cibound"

873+ title="0.95 confidence level">upper bound</th>

874+ </thead>

875+ <tbody>

876+ <tr>

877+ <td>OLS regression</td>

878+ <td><span class="confinterval olstimelb10">xxx</span></td>

879+ <td><span class="olstimept10">xxx</span></td>

880+ <td><span class="confinterval olstimeub10">xxx</span></td>

881+ </tr>

882+ <tr>

883+ <td>R² goodness-of-fit</td>

884+ <td><span class="confinterval olsr2lb10">xxx</span></td>

885+ <td><span class="olsr2pt10">xxx</span></td>

886+ <td><span class="confinterval olsr2ub10">xxx</span></td>

887+ </tr>

888+ <tr>

889+ <td>Mean execution time</td>

890+ <td><span class="confinterval citime">0.1040023584088178</span></td>

891+ <td><span class="time">0.10482248682469514</span></td>

892+ <td><span class="confinterval citime">0.10534815795558282</span></td>

893+ </tr>

894+ <tr>

895+ <td>Standard deviation</td>

896+ <td><span class="confinterval citime">5.86339084666882e-4</span></td>

897+ <td><span class="time">1.080285904740125e-3</span></td>

898+ <td><span class="confinterval citime">1.5634852865472032e-3</span></td>

899+ </tr>

900+ </tbody>

901+ </table>

902+

903+ <span class="outliers">

904+ <p>Outlying measurements have slight

905+ (<span class="percent">9.87654320987654e-2</span>%)

906+ effect on estimated standard deviation.</p>

907+ </span>

908+

909+ <h2><a name="grokularation">understanding this report</a></h2>

910+

911+ <p>In this report, each function benchmarked by criterion is assigned

912+ a section of its own. The charts in each section are active; if

913+ you hover your mouse over data points and annotations, you will see

914+ more details.</p>

915+

916+ <ul>

917+ <li>The chart on the left is a

918+ <a href="http://en.wikipedia.org/wiki/Kernel_density_estimation">kernel

919+ density estimate</a> (also known as a KDE) of time

920+ measurements. This graphs the probability of any given time

921+ measurement occurring. A spike indicates that a measurement of a

922+ particular time occurred; its height indicates how often that

923+ measurement was repeated.</li>

924+

925+ <li>The chart on the right is the raw data from which the kernel

926+ density estimate is built. The <i>x</i> axis indicates the

927+ number of loop iterations, while the <i>y</i> axis shows measured

928+ execution time for the given number of loop iterations. The

929+ line behind the values is the linear regression prediction of

930+ execution time for a given number of iterations. Ideally, all

931+ measurements will be on (or very near) this line.</li>

932+ </ul>

933+

934+ <p>Under the charts is a small table.

935+ The first two rows are the results of a linear regression run

936+ on the measurements displayed in the right-hand chart.</p>

937+

938+ <ul>

939+ <li><i>OLS regression</i> indicates the

940+ time estimated for a single loop iteration using an ordinary

941+ least-squares regression model. This number is more accurate

942+ than the <i>mean</i> estimate below it, as it more effectively

943+ eliminates measurement overhead and other constant factors.</li>

944+ <li><i>R² goodness-of-fit</i> is a measure of how

945+ accurately the linear regression model fits the observed

946+ measurements. If the measurements are not too noisy, R²

947+ should lie between 0.99 and 1, indicating an excellent fit. If

948+ the number is below 0.99, something is confounding the accuracy

949+ of the linear model.</li>

950+ <li><i>Mean execution time</i> and <i>standard deviation</i> are

951+ statistics calculated from execution time

952+ divided by number of iterations.</li>

953+ </ul>

954+

955+ <p>We use a statistical technique called

956+ the <a href="http://en.wikipedia.org/wiki/Bootstrapping_(statistics)">bootstrap</a>

957+ to provide confidence intervals on our estimates. The

958+ bootstrap-derived upper and lower bounds on estimates let you see

959+ how accurate we believe those estimates to be. (Hover the mouse

960+ over the table headers to see the confidence levels.)</p>

961+

962+ <p>A noisy benchmarking environment can cause some or many

963+ measurements to fall far from the mean. These outlying

964+ measurements can have a significant inflationary effect on the

965+ estimate of the standard deviation. We calculate and display an

966+ estimate of the extent to which the standard deviation has been

967+ inflated by outliers.</p>

968+

969+<script type="text/javascript">

970+$(function () {

971+ function mangulate(rpt) {

972+ var measured = function(key) {

973+ var idx = rpt.reportKeys.indexOf(key);

974+ return rpt.reportMeasured.map(function(r) { return r[idx]; });

975+ };

976+ var lowerBound = function(est) {

977+ return est.estPoint - est.estError.confIntLDX;

978+ };

979+ var upperBound = function(est) {

980+ return est.estPoint + est.estError.confIntUDX;

981+ };

982+ var number = rpt.reportNumber;

983+ var name = rpt.reportName;

984+ var mean = rpt.reportAnalysis.anMean.estPoint;

985+ var iters = measured("iters");

986+ var times = measured("time");

987+ var kdetimes = rpt.reportKDEs[0].kdeValues;

988+ var kdepdf = rpt.reportKDEs[0].kdePDF;

989+

990+ var meanSecs = mean;

991+ var units = $.timeUnits(mean);

992+ var rgrs = rpt.reportAnalysis.anRegress[0];

993+ var scale = units[0];

994+ var olsTime = rgrs.regCoeffs.iters;

995+ $(".olstimept" + number).text(function() {

996+ return $.renderTime(olsTime.estPoint);

997+ });

998+ $(".olstimelb" + number).text(function() {

999+ return $.renderTime(lowerBound(olsTime));

1000+ });

1001+ $(".olstimeub" + number).text(function() {

1002+ return $.renderTime(upperBound(olsTime));

1003+ });

1004+ $(".olsr2pt" + number).text(function() {

1005+ return rgrs.regRSquare.estPoint.toFixed(3);

1006+ });

1007+ $(".olsr2lb" + number).text(function() {

1008+ return lowerBound(rgrs.regRSquare).toFixed(3);

1009+ });

1010+ $(".olsr2ub" + number).text(function() {

1011+ return upperBound(rgrs.regRSquare).toFixed(3);

1012+ });

1013+ mean *= scale;

1014+ kdetimes = $.scaleBy(scale, kdetimes);

1015+ var kq = $("#kde" + number);

1016+ var k = $.plot(kq,

1017+ [{ label: name + " time densities",

1018+ data: $.zip(kdetimes, kdepdf),

1019+ }],

1020+ { xaxis: { tickFormatter: $.unitFormatter(scale) },

1021+ yaxis: { ticks: false },

1022+ grid: { borderColor: "#777",

1023+ hoverable: true, markings: [ { color: '#6fd3fb',

1024+ lineWidth: 1.5, xaxis: { from: mean, to: mean } } ] },

1025+ });

1026+ var o = k.pointOffset({ x: mean, y: 0});

1027+ kq.append('<div class="meanlegend" title="' + $.renderTime(meanSecs) +

1028+ '" style="position:absolute;left:' + (o.left + 4) +

1029+ 'px;bottom:139px;">mean</div>');

1030+ $.addTooltip("#kde" + number,

1031+ function(secs) { return $.renderTime(secs / scale); });

1032+ var timepairs = new Array(times.length);

1033+ var lastiter = iters[iters.length-1];

1034+ var olspairs = [[0,0], [lastiter, lastiter * scale * olsTime.estPoint]];

1035+ for (var i = 0; i < times.length; i++)

1036+ timepairs[i] = [iters[i],times[i]*scale];

1037+ iterFormatter = function() {

1038+ var denom = 0;

1039+ return function(iters) {

1040+ if (iters == 0)

1041+ return '';

1042+ if (denom > 0)

1043+ return (iters / denom).toFixed();

1044+ var power;

1045+ if (iters >= 1e9) {

1046+ denom = '1e9'; power = '⁹';

1047+ }

1048+ if (iters >= 1e6) {

1049+ denom = '1e6'; power = '⁶';

1050+ }

1051+ else if (iters >= 1e3) {

1052+ denom = '1e3'; power = '³';

1053+ }

1054+ else denom = 1;

1055+ if (denom > 1) {

1056+ iters = (iters / denom).toFixed();

1057+ iters += '×10' + power + ' iters';

1058+ } else {

1059+ iters += ' iters';

1060+ }

1061+ return iters;

1062+ };

1063+ };

1064+ $.plot($("#time" + number),

1065+ [{ label: "regression", data: olspairs,

1066+ lines: { show: true } },

1067+ { label: name + " times", data: timepairs,

1068+ points: { show: true } }],

1069+ { grid: { borderColor: "#777", hoverable: true },

1070+ xaxis: { tickFormatter: iterFormatter() },

1071+ yaxis: { tickFormatter: $.unitFormatter(scale) } });

1072+ $.addTooltip("#time" + number,

1073+ function(iters,secs) {

1074+ return ($.renderTime(secs / scale) + ' / ' +

1075+ iters.toLocaleString() + ' iters');

1076+ });

1077+ if (0) {

1078+ var cyclepairs = new Array(cycles.length);

1079+ for (var i = 0; i < cycles.length; i++)

1080+ cyclepairs[i] = [cycles[i],i];

1081+ $.plot($("#cycle" + number),

1082+ [{ label: name + " cycles",

1083+ data: cyclepairs }],

1084+ { points: { show: true },

1085+ grid: { borderColor: "#777", hoverable: true },

1086+ xaxis: { tickFormatter:

1087+ function(cycles,axis) { return cycles + ' cycles'; }},

1088+ yaxis: { ticks: false },

1089+ });

1090+ $.addTooltip("#cycles" + number, function(x,y) { return x + ' cycles'; });

1091+ }

1092+ };

1093+ var reports = [{"reportAnalysis":{"anMean":{"estError":{"confIntLDX":8.180656380381139e-7,"confIntUDX":1.0607893850293412e-6,"confIntCL":5.0e-2},"estPoint":1.2521282696584778e-4},"anRegress":[{"regRSquare":{"estError":{"confIntLDX":6.825747934032789e-4,"confIntUDX":5.601346577008837e-4,"confIntCL":5.0e-2},"estPoint":0.9987363907467321},"regResponder":"time","regCoeffs":{"y":{"estError":{"confIntLDX":3.903258473575619e-4,"confIntUDX":4.255637307837121e-4,"confIntCL":5.0e-2},"estPoint":4.7414397131182774e-4},"iters":{"estError":{"confIntLDX":1.3700120579303332e-6,"confIntUDX":1.4372757058700198e-6,"confIntCL":5.0e-2},"estPoint":1.253562632314857e-4}}}],"anStdDev":{"estError":{"confIntLDX":6.230396568923988e-7,"confIntUDX":8.686123313082005e-7,"confIntCL":5.0e-2},"estPoint":3.0000227210624054e-6},"anOutlierVar":{"ovFraction":0.19510840974237945,"ovDesc":"moderate","ovEffect":"Moderate"}},"reportKDEs":[{"kdeValues":[1.1947612098990151e-4,1.1958993323133807e-4,1.1970374547277462e-4,1.1981755771421118e-4,1.1993136995564774e-4,1.200451821970843e-4,1.2015899443852085e-4,1.2027280667995741e-4,1.2038661892139398e-4,1.2050043116283052e-4,1.2061424340426709e-4,1.2072805564570365e-4,1.2084186788714021e-4,1.2095568012857676e-4,1.2106949237001332e-4,1.2118330461144988e-4,1.2129711685288643e-4,1.2141092909432299e-4,1.2152474133575955e-4,1.2163855357719612e-4,1.2175236581863267e-4,1.2186617806006923e-4,1.2197999030150579e-4,1.2209380254294235e-4,1.222076147843789e-4,1.2232142702581545e-4,1.22435239267252e-4,1.2254905150868857e-4,1.2266286375012513e-4,1.227766759915617e-4,1.2289048823299826e-4,1.2300430047443482e-4,1.2311811271587135e-4,1.2323192495730792e-4,1.2334573719874448e-4,1.2345954944018104e-4,1.235733616816176e-4,1.2368717392305416e-4,1.2380098616449073e-4,1.2391479840592726e-4,1.2402861064736382e-4,1.2414242288880039e-4,1.2425623513023695e-4,1.243700473716735e-4,1.2448385961311007e-4,1.2459767185454663e-4,1.247114840959832e-4,1.2482529633741973e-4,1.249391085788563e-4,1.2505292082029285e-4,1.2516673306172942e-4,1.2528054530316598e-4,1.2539435754460254e-4,1.255081697860391e-4,1.2562198202747564e-4,1.257357942689122e-4,1.2584960651034876e-4,1.2596341875178532e-4,1.2607723099322188e-4,1.2619104323465845e-4,1.26304855476095e-4,1.2641866771753154e-4,1.265324799589681e-4,1.2664629220040467e-4,1.2676010444184123e-4,1.268739166832778e-4,1.2698772892471435e-4,1.2710154116615091e-4,1.2721535340758745e-4,1.27329165649024e-4,1.2744297789046057e-4,1.2755679013189714e-4,1.276706023733337e-4,1.2778441461477026e-4,1.2789822685620682e-4,1.2801203909764336e-4,1.2812585133907992e-4,1.2823966358051648e-4,1.2835347582195304e-4,1.284672880633896e-4,1.2858110030482617e-4,1.2869491254626273e-4,1.2880872478769926e-4,1.2892253702913582e-4,1.290363492705724e-4,1.2915016151200895e-4,1.292639737534455e-4,1.2937778599488207e-4,1.2949159823631863e-4,1.2960541047775517e-4,1.2971922271919173e-4,1.298330349606283e-4,1.2994684720206486e-4,1.3006065944350142e-4,1.3017447168493798e-4,1.3028828392637454e-4,1.3040209616781108e-4,1.3051590840924764e-4,1.306297206506842e-4,1.3074353289212076e-4,1.3085734513355732e-4,1.3097115737499389e-4,1.3108496961643045e-4,1.3119878185786698e-4,1.3131259409930354e-4,1.314264063407401e-4,1.3154021858217667e-4,1.3165403082361323e-4,1.317678430650498e-4,1.3188165530648635e-4,1.319954675479229e-4,1.3210927978935945e-4,1.32223092030796e-4,1.3233690427223258e-4,1.3245071651366914e-4,1.325645287551057e-4,1.3267834099654226e-4,1.327921532379788e-4,1.3290596547941536e-4,1.3301977772085192e-4,1.3313358996228848e-4,1.3324740220372504e-4,1.333612144451616e-4,1.3347502668659817e-4,1.335888389280347e-4,1.3370265116947126e-4,1.3381646341090783e-4,1.339302756523444e-4],"kdeType":"time","kdePDF":[16344.224721396367,16786.863961441533,17652.035958217843,18901.341011908647,20481.597893490936,22329.821273980273,24379.311900296158,26566.390072595026,28837.203045162216,31153.97080832464,33500.02069778121,35883.01455498359,38335.90036997744,40915.3205073886,43697.46584110846,46771.6532895002,50232.188695555335,54169.31877001343,58660.236916983326,63761.156927105796,69501.38680064806,75880.12036000454,82866.33463143324,90401.77394472176,98406.57169169483,106786.67187676889,115441.92914198182,124273.64066898884,133190.32706501693,142110.8332544853,150964.2336573813,159686.53917556253,168214.7381874761,176479.17544911715,184395.60576382722,191858.39924118665,198736.2976836007,204871.8358658008,210085.08620552858,214181.82256538884,216965.60377808282,218252.72755516367,217888.5711203222,215763.57150685805,211827.0404921532,206097.16686889247,198665.91694458944,189698.0632660416,179424.19152831484,168128.18248235655,156130.26056722223,143767.17078572346,131371.3329193951,119250.8949435357,107672.46205246242,96847.93975504121,86926.4490256187,77991.71412750428,70064.7602360628,63111.253956206434,57052.42732616571,51778.27831869549,47161.651157408065,43071.86170745317,39386.7245806443,36002.12565751339,32838.62589235005,29844.936801268028,26998.434478220574,2430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1094+ reports.map(mangulate);

1095+

1098+ var means = $.scaleTimes([1.2521282696584778e-4,1.532024430909428e-4,0.11922032795600032,0.11758616896428131,1.0404128327718354,1.1075485033964771,2.3478542657700623,1.7931655457283859e-3,9.038536710022285e-4,0.20792234497182815,0.10482248682469514,]);

1099+ var stddevs = [3.0000227210624054e-6,3.649213223188502e-5,9.77563027930971e-3,8.150134548496543e-3,6.182803786470918e-2,7.979551817654461e-3,1.2441745894453989e-2,5.021999918501304e-4,3.1773226135504875e-4,1.5104002558460128e-3,1.080285904740125e-3,];

1100+ stddevs = $.scaleBy(means[1], stddevs);

1101+ var xs = [];

1102+ var prev = null;

1103+ var colors = ["#edc240","#afd8f8","#cb4b4b","#4da74d","#9440ed"];

1104+ var max_time = 0;

1105+ for (var i = 0; i < means[0].length; i++) {

1106+ var name = benches[i].split(/\//);

1107+ name.pop();

1108+ name = name.join('/');

1109+ if (name != prev) {

1110+ var color = colors[xs.length / 2 % colors.length];

1111+ xs.push({ data: [[means[0][i], -i]], label: name, color: color,

1112+ bars: { show: true, horizontal: true, barWidth: 0.75,

1113+ align: "center" } });

1114+ xs.push({ data: [[means[0][i], -i, stddevs[i]]], color: color,

1115+ lines: { show: false },

1116+ points: { radius: 0, errorbars: "x",

1117+ xerr: { show: true, radius: 5,

1118+ lowerCap: "-", upperCap: "-" } } });

1119+ prev = name;

1120+ } else {

1121+ xs[xs.length - 2].data.push([means[0][i], -i]);

1122+ xs[xs.length - 1].data.push([means[0][i], -i, stddevs[i]]);

1123+ }

1124+ max_time = Math.max(max_time, means[0][i] + stddevs[i]);

1125+ }

1126+ var oq = $("#overview");

1127+ var max_x = max_time * 1.02;

1128+ o = $.plot(oq, xs, { grid: { borderColor: "#777", hoverable: true },

1129+ legend: { show: xs.length > 1 },

1130+ xaxis: { max: max_x, zoomRange: [false, max_x], panRange: [0, max_x] },

1131+ yaxis: { ticks: ylabels, tickColor: '#ffffff', zoomRange: false, panRange: false },

1132+ zoom: { interactive: true, amount: 1.05 },

1133+ pan: { interactive: true } });

1134+ if (benches.length > 3)

1135+ o.getPlaceholder().height(28*benches.length);

1136+ o.resize();

1137+ o.setupGrid();

1138+ o.draw();

1139+ $.addTooltip("#overview", function(x,y) { return $.renderTime(x / means[1]); });

1140+});

1141+$(document).ready(function () {

1142+ $(".time").text(function(_, text) {

1143+ return $.renderTime(text);

1144+ });

1145+ $(".citime").text(function(_, text) {

1146+ return $.renderTime(text);

1147+ });

1148+ $(".percent").text(function(_, text) {

1149+ return (text*100).toFixed(1);

1150+ });

1151+ });

1152+</script>

1153+

1154+ </div>

1155+ </div>

1156+ <div id="footer">

1157+ <div class="body">

1158+ <div class="footfirst">

1159+ <h2>colophon</h2>

1160+ <p>This report was created using the

1161+ <a href="http://hackage.haskell.org/package/criterion">criterion</a>

1162+ benchmark execution and performance analysis tool.</p>

1163+ <p>Criterion is developed and maintained

1164+ by <a href="http://www.serpentine.com/blog/">Bryan O'Sullivan</a>.</p>

1165+ </div>

1166+ </div>

1167+ </div>

1168+ </body>

1169+</html>

report-strict.pdfnew file

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src/LAoP/Dist.hs+2−2

@@ -39,8 +39,8 @@ module LAoP.Dist

3939 -- * Constraint type synonyms

4040 Countable,

4141 CountableN,

42− CountableDimsN,

43− FLN,

42+ CountableDimensionsN,

43+ FromListsN,

4444 Liftable,

4545 TrivialP,

4646

src/LAoP/Dist/Internal.hs+45−46

@@ -16,8 +16,8 @@ module LAoP.Dist.Internal

1616

1717 Countable,

1818 CountableN,

19− CountableDimsN,

20− FLN,

19+ CountableDimensionsN,

20+ FromListsN,

2121 Liftable,

2222 TrivialP,

2323

@@ -43,8 +43,7 @@ module LAoP.Dist.Internal

4343 )

4444 where

4545

46−import LAoP.Matrix.Type hiding (TrivialP, Countable, CountableDims, CountableN, CountableDimsN, Liftable, FLN)

47−import Prelude hiding (id, (.))

46+import LAoP.Matrix.Type hiding (TrivialP, Countable, CountableDimensions, CountableN, CountableDimensionsN, Liftable, FromListsN)

4847import qualified LAoP.Matrix.Internal as I

4948import LAoP.Utils

5049import GHC.TypeLits

@@ -62,18 +61,18 @@ newtype Dist a = D (Matrix Prob () a)

6261 deriving (Show, Num, Eq, Ord, NFData) via (Matrix Prob () a)

6362

6463-- | Constraint type synonyms to keep the type signatures less convoluted

65−type Countable a = KnownNat (I.Count a)

66−type CountableN a = KnownNat (I.Count (I.Normalize a))

67−type CountableDimsN a b = (CountableN a, CountableN b)

68−type FLN a b = I.FL (I.Normalize a) (I.Normalize b)

69−type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Prob, Ord Prob)

70−type TrivialP a b = Normalize (a, b) ~ Normalize (Normalize a, Normalize b)

64+type Countable a = KnownNat (I.Count a)

65+type CountableN a = KnownNat (I.Count (I.Normalize a))

66+type CountableDimensionsN a b = (CountableN a, CountableN b)

67+type FromListsN a b = I.FromLists Prob (I.Normalize a) (I.Normalize b)

68+type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Prob, Ord Prob)

69+type TrivialP a b = Normalize (a, b) ~ Normalize (Normalize a, Normalize b)

7170

7271-- | Functor instance

7372fmapD ::

7473 ( Liftable a b,

75− CountableDimsN a b,

76− FLN b a

74+ CountableDimensionsN a b,

75+ FromListsN b a

7776 )

7877 =>

7978 (a -> b) -> Dist a -> Dist b

@@ -85,17 +84,17 @@ unitD = D (one 1)

8584

8685-- | Applicative/Monoidal instance 'mult' function

8786multD ::

88− ( CountableDimsN a b,

87+ ( CountableDimensionsN a b,

8988 CountableN (a, b),

90− FLN (a, b) a,

91− FLN (a, b) b,

89+ FromListsN (a, b) a,

90+ FromListsN (a, b) b,

9291 TrivialP a b

9392 ) => Dist a -> Dist b -> Dist (a, b)

94−multD (D a) (D b) = D (kr a b)

93+multD (D a) (D b) = D (khatri a b)

9594

9695-- | Selective instance function

9796selectD ::

98− ( FLN b b,

97+ ( FromListsN b b,

9998 CountableN b

10099 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b

101100selectD (D d) m = D (selectM d m)

@@ -104,31 +103,31 @@ selectD (D d) m = D (selectM d m)

104103-- functions to apply to a given argument;

105104branchD ::

106105 ( Num e,

107− CountableDimsN a b,

108− CountableDimsN c (Either b c),

109− FLN c b,

110− FLN a b,

111− FLN a a,

112− FLN b b,

113− FLN c c,

114− FLN b a,

115− FLN b c,

116− FLN (Either b c) b,

117− FLN (Either b c) c

106+ CountableDimensionsN a b,

107+ CountableDimensionsN c (Either b c),

108+ FromListsN c b,

109+ FromListsN a b,

110+ FromListsN a a,

111+ FromListsN b b,

112+ FromListsN c c,

113+ FromListsN b a,

114+ FromListsN b c,

115+ FromListsN (Either b c) b,

116+ FromListsN (Either b c) c

118117 )

119118 => Dist (Either a b) -> Matrix Prob a c -> Matrix Prob b c -> Dist c

120119branchD x l r = f x `selectD` g l `selectD` r

121120 where

122− f (D m) = D (fork (tr i1) (i1 `comp` tr i2) `comp` m)

121+ f (D m) = D (split (tr i1) (i1 `comp` tr i2) `comp` m)

123122 g m = i2 `comp` m

124123

125124-- | Branch on a Boolean value, skipping unnecessary computations.

126125ifD ::

127− ( CountableDimsN a (Either () a),

128− FLN a a,

129− FLN a (),

130− FLN () a,

131− FLN (Either () a) a

126+ ( CountableDimensionsN a (Either () a),

127+ FromListsN a a,

128+ FromListsN a (),

129+ FromListsN () a,

130+ FromListsN (Either () a) a

132131 )

133132 => Dist Bool -> Dist a -> Dist a -> Dist a

134133ifD x (D t) (D e) = branchD x' t e

@@ -136,7 +135,7 @@ ifD x (D t) (D e) = branchD x' t e

136135 x' = bool (Right ()) (Left ()) `fmapD` x

137136

138137-- | Monad instance 'return' function

139−returnD :: forall a . (Enum a, FLN () a, Countable a) => a -> Dist a

138+returnD :: forall a . (Enum a, FromListsN () a, Countable a) => a -> Dist a

140139returnD a = D (col l)

141140 where

142141 i = fromInteger $ natVal (Proxy :: Proxy (Count a))

@@ -151,7 +150,7 @@ bindD (D d) m = D (m `comp` d)

151150(??) ::

152151 ( Enum a,

153152 Countable a,

154− FLN () a

153+ FromListsN () a

155154 ) => (a -> Bool) -> Dist a -> Prob

156155(??) p d =

157156 let l = toValues d

@@ -161,11 +160,11 @@ bindD (D d) m = D (m `comp` d)

161160-- Distribution Construction

162161

163162-- | Constructs a Bernoulli distribution

164−choose :: (FLN () a) => Prob -> Dist a

163+choose :: (FromListsN () a) => Prob -> Dist a

165164choose prob = D (col [prob, 1 - prob])

166165

167166-- | Creates a distribution given a shape function

168−shape :: (FLN () a) => (Prob -> Prob) -> [a] -> Dist a

167+shape :: (FromListsN () a) => (Prob -> Prob) -> [a] -> Dist a

169168shape _ [] = error "Probability.shape: empty list"

170169shape f xs =

171170 let incr = 1 / fromIntegral (length xs - 1)

@@ -173,23 +172,23 @@ shape f xs =

173172 in fromFreqs (zip xs ps)

174173

175174-- | Constructs a Linear distribution

176−linear :: (FLN () a) => [a] -> Dist a

175+linear :: (FromListsN () a) => [a] -> Dist a

177176linear = shape id

178177

179178-- | Constructs an Uniform distribution

180−uniform :: (FLN () a) => [a] -> Dist a

179+uniform :: (FromListsN () a) => [a] -> Dist a

181180uniform = shape (const 1)

182181

183182-- | Constructs an Negative Exponential distribution

184−negExp :: (FLN () a) => [a] -> Dist a

183+negExp :: (FromListsN () a) => [a] -> Dist a

185184negExp = shape (\x -> exp (-x))

186185

187186-- | Constructs an Normal distribution

188−normal :: (FLN () a) => [a] -> Dist a

187+normal :: (FromListsN () a) => [a] -> Dist a

189188normal = shape (normalCurve 0.5 0.5)

190189

191190-- | Transforms a 'Dist' into a list of pairs.

192−toValues :: forall a . (Enum a, Countable a, FLN () a) => Dist a -> [(a, Prob)]

191+toValues :: forall a . (Enum a, Countable a, FromListsN () a) => Dist a -> [(a, Prob)]

193192toValues (D d) =

194193 let rows = fromInteger (natVal (Proxy :: Proxy (Count a)))

195194 probs = toList d

@@ -197,7 +196,7 @@ toValues (D d) =

197196 in res

198197

199198-- | Pretty a distribution

200−prettyDist :: forall a. (Show a, Enum a, Countable a, FLN () a) => Dist a -> String

199+prettyDist :: forall a. (Show a, Enum a, Countable a, FromListsN () a) => Dist a -> String

201200prettyDist d =

202201 let values = sortBy (\(a, p1) (b, p2) -> compare p2 p1) (toValues @a d)

203202 w = maximum (map (length . show . fst) values)

@@ -209,12 +208,12 @@ prettyDist d =

209208 showR n x = show x ++ " "

210209

211210-- | Pretty Print a distribution

212−prettyPrintDist :: forall a . (Show a, Enum a, Countable a, FLN () a) => Dist a -> IO ()

211+prettyPrintDist :: forall a . (Show a, Enum a, Countable a, FromListsN () a) => Dist a -> IO ()

213212prettyPrintDist = putStrLn . prettyDist @a

214213

215214-- Auxiliary functions

216215

217−fromFreqs :: (FLN () a) => [(a,Prob)] -> Dist a

216+fromFreqs :: (FromListsN () a) => [(a,Prob)] -> Dist a

218217fromFreqs xs = D (col (map (\(x,p) -> p/q) xs))

219218 where q = sum $ map snd xs

220219

src/LAoP/Matrix/Internal.hs+390−371

@@ -30,7 +30,7 @@

3030-- motivation behind the library, the underlying theory, and implementation details.

3131--

3232-- This module offers many of the combinators mentioned in the work of

33−-- Macedo (2012) and Oliveira (2012).

33+-- Macedo (2012) and Oliveira (2012).

3434--

3535-- This is an Internal module and it is no supposed to be imported.

3636--

@@ -43,26 +43,17 @@ module LAoP.Matrix.Internal

4343 --

4444 -- There exists two type families that make it easier to write

4545 -- matrix dimensions: 'FromNat' and 'Count'. This approach

46− -- leads to a very straightforward implementation

47− -- of LAoP combinators.

46+ -- leads to a very straightforward implementation

47+ -- of LAoP combinators.

4848

4949 -- * Type safe matrix representation

5050 Matrix (..),

5151

52− -- * Constraint type aliases

53− Countable,

54− CountableDims,

55− CountableN,

56− CountableDimsN,

57− FL,

58− FLN,

59− Liftable,

60− Trivial,

61−

6252 -- * Primitives

53+ empty,

6354 one,

64− join,

65− fork,

55+ junc,

56+ split,

6657

6758 -- * Auxiliary type families

6859 FromNat,

@@ -75,7 +66,6 @@ module LAoP.Matrix.Internal

7566 toLists,

7667 toList,

7768 matrixBuilder,

78− matrixBuilder',

7969 row,

8070 col,

8171 zeros,

@@ -86,17 +76,11 @@ module LAoP.Matrix.Internal

8676 -- * Misc

8777 -- ** Get dimensions

8878 columns,

89− columns',

9079 rows,

91− rows',

9280

9381 -- ** Matrix Transposition

9482 tr,

9583

96− -- ** Scalar multiplication/division of matrices

97− (.|),

98− (./),

99−

10084 -- ** Selective operator

10185 select,

10286 branch,

@@ -105,19 +89,16 @@ module LAoP.Matrix.Internal

10589 cond,

10690

10791 -- ** Matrix "abiding"

108− abideJF,

109− abideFJ,

110−

111− -- ** Zip matrices

112− zipWithM,

92+ abideJS,

93+ abideSJ,

11394

11495 -- * Biproduct approach

115− -- ** Fork

96+ -- ** Split

11697 (===),

11798 -- *** Projections

11899 p1,

119100 p2,

120− -- ** Join

101+ -- ** Junc

121102 (|||),

122103 -- *** Injections

123104 i1,

@@ -130,13 +111,12 @@ module LAoP.Matrix.Internal

130111

131112 -- | Note that given the restrictions imposed it is not possible to

132113 -- implement the standard type classes present in standard Haskell.

133−

134114 -- *** Matrix pairing projections

135− fstM,

136− sndM,

115+ kp1,

116+ kp2,

137117

138118 -- *** Matrix pairing

139− kr,

119+ khatri,

140120

141121 -- * Matrix composition and lifting

142122

@@ -144,10 +124,10 @@ module LAoP.Matrix.Internal

144124

145125 -- | Note that given the restrictions imposed it is not possible to

146126 -- implement the standard type classes present in standard Haskell.

147− iden,

127+ identity,

148128 comp,

149− fromF',

150129 fromF,

130+ fromF',

151131

152132 -- * Matrix printing

153133 pretty,

@@ -176,20 +156,20 @@ import Data.Kind

176156import Data.List

177157import Data.Maybe

178158import Data.Proxy

179−import Data.Typeable

180159import Data.Void

181160import GHC.TypeLits

182161import Data.Type.Equality

183162import GHC.Generics

184163import Control.DeepSeq

185−import Prelude hiding (id, (.))

186−import qualified Prelude (id, (.))

164+import Control.Category

165+import Prelude hiding ((.))

187166

188167-- | LAoP (Linear Algebra of Programming) Inductive Matrix definition.

189168data Matrix e cols rows where

169+ Empty :: Matrix e Void Void

190170 One :: e -> Matrix e () ()

191− Join :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

192− Fork :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

171+ Junc :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

172+ Split :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

193173

194174deriving instance (Show e) => Show (Matrix e cols rows)

195175

@@ -216,6 +196,7 @@ type family Count (d :: Type) :: Nat where

216196--

217197-- Thanks to Li-Yao Xia this type family is super fast.

218198type family FromNat (n :: Nat) :: Type where

199+ FromNat 0 = Void

219200 FromNat 1 = ()

220201 FromNat n = FromNat' (Mod n 2 == 0) (FromNat (Div n 2))

221202

@@ -232,79 +213,105 @@ type family Normalize (d :: Type) :: Type where

232213-- | Constraint type synonyms to keep the type signatures less convoluted

233214type Countable a = KnownNat (Count a)

234215type CountableN a = KnownNat (Count (Normalize a))

235−type CountableDims a b = (Countable a, Countable b)

236−type CountableDimsN a b = (CountableN a, CountableN b)

237−type FL a b = FromLists a b

238−type FLN a b = FromLists (Normalize a) (Normalize b)

216+type CountableDimensions a b = (Countable a, Countable b)

217+type CountableDimensionsN a b = (CountableN a, CountableN b)

218+type FromListsN e a b = FromLists e (Normalize a) (Normalize b)

239219type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)

240220type Trivial a = FromNat (Count a) ~ a

241221

242−-- | It is possible to implement a constrained version of the category type

243−-- class.

222+-- | It isn't possible to implement the 'id' function so it's

223+-- implementation is 'undefined'. However 'comp' can be and this partial

224+-- class implementation exists just to make the code more readable.

225+--

226+-- Please use 'identity' instead.

244227instance (Num e) => Category (Matrix e) where

245− type Object (Matrix e) a = (FL a a, Countable a)

246− id = iden

247− (.) = comp

228+ id = undefined

229+ (.) = comp

248230

249231instance NFData e => NFData (Matrix e cols rows) where

250− rnf (One e) = rnf e

251− rnf (Join a b) = rnf a `seq` rnf b

252− rnf (Fork a b) = rnf a `seq` rnf b

232+ rnf Empty = ()

233+ rnf (One e) = rnf e

234+ rnf (Junc a b) = rnf a `seq` rnf b

235+ rnf (Split a b) = rnf a `seq` rnf b

253236

254237instance Eq e => Eq (Matrix e cols rows) where

255− (One a) == (One b) = a == b

256− (Join a b) == (Join c d) = a == c && b == d

257− (Fork a b) == (Fork c d) = a == c && b == d

258− x@(Fork _ _) == y@(Join _ _) = x == abideJF y

259− x@(Join _ _) == y@(Fork _ _) = abideJF x == y

238+ Empty == Empty = True

239+ (One a) == (One b) = a == b

240+ (Junc a b) == (Junc c d) = a == c && b == d

241+ (Split a b) == (Split c d) = a == c && b == d

242+ x@(Split _ _) == y@(Junc _ _) = x == abideJS y

243+ x@(Junc _ _) == y@(Split _ _) = abideJS x == y

260244

261245instance Num e => Num (Matrix e cols rows) where

262− a + b = zipWithM (+) a b

263−

264− a - b = zipWithM (-) a b

265−

266− a * b = zipWithM (*) a b

267246

268− abs (One a) = One (abs a)

269− abs (Join a b) = Join (abs a) (abs b)

270− abs (Fork a b) = Fork (abs a) (abs b)

271−

272− signum (One a) = One (signum a)

273− signum (Join a b) = Join (signum a) (signum b)

274− signum (Fork a b) = Fork (signum a) (signum b)

247+ Empty + Empty = Empty

248+ (One a) + (One b) = One (a + b)

249+ (Junc a b) + (Junc c d) = Junc (a + c) (b + d)

250+ (Split a b) + (Split c d) = Split (a + c) (b + d)

251+ x@(Split _ _) + y@(Junc _ _) = x + abideJS y

252+ x@(Junc _ _) + y@(Split _ _) = abideJS x + y

253+

254+ Empty - Empty = Empty

255+ (One a) - (One b) = One (a - b)

256+ (Junc a b) - (Junc c d) = Junc (a - c) (b - d)

257+ (Split a b) - (Split c d) = Split (a - c) (b - d)

258+ x@(Split _ _) - y@(Junc _ _) = x - abideJS y

259+ x@(Junc _ _) - y@(Split _ _) = abideJS x - y

260+

261+ Empty * Empty = Empty

262+ (One a) * (One b) = One (a * b)

263+ (Junc a b) * (Junc c d) = Junc (a * c) (b * d)

264+ (Split a b) * (Split c d) = Split (a * c) (b * d)

265+ x@(Split _ _) * y@(Junc _ _) = x * abideJS y

266+ x@(Junc _ _) * y@(Split _ _) = abideJS x * y

267+

268+ abs Empty = Empty

269+ abs (One a) = One (abs a)

270+ abs (Junc a b) = Junc (abs a) (abs b)

271+ abs (Split a b) = Split (abs a) (abs b)

272+

273+ signum Empty = Empty

274+ signum (One a) = One (signum a)

275+ signum (Junc a b) = Junc (signum a) (signum b)

276+ signum (Split a b) = Split (signum a) (signum b)

275277

276278instance Ord e => Ord (Matrix e cols rows) where

277− (One a) <= (One b) = a <= b

278− (Join a b) <= (Join c d) = (a <= c) && (b <= d)

279− (Fork a b) <= (Fork c d) = (a <= c) && (b <= d)

280− x@(Fork _ _) <= y@(Join _ _) = x <= abideJF y

281− x@(Join _ _) <= y@(Fork _ _) = abideJF x <= y

279+ Empty <= Empty = True

280+ (One a) <= (One b) = a <= b

281+ (Junc a b) <= (Junc c d) = (a <= c) && (b <= d)

282+ (Split a b) <= (Split c d) = (a <= c) && (b <= d)

283+ x@(Split _ _) <= y@(Junc _ _) = x <= abideJS y

284+ x@(Junc _ _) <= y@(Split _ _) = abideJS x <= y

282285

283286-- Primitives

284287

288+-- | Empty matrix constructor

289+empty :: Matrix e Void Void

290+empty = Empty

291+

285292-- | Unit matrix constructor

286293one :: e -> Matrix e () ()

287294one = One

288295

289−-- | Matrix 'Join' constructor

290−join :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

291−join = Join

296+-- | Matrix 'Junc' constructor

297+junc :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

298+junc = Junc

292299

293300infixl 3 |||

294301

295−-- | Matrix 'Join' constructor

302+-- | Matrix 'Junc' constructor

296303(|||) :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

297−(|||) = Join

304+(|||) = Junc

298305

299−-- | Matrix 'Fork' constructor

300−fork :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

301−fork = Fork

306+-- | Matrix 'Split' constructor

307+split :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

308+split = Split

302309

303310infixl 2 ===

304311

305−-- | Matrix 'Fork' constructor

312+-- | Matrix 'Split' constructor

306313(===) :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

307−(===) = Fork

314+(===) = Split

308315

309316-- Construction

310317

@@ -312,101 +319,84 @@ infixl 2 ===

312319--

313320-- Given that it is not possible to branch on types at the term level type

314321-- classes are needed very much like an inductive definition but on types.

315−class FromLists cols rows where

322+class FromLists e cols rows where

316323 -- | Build a matrix out of a list of list of elements. Throws a runtime

317324 -- error if the dimensions do not match.

318325 fromLists :: [[e]] -> Matrix e cols rows

319326

320−instance FromLists () () where

327+instance FromLists e Void Void where

328+ fromLists [] = Empty

329+ fromLists _ = error "Wrong dimensions"

330+

331+instance {-# OVERLAPPING #-} FromLists e () () where

321332 fromLists [[e]] = One e

322333 fromLists _ = error "Wrong dimensions"

323334

324−instance (FromLists cols ()) => FromLists (Either () cols) () where

325− fromLists [h : t] = Join (One h) (fromLists [t])

335+instance {-# OVERLAPPING #-} (FromLists e cols ()) => FromLists e (Either () cols) () where

336+ fromLists [h : t] = Junc (One h) (fromLists [t])

326337 fromLists _ = error "Wrong dimensions"

327338

328−instance {-# OVERLAPPABLE #-}

329− (FromLists a (), FromLists b (), Countable a) => FromLists (Either a b) () where

330− fromLists [l] =

339+instance {-# OVERLAPPABLE #-} (FromLists e a (), FromLists e b (), Countable a) => FromLists e (Either a b) () where

340+ fromLists [l] =

331341 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

332− in Join (fromLists [take rowsA l]) (fromLists [drop rowsA l])

342+ in Junc (fromLists [take rowsA l]) (fromLists [drop rowsA l])

333343 fromLists _ = error "Wrong dimensions"

334344

335−instance (FromLists () rows) => FromLists () (Either () rows) where

336− fromLists ([h] : t) = Fork (One h) (fromLists t)

345+instance {-# OVERLAPPING #-} (FromLists e () rows) => FromLists e () (Either () rows) where

346+ fromLists ([h] : t) = Split (One h) (fromLists t)

337347 fromLists _ = error "Wrong dimensions"

338348

339−instance {-# OVERLAPPABLE #-}

340− (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where

341− fromLists l@([_] : _) =

349+instance {-# OVERLAPPABLE #-} (FromLists e () a, FromLists e () b, Countable a) => FromLists e () (Either a b) where

350+ fromLists l@([_] : _) =

342351 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

343− in Fork (fromLists (take rowsA l)) (fromLists (drop rowsA l))

352+ in Split (fromLists (take rowsA l)) (fromLists (drop rowsA l))

344353 fromLists _ = error "Wrong dimensions"

345354

346−instance (FromLists (Either a b) c, FromLists (Either a b) d, Countable c)

347− => FromLists (Either a b) (Either c d) where

355+instance {-# OVERLAPPABLE #-} (FromLists e (Either a b) c, FromLists e (Either a b) d, Countable c) => FromLists e (Either a b) (Either c d) where

348356 fromLists l@(h : t) =

349357 let lh = length h

350358 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))

351− condition = all ((== lh) . length) t

359+ condition = all (== lh) (map length t)

352360 in if lh > 0 && condition

353− then Fork (fromLists (take rowsC l)) (fromLists (drop rowsC l))

361+ then Split (fromLists (take rowsC l)) (fromLists (drop rowsC l))

354362 else error "Not all rows have the same length"

355363

356364-- | Matrix builder function. Constructs a matrix provided with

357−-- a construction function that operates with indices.

358−matrixBuilder' ::

365+-- a construction function.

366+matrixBuilder ::

359367 forall e cols rows.

360− ( FL cols rows,

361− CountableDims cols rows

362− ) => ((Int, Int) -> e) -> Matrix e cols rows

363−matrixBuilder' f =

368+ ( FromLists e cols rows,

369+ CountableDimensions cols rows

370+ ) =>

371+ ((Int, Int) -> e) ->

372+ Matrix e cols rows

373+matrixBuilder f =

364374 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))

365375 r = fromInteger $ natVal (Proxy :: Proxy (Count rows))

366376 positions = [(a, b) | a <- [0 .. (r - 1)], b <- [0 .. (c - 1)]]

367377 in fromLists . map (map f) . groupBy (\(x, _) (w, _) -> x == w) $ positions

368378

369−-- | Matrix builder function. Constructs a matrix provided with

370−-- a construction function that operates with arbitrary types.

371−matrixBuilder ::

372− forall e a b.

373− ( FLN a b,

374− Enum a,

375− Enum b,

376− Bounded a,

377− Bounded b,

378− Eq a,

379− Countable b

380− ) => ((a, b) -> e) -> Matrix e (Normalize a) (Normalize b)

381−matrixBuilder f =

382− let r = fromInteger $ natVal (Proxy :: Proxy (Count b))

383− positions = [(a, b) | a <- [minBound .. maxBound], b <- [minBound .. maxBound]]

384− in fromLists . map (map f) . transpose . buildList r $ positions

385− where

386− buildList _ [] = []

387− buildList r l = take r l : buildList r (drop r l)

388−

389379-- | Constructs a column vector matrix

390−col :: (FL () rows) => [e] -> Matrix e () rows

380+col :: (FromLists e () rows) => [e] -> Matrix e () rows

391381col = fromLists . map (: [])

392382

393383-- | Constructs a row vector matrix

394−row :: (FL cols ()) => [e] -> Matrix e cols ()

384+row :: (FromLists e cols ()) => [e] -> Matrix e cols ()

395385row = fromLists . (: [])

396386

397387-- | Lifts functions to matrices with arbitrary dimensions.

398388--

399389-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of

400390-- types @a@ or @b@ allows.

401−fromF' ::

391+fromF ::

402392 forall a b cols rows e.

403393 ( Liftable e a b,

404− CountableDims cols rows,

405− FL rows cols

394+ CountableDimensions cols rows,

395+ FromLists e rows cols

406396 ) =>

407397 (a -> b) ->

408398 Matrix e cols rows

409−fromF' f =

399+fromF f =

410400 let minA = minBound @a

411401 maxA = maxBound @a

412402 minB = minBound @b

@@ -416,8 +406,8 @@ fromF' f =

416406 elementsA = take ccols [minA .. maxA]

417407 elementsB = take rrows [minB .. maxB]

418408 combinations = (,) <$> elementsA <*> elementsB

419− combAp = map snd . sort . map (\(a, b) -> if f a == b

420− then ((fromEnum a, fromEnum b), 1)

409+ combAp = map snd . sort . map (\(a, b) -> if f a == b

410+ then ((fromEnum a, fromEnum b), 1)

421411 else ((fromEnum a, fromEnum b), 0)) $ combinations

422412 mList = buildList combAp rrows

423413 in tr $ fromLists mList

@@ -427,23 +417,41 @@ fromF' f =

427417

428418-- | Lifts functions to matrices with dimensions matching @a@ and @b@

429419-- cardinality's.

430−fromF ::

420+fromF' ::

431421 forall a b e.

432422 ( Liftable e a b,

433− CountableDimsN a b,

434− FLN b a

423+ CountableDimensionsN a b,

424+ FromListsN e b a

435425 ) =>

436426 (a -> b) ->

437427 Matrix e (Normalize a) (Normalize b)

438−fromF = fromF'

428+fromF' f =

429+ let minA = minBound @a

430+ maxA = maxBound @a

431+ minB = minBound @b

432+ maxB = maxBound @b

433+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))

434+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))

435+ elementsA = take ccols [minA .. maxA]

436+ elementsB = take rrows [minB .. maxB]

437+ combinations = (,) <$> elementsA <*> elementsB

438+ combAp = map snd . sort . map (\(a, b) -> if f a == b

439+ then ((fromEnum a, fromEnum b), 1)

440+ else ((fromEnum a, fromEnum b), 0)) $ combinations

441+ mList = buildList combAp rrows

442+ in tr $ fromLists mList

443+ where

444+ buildList [] _ = []

445+ buildList l r = take r l : buildList (drop r l) r

439446

440447-- Conversion

441448

442449-- | Converts a matrix to a list of lists of elements.

443450toLists :: Matrix e cols rows -> [[e]]

451+toLists Empty = []

444452toLists (One e) = [[e]]

445−toLists (Fork l r) = toLists l ++ toLists r

446−toLists (Join l r) = zipWith (++) (toLists l) (toLists r)

453+toLists (Split l r) = toLists l ++ toLists r

454+toLists (Junc l r) = zipWith (++) (toLists l) (toLists r)

447455

448456-- | Converts a matrix to a list of elements.

449457toList :: Matrix e cols rows -> [e]

@@ -452,38 +460,38 @@ toList = concat . toLists

452460-- Zeros Matrix

453461

454462-- | The zero matrix. A matrix wholly filled with zeros.

455−zeros :: (Num e, FL cols rows, CountableDims cols rows) => Matrix e cols rows

456−zeros = matrixBuilder' (const 0)

463+zeros :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => Matrix e cols rows

464+zeros = matrixBuilder (const 0)

457465

458466-- Ones Matrix

459467

460468-- | The ones matrix. A matrix wholly filled with ones.

461469--

462470-- Also known as T (Top) matrix.

463−ones :: (Num e, FL cols rows, CountableDims cols rows) => Matrix e cols rows

464−ones = matrixBuilder' (const 1)

471+ones :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => Matrix e cols rows

472+ones = matrixBuilder (const 1)

465473

466474-- Const Matrix

467475

468476-- | The constant matrix constructor. A matrix wholly filled with a given

469477-- value.

470−constant :: (Num e, FL cols rows, CountableDims cols rows) => e -> Matrix e cols rows

471−constant e = matrixBuilder' (const e)

478+constant :: (Num e, FromLists e cols rows, CountableDimensions cols rows) => e -> Matrix e cols rows

479+constant e = matrixBuilder (const e)

472480

473481-- Bang Matrix

474482

475483-- | The T (Top) row vector matrix.

476−bang :: forall e cols. (Num e, Enum e, FL cols (), Countable cols) => Matrix e cols ()

484+bang :: forall e cols. (Num e, Enum e, FromLists e cols (), Countable cols) => Matrix e cols ()

477485bang =

478486 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))

479487 in fromLists [take c [1, 1 ..]]

480488

481−-- iden Matrix

489+-- Identity Matrix

482490

483−-- | iden matrix.

484−iden :: forall e cols . (Num e, FL cols cols, Countable cols) => Matrix e cols cols

485−iden = matrixBuilder' (bool 0 1 . uncurry (==))

486−{-# NOINLINE iden #-}

491+-- | Identity matrix.

492+identity :: (Num e, FromLists e cols cols, Countable cols) => Matrix e cols cols

493+identity = matrixBuilder (bool 0 1 . uncurry (==))

494+{-# NOINLINE identity #-}

487495

488496-- Matrix composition (MMM)

489497

@@ -492,90 +500,65 @@ iden = matrixBuilder' (bool 0 1 . uncurry (==))

492500-- This definition takes advantage of divide-and-conquer and fusion laws

493501-- from LAoP.

494502comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

495−comp (One a) (One b) = One (a * b)

496−comp (Join a b) (Fork c d) = comp a c + comp b d -- Divide-and-conquer law

497−comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law

498−comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law

503+comp Empty Empty = Empty

504+comp (One a) (One b) = One (a * b)

505+comp (Junc a b) (Split c d) = comp a c + comp b d -- Divide-and-conquer law

506+comp (Split a b) c = Split (comp a c) (comp b c) -- Split fusion law

507+comp c (Junc a b) = Junc (comp c a) (comp c b) -- Junc fusion law

499508{-# NOINLINE comp #-}

500−{-# RULES

501− "comp/iden1" forall m. comp m iden = m ;

502− "comp/iden2" forall m. comp iden m = m

509+{-# RULES

510+ "comp/identity1" forall m. comp m identity = m ;

511+ "comp/identity2" forall m. comp identity m = m

503512#-}

504513

505−-- Scalar multiplication of matrices

506−

507−infixl 7 .|

508−-- | Scalar multiplication of matrices.

509−(.|) :: Num e => e -> Matrix e cols rows -> Matrix e cols rows

510−(.|) e (One a) = One (e * a)

511−(.|) e (Join a b) = Join (e .| a) (e .| b)

512−(.|) e (Fork a b) = Fork (e .| a) (e .| b)

513−

514−-- Scalar division of matrices

515−

516−infixl 7 ./

517−-- | Scalar multiplication of matrices.

518−(./) :: Fractional e => Matrix e cols rows -> e -> Matrix e cols rows

519−(./) (One a) e = One (a / e)

520−(./) (Join a b) e = Join (a ./ e) (b ./ e)

521−(./) (Fork a b) e = Fork (a ./ e) (b ./ e)

522−

523514-- Projections

524515

525516-- | Biproduct first component projection

526−p1 :: (Num e, CountableDims n m, FL n m, FL m m) => Matrix e (Either m n) m

527−p1 = join id zeros

517+p1 :: forall e m n. (Num e, CountableDimensions n m, FromLists e n m, FromLists e m m) => Matrix e (Either m n) m

518+p1 =

519+ let iden = identity :: Matrix e m m

520+ zero = zeros :: Matrix e n m

521+ in junc iden zero

528522

529523-- | Biproduct second component projection

530−p2 :: (Num e, CountableDims n m, FL m n, FL n n) => Matrix e (Either m n) n

531−p2 = join zeros id

524+p2 :: forall e m n. (Num e, CountableDimensions n m, FromLists e m n, FromLists e n n) => Matrix e (Either m n) n

525+p2 =

526+ let iden = identity :: Matrix e n n

527+ zero = zeros :: Matrix e m n

528+ in junc zero iden

532529

533530-- Injections

534531

535532-- | Biproduct first component injection

536−i1 :: (Num e, CountableDims n m, FL n m, FL m m) => Matrix e m (Either m n)

533+i1 :: (Num e, CountableDimensions n m, FromLists e n m, FromLists e m m) => Matrix e m (Either m n)

537534i1 = tr p1

538535

539536-- | Biproduct second component injection

540−i2 :: (Num e, CountableDims n m, FL m n, FL n n) => Matrix e n (Either m n)

537+i2 :: (Num e, CountableDimensions n m, FromLists e m n, FromLists e n n) => Matrix e n (Either m n)

541538i2 = tr p2

542539

543540-- Dimensions

544541

545542-- | Obtain the number of rows.

546543--

547−-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

548−-- dimensions in constant time. For a version that doesn't require the

549−-- constraint see 'rows''.

544+-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

545+-- dimensions in constant time.

546+--

547+-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in

548+-- exchange for performance.

550549rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int

551550rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))

552551

553−-- | Obtain the number of rows in an inefficient manner, but without any

554−-- constraints.

555−--

556−-- For a more efficient version see 'rows'.

557−rows' :: Matrix e cols rows -> Int

558−rows' (One _) = 1

559−rows' (Join lhs _) = rows' lhs

560−rows' (Fork top bottom) = rows' top + rows' bottom

561−

562552-- | Obtain the number of columns.

553+--

554+-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

555+-- dimensions in constant time.

563556--

564−-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

565−-- dimensions in constant time. For a version that doesn't require the

566−-- constraint see 'columns''.

557+-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in

558+-- exchange for performance.

567559columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int

568560columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))

569561

570−-- | Obtain the number of columns in an inefficient manner, but without any

571−-- constraints.

572−--

573−-- For a more efficient version see 'columns'.

574−columns' :: Matrix e cols rows -> Int

575−columns' (One _) = 1

576−columns' (Join lhs rhs) = columns' lhs + columns' rhs

577−columns' (Fork top _) = columns' top

578−

579562-- Coproduct Bifunctor

580563

581564infixl 5 -|-

@@ -584,161 +567,164 @@ infixl 5 -|-

584567(-|-) ::

585568 forall e n k m j.

586569 ( Num e,

587− CountableDims j k,

588− FL k k,

589− FL j k,

590− FL k j,

591− FL j j

570+ CountableDimensions j k,

571+ FromLists e k k,

572+ FromLists e j k,

573+ FromLists e k j,

574+ FromLists e j j

592575 ) =>

593576 Matrix e n k ->

594577 Matrix e m j ->

595578 Matrix e (Either n m) (Either k j)

596−(-|-) a b = Join (i1 . a) (i2 . b)

579+(-|-) a b = Junc (i1 . a) (i2 . b)

597580

598581-- Khatri Rao Product and projections

599582

600583-- | Khatri Rao product first component projection matrix.

601−fstM ::

584+kp1 ::

602585 forall e m k .

603586 ( Num e,

604− CountableDims k m,

605− FL (Normalize (m, k)) m,

587+ CountableDimensions k m,

588+ FromLists e (Normalize (m, k)) m,

606589 CountableN (m, k)

607590 ) => Matrix e (Normalize (m, k)) m

608−fstM = matrixBuilder' f

591+kp1 = matrixBuilder f

609592 where

610593 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))

611594 f (x, y)

612595 | y >= (x * offset) && y <= (x * offset + offset - 1) = 1

613− | otherwise = 0

596+ | otherwise = 0

614597

615598-- | Khatri Rao product second component projection matrix.

616−sndM ::

599+kp2 ::

617600 forall e m k .

618601 ( Num e,

619− CountableDims k m,

620− FL (Normalize (m, k)) k,

602+ CountableDimensions k m,

603+ FromLists e (Normalize (m, k)) k,

621604 CountableN (m, k)

622605 ) => Matrix e (Normalize (m, k)) k

623−sndM = matrixBuilder' f

606+kp2 = matrixBuilder f

624607 where

625608 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))

626609 f (x, y)

627610 | x == y || mod (y - x) offset == 0 = 1

628− | otherwise = 0

611+ | otherwise = 0

629612

630613-- | Khatri Rao Matrix product also known as matrix pairing.

631614--

632615-- NOTE: That this is not a true categorical product, see for instance:

633−--

616+--

634617-- @

635−-- | fstM . kr a b == a

636−-- kr a b ==> |

637−-- | sndM . kr a b == b

618+-- | kp1 . khatri a b == a

619+-- khatri a b ==> |

620+-- | kp2 . khatri a b == b

638621-- @

639622--

640623-- __Emphasis__ on the implication symbol.

641−kr ::

642− forall e cols a b.

624+khatri ::

625+ forall e cols a b.

643626 ( Num e,

644− CountableDims a b,

627+ CountableDimensions a b,

645628 CountableN (a, b),

646− FL (Normalize (a, b)) a,

647− FL (Normalize (a, b)) b

629+ FromLists e (Normalize (a, b)) a,

630+ FromLists e (Normalize (a, b)) b

648631 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (Normalize (a, b))

649−kr a b =

650− let fstM' = fstM @e @a @b

651− sndM' = sndM @e @a @b

652− in (tr fstM' . a) * (tr sndM' . b)

632+khatri a b =

633+ let kp1' = kp1 @e @a @b

634+ kp2' = kp2 @e @a @b

635+ in (tr kp1') . a * (tr kp2') . b

653636

654637-- Product Bifunctor (Kronecker)

655638

656639infixl 4 ><

657640

658641-- | Matrix product functor also known as kronecker product

659−(><) ::

660− forall e m p n q.

642+(><) ::

643+ forall e m p n q.

661644 ( Num e,

662− CountableDims m n,

663− CountableDims p q,

664− CountableDimsN (m, n) (p, q),

665− FL (Normalize (m, n)) m,

666− FL (Normalize (m, n)) n,

667− FL (Normalize (p, q)) p,

668− FL (Normalize (p, q)) q

669− )

645+ CountableDimensions m n,

646+ CountableDimensions p q,

647+ CountableDimensionsN (m, n) (p, q),

648+ FromLists e (Normalize (m, n)) m,

649+ FromLists e (Normalize (m, n)) n,

650+ FromLists e (Normalize (p, q)) p,

651+ FromLists e (Normalize (p, q)) q

652+ )

670653 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))

671654(><) a b =

672− let fstM' = fstM @e @m @n

673− sndM' = sndM @e @m @n

674− in kr (a . fstM') (b . sndM')

655+ let kp1' = kp1 @e @m @n

656+ kp2' = kp2 @e @m @n

657+ in khatri (a . kp1') (b . kp2')

675658

676−-- Matrix abide Join Fork

659+-- Matrix abide Junc Split

677660

678−-- | Matrix "abiding" following the 'Join'-'Fork' exchange law.

679−--

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

662+--

680663-- Law:

681664--

682665-- @

683−-- 'Join' ('Fork' a c) ('Fork' b d) == 'Fork' ('Join' a b) ('Join' c d)

666+-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)

684667-- @

685−abideJF :: Matrix e cols rows -> Matrix e cols rows

686−abideJF (Join (Fork a c) (Fork b d)) = Fork (Join (abideJF a) (abideJF b)) (Join (abideJF c) (abideJF d)) -- Join-Fork abide law

687−abideJF (One e) = One e

688−abideJF (Join a b) = Join (abideJF a) (abideJF b)

689−abideJF (Fork a b) = Fork (abideJF a) (abideJF b)

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

669+abideJS (Junc (Split a c) (Split b d)) = Split (Junc (abideJS a) (abideJS b)) (Junc (abideJS c) (abideJS d)) -- Junc-Split abide law

670+abideJS Empty = Empty

671+abideJS (One e) = One e

672+abideJS (Junc a b) = Junc (abideJS a) (abideJS b)

673+abideJS (Split a b) = Split (abideJS a) (abideJS b)

690674

691−-- Matrix abide Fork Join

675+-- Matrix abide Split Junc

692676

693−-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.

694−--

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

678+--

695679-- @

696−-- 'Fork' ('Join' a b) ('Join' c d) == 'Join' ('Fork' a c) ('Fork' b d)

680+-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)

697681-- @

698−abideFJ :: Matrix e cols rows -> Matrix e cols rows

699−abideFJ (Fork (Join a b) (Join c d)) = Join (Fork (abideFJ a) (abideFJ c)) (Fork (abideFJ b) (abideFJ d)) -- Fork-Join abide law

700−abideFJ (One e) = One e

701−abideFJ (Join a b) = Join (abideFJ a) (abideFJ b)

702−abideFJ (Fork a b) = Fork (abideFJ a) (abideFJ b)

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

683+abideSJ (Split (Junc a b) (Junc c d)) = Junc (Split (abideSJ a) (abideSJ c)) (Split (abideSJ b) (abideSJ d)) -- Split-Junc abide law

684+abideSJ Empty = Empty

685+abideSJ (One e) = One e

686+abideSJ (Junc a b) = Junc (abideSJ a) (abideSJ b)

687+abideSJ (Split a b) = Split (abideSJ a) (abideSJ b)

703688

704689-- Matrix transposition

705690

706691-- | Matrix transposition.

707692tr :: Matrix e cols rows -> Matrix e rows cols

708−tr (One e) = One e

709−tr (Join a b) = Fork (tr a) (tr b)

710−tr (Fork a b) = Join (tr a) (tr b)

693+tr Empty = Empty

694+tr (One e) = One e

695+tr (Junc a b) = Split (tr a) (tr b)

696+tr (Split a b) = Junc (tr a) (tr b)

711697

712698-- Selective 'select' operator

713699

714700-- | Selective functors 'select' operator equivalent inspired by the

715701-- ArrowMonad solution presented in the paper.

716−select :: (Num e, FL b b, Countable b) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b

717−select (Fork a b) y = y . a + b -- Divide-and-conquer law

718−select (Join (Fork a c) (Fork b d)) y = join (y . a + c) (y . b + d) -- Pattern matching + DnC law

719−select m y = join y id . m

702+select :: (Num e, FromLists e b b, Countable b) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b

703+select (Split a b) y = y . a + b -- Divide-and-conquer law

704+select (Junc (Split a c) (Split b d)) y = junc (y . a + c) (y . b + d) -- Pattern matching + DnC law

705+select m y = junc y identity . m

720706

721707branch ::

722708 ( Num e,

723− CountableDims a b,

724− CountableDims c (Either b c),

725− FL c b,

726− FL a b,

727− FL a a,

728− FL b b,

729− FL c c,

730− FL b a,

731− FL b c,

732− FL (Either b c) b,

733− FL (Either b c) c

709+ CountableDimensions a b,

710+ CountableDimensions c (Either b c),

711+ FromLists e c b,

712+ FromLists e a b,

713+ FromLists e a a,

714+ FromLists e b b,

715+ FromLists e c c,

716+ FromLists e b a,

717+ FromLists e b c,

718+ FromLists e (Either b c) b,

719+ FromLists e (Either b c) c

734720 )

735721 => Matrix e cols (Either a b) -> Matrix e a c -> Matrix e b c -> Matrix e cols c

736722branch x l r = f x `select` g l `select` r

737723 where

738− f :: (Num e, Countable a, CountableDims b c, FL a b, FL c b, FL b b, FL b a, FL a a)

724+ f :: (Num e, Countable a, CountableDimensions b c, FromLists e a b, FromLists e c b, FromLists e b b, FromLists e b a, FromLists e a a)

739725 => Matrix e cols (Either a b) -> Matrix e cols (Either a (Either b c))

740− f m = fork (tr i1) (i1 . tr i2) . m

741− g :: (Num e, CountableDims b c, FL b c, FL c c) => Matrix e a c -> Matrix e a (Either b c)

726+ f m = split (tr i1) (i1 . tr i2) . m

727+ g :: (Num e, CountableDimensions b c, FromLists e b c, FromLists e c c) => Matrix e a c -> Matrix e a (Either b c)

742728 g m = i2 . m

743729

744730-- McCarthy's Conditional

@@ -747,9 +733,9 @@ branch x l r = f x `select` g l `select` r

747733cond ::

748734 ( Trivial cols,

749735 Countable cols,

750− FL () cols,

751− FL cols (),

752− FL cols cols,

736+ FromLists e () cols,

737+ FromLists e cols (),

738+ FromLists e cols cols,

753739 Bounded a,

754740 Enum a,

755741 Num e,

@@ -757,14 +743,14 @@ cond ::

757743 )

758744 =>

759745 (a -> Bool) -> Matrix e cols rows -> Matrix e cols rows -> Matrix e cols rows

760−cond p f g = join f g . grd p

746+cond p f g = junc f g . grd p

761747

762−grd ::

748+grd ::

763749 ( Trivial q,

764750 Countable q,

765− FL () q,

766− FL q (),

767− FL q q,

751+ FromLists e () q,

752+ FromLists e q (),

753+ FromLists e q q,

768754 Bounded a,

769755 Enum a,

770756 Num e,

@@ -772,44 +758,44 @@ grd ::

772758 )

773759 =>

774760 (a -> Bool) -> Matrix e q (Either q q)

775−grd f = fork (corr f) (corr (not . f))

761+grd f = split (corr f) (corr (not . f))

776762

777−corr ::

778− forall e a q .

763+corr ::

764+ forall e a q .

779765 ( Trivial q,

780766 Countable q,

781− FL () q,

782− FL q (),

783− FL q q,

767+ FromLists e () q,

768+ FromLists e q (),

769+ FromLists e q q,

784770 Liftable e a Bool

785− )

771+ )

786772 => (a -> Bool) -> Matrix e q q

787−corr p = let f = fromF' p :: Matrix e q ()

788− in kr f (id :: Matrix e q q)

773+corr p = let f = fromF p :: Matrix e q ()

774+ in khatri f (identity :: Matrix e q q)

789775

790776-- Pretty print

791777

792778prettyAux :: Show e => [[e]] -> [[e]] -> String

793779prettyAux [] _ = ""

794−prettyAux [[e]] m = "│ " ++ fill (show e) ++ " │\n"

780+prettyAux [[e]] m = "│ " ++ fill (show e) ++ " │\n"

795781 where

796782 v = fmap show m

797783 widest = maximum $ fmap length v

798784 fill str = replicate (widest - length str - 2) ' ' ++ str

799−prettyAux [h] m = "│ " ++ fill (unwords $ map show h) ++ " │\n"

785+prettyAux [h] m = "│ " ++ fill (unwords $ map show h) ++ " │\n"

800786 where

801− v = fmap show m

802− widest = maximum $ fmap length v

787+ v = fmap show m

788+ widest = maximum $ fmap length v

803789 fill str = replicate (widest - length str - 2) ' ' ++ str

804−prettyAux (h : t) l = "│ " ++ fill (unwords $ map show h) ++ " │\n" ++

790+prettyAux (h : t) l = "│ " ++ fill (unwords $ map show h) ++ " │\n" ++

805791 prettyAux t l

806792 where

807− v = fmap show l

808− widest = maximum $ fmap length v

793+ v = fmap show l

794+ widest = maximum $ fmap length v

809795 fill str = replicate (widest - length str - 2) ' ' ++ str

810796

811797-- | Matrix pretty printer

812−pretty :: (CountableDims cols rows, Show e) => Matrix e cols rows -> String

798+pretty :: (CountableDimensions cols rows, Show e) => Matrix e cols rows -> String

813799pretty m = concat

814800 [ "┌ ", unwords (replicate (columns m) blank), " ┐\n"

815801 , unlines

@@ -817,16 +803,16 @@ pretty m = concat

817803 , "└ ", unwords (replicate (columns m) blank), " ┘"

818804 ]

819805 where

820− strings = map show (toList m)

821− widest = maximum $ map length strings

806+ strings = map show (toList m)

807+ widest = maximum $ map length strings

822808 fill str = replicate (widest - length str) ' ' ++ str

823− blank = fill ""

809+ blank = fill ""

824810 safeGet i j m

825811 | i > rows m || j > columns m || i < 1 || j < 1 = Nothing

826812 | otherwise = Just $ unsafeGet i j m (toList m)

827813 unsafeGet i j m l = l !! encode (columns m) (i,j)

828− encode m (i,j) = (i-1)*m + j - 1

829− getElem i j m =

814+ encode m (i,j) = (i-1)*m + j - 1

815+ getElem i j m =

830816 fromMaybe

831817 (error $

832818 "getElem: Trying to get the "

@@ -838,20 +824,12 @@ pretty m = concat

838824 (safeGet i j m)

839825

840826-- | Matrix pretty printer

841−prettyPrint :: (CountableDims cols rows, Show e) => Matrix e cols rows -> IO ()

827+prettyPrint :: (CountableDimensions cols rows, Show e) => Matrix e cols rows -> IO ()

842828prettyPrint = putStrLn . pretty

843829

844−-- | Zip two matrices with a given binary function

845−zipWithM :: (e -> f -> g) -> Matrix e cols rows -> Matrix f cols rows -> Matrix g cols rows

846−zipWithM f (One a) (One b) = One (f a b)

847−zipWithM f (Join a b) (Join c d) = Join (zipWithM f a c) (zipWithM f b d)

848−zipWithM f (Fork a b) (Fork c d) = Fork (zipWithM f a c) (zipWithM f b d)

849−zipWithM f x@(Fork _ _) y@(Join _ _) = zipWithM f x (abideJF y)

850−zipWithM f x@(Join _ _) y@(Fork _ _) = zipWithM f (abideJF x) y

851−

852830-- Relational operators functions

853831

854−type Boolean = Natural 0 1

832+type Boolean = Natural 0 1

855833type Relation a b = Matrix Boolean a b

856834

857835-- | Helper conversion function

@@ -867,47 +845,54 @@ fromBool False = nat 0

867845

868846-- | Relational negation

869847negateM :: Relation cols rows -> Relation cols rows

870−negateM (One (Nat p)) = One (Nat (negate p))

871−negateM (Join a b) = Join (negateM a) (negateM b)

872−negateM (Fork a b) = Fork (negateM a) (negateM b)

848+negateM Empty = Empty

849+negateM (One (Nat 0)) = One (Nat 1)

850+negateM (One (Nat 1)) = One (Nat 0)

851+negateM (Junc a b) = Junc (negateM a) (negateM b)

852+negateM (Split a b) = Split (negateM a) (negateM b)

873853

874854-- | Relational addition

875855orM :: Relation cols rows -> Relation cols rows -> Relation cols rows

876−orM (One a) (One b) = One (fromBool (toBool a || toBool b))

877−orM (Join a b) (Join c d) = Join (orM a c) (orM b d)

878−orM (Fork a b) (Fork c d) = Fork (orM a c) (orM b d)

879−orM x@(Fork _ _) y@(Join _ _) = orM x (abideJF y)

880−orM x@(Join _ _) y@(Fork _ _) = orM (abideJF x) y

856+orM Empty Empty = Empty

857+orM (One a) (One b) = One (fromBool (toBool a || toBool b))

858+orM (Junc a b) (Junc c d) = Junc (orM a c) (orM b d)

859+orM (Split a b) (Split c d) = Split (orM a c) (orM b d)

860+orM x@(Split _ _) y@(Junc _ _) = orM x (abideJS y)

861+orM x@(Junc _ _) y@(Split _ _) = orM (abideJS x) y

881862

882863-- | Relational multiplication

883864andM :: Relation cols rows -> Relation cols rows -> Relation cols rows

884−andM (One a) (One b) = One (fromBool (toBool a && toBool b))

885−andM (Join a b) (Join c d) = Join (andM a c) (andM b d)

886−andM (Fork a b) (Fork c d) = Fork (andM a c) (andM b d)

887−andM x@(Fork _ _) y@(Join _ _) = andM x (abideJF y)

888−andM x@(Join _ _) y@(Fork _ _) = andM (abideJF x) y

865+andM Empty Empty = Empty

866+andM (One a) (One b) = One (fromBool (toBool a && toBool b))

867+andM (Junc a b) (Junc c d) = Junc (andM a c) (andM b d)

868+andM (Split a b) (Split c d) = Split (andM a c) (andM b d)

869+andM x@(Split _ _) y@(Junc _ _) = andM x (abideJS y)

870+andM x@(Junc _ _) y@(Split _ _) = andM (abideJS x) y

889871

890872-- | Relational subtraction

891873subM :: Relation cols rows -> Relation cols rows -> Relation cols rows

892−subM (One a) (One b) = if a - b < nat 0 then One (nat 0) else One (a - b)

893−subM (Join a b) (Join c d) = Join (subM a c) (subM b d)

894−subM (Fork a b) (Fork c d) = Fork (subM a c) (subM b d)

895−subM x@(Fork _ _) y@(Join _ _) = subM x (abideJF y)

896−subM x@(Join _ _) y@(Fork _ _) = subM (abideJF x) y

874+subM Empty Empty = Empty

875+subM (One a) (One b) = if a - b < nat 0 then One (nat 0) else One (a - b)

876+subM (Junc a b) (Junc c d) = Junc (subM a c) (subM b d)

877+subM (Split a b) (Split c d) = Split (subM a c) (subM b d)

878+subM x@(Split _ _) y@(Junc _ _) = subM x (abideJS y)

879+subM x@(Junc _ _) y@(Split _ _) = subM (abideJS x) y

897880

898881-- | Matrix relational composition.

899882compRel :: Relation cr rows -> Relation cols cr -> Relation cols rows

900−compRel (One a) (One b) = One (fromBool (toBool a && toBool b))

901−compRel (Join a b) (Fork c d) = orM (compRel a c) (compRel b d) -- Divide-and-conquer law

902−compRel (Fork a b) c = Fork (compRel a c) (compRel b c) -- Fork fusion law

903−compRel c (Join a b) = Join (compRel c a) (compRel c b) -- Join fusion law

883+compRel Empty Empty = Empty

884+compRel (One a) (One b) = One (fromBool (toBool a && toBool b))

885+compRel (Junc a b) (Split c d) = orM (compRel a c) (compRel b d) -- Divide-and-conquer law

886+compRel (Split a b) c = Split (compRel a c) (compRel b c) -- Split fusion law

887+compRel c (Junc a b) = Junc (compRel c a) (compRel c b) -- Junc fusion law

904888

905889-- | Matrix relational right division

906890divR :: Relation b c -> Relation b a -> Relation a c

891+divR Empty Empty = Empty

907892divR (One a) (One b) = One (fromBool (not (toBool b) || toBool a)) -- b implies a

908−divR (Join a b) (Join c d) = andM (divR a c) (divR b d)

909−divR (Fork a b) c = Fork (divR a c) (divR b c)

910−divR c (Fork a b) = Join (divR c a) (divR c b)

893+divR (Junc a b) (Junc c d) = andM (divR a c) (divR b d)

894+divR (Split a b) c = Split (divR a c) (divR b c)

895+divR c (Split a b) = Junc (divR c a) (divR c b)

911896

912897-- | Matrix relational left division

913898divL :: Relation c b -> Relation a b -> Relation a c

@@ -923,52 +908,86 @@ divS s r = divL r s `intersection` divR (tr r) (tr s)

923908--

924909-- NOTE: Be careful to not ask for a relation bigger than the cardinality of

925910-- types @a@ or @b@ allows.

926−fromFRel' ::

911+fromFRel ::

927912 forall a b cols rows.

928913 ( Liftable Boolean a b,

929− CountableDims cols rows,

930− FL rows cols

914+ CountableDimensions cols rows,

915+ FromLists Boolean rows cols

931916 ) =>

932917 (a -> b) ->

933918 Relation cols rows

934−fromFRel' = fromF'

919+fromFRel f =

920+ let minA = minBound @a

921+ maxA = maxBound @a

922+ minB = minBound @b

923+ maxB = maxBound @b

924+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count cols))

925+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count rows))

926+ elementsA = take ccols [minA .. maxA]

927+ elementsB = take rrows [minB .. maxB]

928+ combinations = (,) <$> elementsA <*> elementsB

929+ combAp = map snd . sort . map (\(a, b) -> if f a == b

930+ then ((fromEnum a, fromEnum b), nat 1)

931+ else ((fromEnum a, fromEnum b), nat 0)) $ combinations

932+ mList = buildList combAp rrows

933+ in tr $ fromLists mList

934+ where

935+ buildList [] _ = []

936+ buildList l r = take r l : buildList (drop r l) r

935937

936938-- | Lifts functions to relations with dimensions matching @a@ and @b@

937939-- cardinality's.

938−fromFRel ::

940+fromFRel' ::

939941 forall a b.

940942 ( Liftable Boolean a b,

941− CountableDimsN a b,

942− FLN b a

943+ CountableDimensionsN a b,

944+ FromLists Boolean (Normalize b) (Normalize a)

943945 ) =>

944946 (a -> b) ->

945947 Relation (Normalize a) (Normalize b)

946−fromFRel = fromFRel'

948+fromFRel' f =

949+ let minA = minBound @a

950+ maxA = maxBound @a

951+ minB = minBound @b

952+ maxB = maxBound @b

953+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))

954+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))

955+ elementsA = take ccols [minA .. maxA]

956+ elementsB = take rrows [minB .. maxB]

957+ combinations = (,) <$> elementsA <*> elementsB

958+ combAp = map snd . sort . map (\(a, b) -> if f a == b

959+ then ((fromEnum a, fromEnum b), nat 1)

960+ else ((fromEnum a, fromEnum b), nat 0)) $ combinations

961+ mList = buildList combAp rrows

962+ in tr $ fromLists mList

963+ where

964+ buildList [] _ = []

965+ buildList l r = take r l : buildList (drop r l) r

947966

948967-- | Lifts a relation function to a Boolean Matrix

949−toRel ::

968+toRel ::

950969 forall a b.

951970 ( Bounded a,

952971 Bounded b,

953972 Enum a,

954973 Enum b,

955974 Eq b,

956− CountableDims a b,

957− FLN b a

958− )

975+ CountableDimensionsN a b,

976+ FromListsN Boolean b a

977+ )

959978 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)

960979toRel f =

961980 let minA = minBound @a

962981 maxA = maxBound @a

963982 minB = minBound @b

964983 maxB = maxBound @b

965− ccols = fromInteger $ natVal (Proxy :: Proxy (Count a))

966− rrows = fromInteger $ natVal (Proxy :: Proxy (Count b))

984+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))

985+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))

967986 elementsA = take ccols [minA .. maxA]

968987 elementsB = take rrows [minB .. maxB]

969988 combinations = (,) <$> elementsA <*> elementsB

970− combAp = map snd . sort . map (\(a, b) -> if uncurry f (a, b)

971− then ((fromEnum a, fromEnum b), nat 1)

989+ combAp = map snd . sort . map (\(a, b) -> if uncurry f (a, b)

990+ then ((fromEnum a, fromEnum b), nat 1)

972991 else ((fromEnum a, fromEnum b), nat 0)) $ combinations

973992 mList = buildList combAp rrows

974993 in tr $ fromLists mList

src/LAoP/Matrix/Nat.hs+124−139

@@ -56,20 +56,21 @@ module LAoP.Matrix.Nat

5656

5757 -- * Constraint type synonyms

5858 Countable,

59− CountableDims,

59+ CountableDimensions,

6060 CountableN,

6161 CountableNz,

62− CountableDimsN,

63− FLN,

64− FLNz,

62+ CountableDimensionsN,

63+ FromListsN,

64+ FromListsNz,

6565 Liftable,

6666 TrivialE,

6767 TrivialP,

6868

6969 -- * Primitives

70+ empty,

7071 one,

71− join,

72− fork,

72+ junc,

73+ split,

7374

7475 -- * Auxiliary type families

7576 I.FromNat,

@@ -77,11 +78,11 @@ module LAoP.Matrix.Nat

7778 I.Normalize,

7879

7980 -- * Matrix construction and conversion

80− I.FL,

81+ I.FromLists,

8182 fromLists,

8283 toLists,

8384 toList,

84− matrixBuilder',

85+ matrixBuilder,

8586 row,

8687 col,

8788 zeros,

@@ -97,10 +98,6 @@ module LAoP.Matrix.Nat

9798 -- ** Matrix Transposition

9899 tr,

99100

100− -- ** Scalar multiplication/division of matrices

101− (.|),

102− (./),

103−

104101 -- ** Selective operator

105102 select,

106103

@@ -108,19 +105,16 @@ module LAoP.Matrix.Nat

108105 cond,

109106

110107 -- ** Matrix "abiding"

111− abideJF,

112− abideFJ,

113−

114− -- ** Zip Matrices

115− zipWithM,

108+ abideJS,

109+ abideSJ,

116110

117111 -- * Biproduct approach

118− -- ** Fork

112+ -- ** Split

119113 (===),

120114 -- *** Projections

121115 p1,

122116 p2,

123− -- ** Join

117+ -- ** Junc

124118 (|||),

125119 -- *** Injections

126120 i1,

@@ -134,11 +128,11 @@ module LAoP.Matrix.Nat

134128 -- | Note that given the restrictions imposed it is not possible to

135129 -- implement the standard type classes present in standard Haskell.

136130 -- *** Matrix pairing projections

137− fstM,

138− sndM,

131+ kp1,

132+ kp2,

139133

140134 -- *** Matrix pairing

141− kr,

135+ khatri,

142136

143137 -- * Matrix composition and lifting

144138

@@ -146,10 +140,10 @@ module LAoP.Matrix.Nat

146140

147141 -- | Note that given the restrictions imposed it is not possible to

148142 -- implement the standard type classes present in standard Haskell.

149− iden,

143+ identity,

150144 comp,

151− fromF',

152145 fromF,

146+ fromF',

153147

154148 -- * Matrix printing

155149 pretty,

@@ -160,34 +154,47 @@ where

160154import Data.Proxy

161155import GHC.TypeLits

162156import Control.DeepSeq

157+import qualified Control.Category as C

163158import qualified LAoP.Matrix.Internal as I

164159

165160newtype Matrix e (cols :: Nat) (rows :: Nat) = M (I.Matrix e (I.FromNat cols) (I.FromNat rows))

166161 deriving (Show, Num, Eq, Ord, NFData) via (I.Matrix e (I.FromNat cols) (I.FromNat rows))

167162

168163-- | Constraint type synonyms to keep the type signatures less convoluted

169−type Countable a = KnownNat (I.Count a)

170−type CountableDims a b = (Countable a, Countable b)

171−type CountableN a = KnownNat (I.Count (I.FromNat a))

172−type CountableNz a = KnownNat (I.Count (I.Normalize a))

173−type CountableDimsN a b = (CountableN a, CountableN b)

174−type FLN e a b = I.FL (I.FromNat a) (I.FromNat b)

175−type FLNz e a b = I.FL (I.Normalize a) (I.Normalize b)

176−type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)

177−type TrivialE a b = I.FromNat (a + b) ~ Either (I.FromNat a) (I.FromNat b)

178−type TrivialP a b = I.FromNat (a * b) ~ I.FromNat (I.Count (I.FromNat a) * I.Count (I.FromNat b))

164+type Countable a = KnownNat (I.Count a)

165+type CountableDimensions a b = (Countable a, Countable b)

166+type CountableN a = KnownNat (I.Count (I.FromNat a))

167+type CountableNz a = KnownNat (I.Count (I.Normalize a))

168+type CountableDimensionsN a b = (CountableN a, CountableN b)

169+type FromListsN e a b = I.FromLists e (I.FromNat a) (I.FromNat b)

170+type FromListsNz e a b = I.FromLists e (I.Normalize a) (I.Normalize b)

171+type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)

172+type TrivialE a b = I.FromNat (a + b) ~ Either (I.FromNat a) (I.FromNat b)

173+type TrivialP a b = I.FromNat (a * b) ~ I.FromNat (I.Count (I.FromNat a) * I.Count (I.FromNat b))

174+

175+-- | It isn't possible to implement the 'id' function so it's

176+-- implementation is 'undefined'. However 'comp' can be and this partial

177+-- class implementation exists just to make the code more readable.

178+--

179+-- Please use 'identity' instead.

180+instance (Num e) => C.Category (Matrix e) where

181+ id = undefined

182+ (.) = comp

179183

180184-- Primitives

181185

186+empty :: Matrix e 0 0

187+empty = M I.Empty

188+

182189one :: e -> Matrix e 1 1

183190one = M . I.One

184191

185−join ::

192+junc ::

186193 (TrivialE a b) =>

187194 Matrix e a rows ->

188195 Matrix e b rows ->

189196 Matrix e (a + b) rows

190−join (M a) (M b) = M (I.Join a b)

197+junc (M a) (M b) = M (I.Junc a b)

191198

192199infixl 3 |||

193200(|||) ::

@@ -195,14 +202,14 @@ infixl 3 |||

195202 Matrix e a rows ->

196203 Matrix e b rows ->

197204 Matrix e (a + b) rows

198−(|||) = join

205+(|||) = junc

199206

200−fork ::

207+split ::

201208 (TrivialE a b) =>

202209 Matrix e cols a ->

203210 Matrix e cols b ->

204211 Matrix e cols (a + b)

205−fork (M a) (M b) = M (I.Fork a b)

212+split (M a) (M b) = M (I.Split a b)

206213

207214infixl 2 ===

208215(===) ::

@@ -210,45 +217,43 @@ infixl 2 ===

210217 Matrix e cols a ->

211218 Matrix e cols b ->

212219 Matrix e cols (a + b)

213−(===) = fork

220+(===) = split

214221

215222-- Construction

216223

217−fromLists :: (FLN e cols rows) => [[e]] -> Matrix e cols rows

224+fromLists :: (FromListsN e cols rows) => [[e]] -> Matrix e cols rows

218225fromLists = M . I.fromLists

219226

220−-- | Matrix builder function. Constructs a matrix provided with

221−-- a construction function that operates with indices.

222−matrixBuilder' ::

223− (FLN e cols rows, CountableN cols, CountableN rows)

227+matrixBuilder ::

228+ (FromListsN e cols rows, CountableN cols, CountableN rows)

224229 => ((Int, Int) -> e) -> Matrix e cols rows

225−matrixBuilder' = M . I.matrixBuilder'

230+matrixBuilder = M . I.matrixBuilder

226231

227−col :: (I.FL () (I.FromNat rows)) => [e] -> Matrix e 1 rows

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

228233col = M . I.col

229234

230−row :: (I.FL (I.FromNat cols) ()) => [e] -> Matrix e cols 1

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

231236row = M . I.row

232237

233−fromF' ::

238+fromF ::

234239 ( Liftable e a b,

235240 CountableN cols,

236241 CountableN rows,

237− FLN e rows cols

242+ FromListsN e rows cols

238243 ) =>

239244 (a -> b) ->

240245 Matrix e cols rows

241−fromF' = M . I.fromF'

246+fromF = M . I.fromF

242247

243−fromF ::

248+fromF' ::

244249 ( Liftable e a b,

245250 CountableNz a,

246251 CountableNz b,

247− FLNz e b a

252+ FromListsNz e b a

248253 ) =>

249254 (a -> b) ->

250255 Matrix e (I.Count a) (I.Count b)

251−fromF = undefined -- M . I.fromF

256+fromF' = undefined -- M . I.fromF'

252257

253258-- Conversion

254259

@@ -261,21 +266,21 @@ toList (M m) = I.toList m

261266-- Zeros Matrix

262267

263268zeros ::

264− (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>

269+ (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>

265270 Matrix e cols rows

266271zeros = M I.zeros

267272

268273-- Ones Matrix

269274

270275ones ::

271− (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>

276+ (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>

272277 Matrix e cols rows

273278ones = M I.ones

274279

275280-- Const Matrix

276281

277282constant ::

278− (Num e, FLN e cols rows, CountableN cols, CountableN rows) =>

283+ (Num e, FromListsN e cols rows, CountableN cols, CountableN rows) =>

279284 e ->

280285 Matrix e cols rows

281286constant = M . I.constant

@@ -284,41 +289,27 @@ constant = M . I.constant

284289

285290bang ::

286291 forall e cols.

287− (Num e, Enum e, I.FL (I.FromNat cols) (), CountableN cols) =>

292+ (Num e, Enum e, I.FromLists e (I.FromNat cols) (), CountableN cols) =>

288293 Matrix e cols 1

289294bang = M I.bang

290295

291−-- iden Matrix

296+-- Identity Matrix

292297

293−iden ::

294− (Num e, FLN e cols cols, CountableN cols) =>

298+identity ::

299+ (Num e, FromListsN e cols cols, CountableN cols) =>

295300 Matrix e cols cols

296−iden = M I.iden

301+identity = M I.identity

297302

298303-- Matrix composition (MMM)

299304

300305comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

301306comp (M a) (M b) = M (I.comp a b)

302307

303−-- Scalar multiplication of matrices

304−

305−infixl 7 .|

306−-- | Scalar multiplication of matrices.

307−(.|) :: Num e => e -> Matrix e cols rows -> Matrix e cols rows

308−(.|) e (M m) = M (e I..| m)

309−

310−-- Scalar division of matrices

311−

312−infixl 7 ./

313−-- | Scalar multiplication of matrices.

314−(./) :: Fractional e => Matrix e cols rows -> e -> Matrix e cols rows

315−(./) (M m) e = M (m I../ e)

316−

317308p1 ::

318309 ( Num e,

319− CountableDimsN n m,

320− FLN e n m,

321− FLN e m m,

310+ CountableDimensionsN n m,

311+ FromListsN e n m,

312+ FromListsN e m m,

322313 TrivialE m n

323314 ) =>

324315 Matrix e (m + n) m

@@ -326,9 +317,9 @@ p1 = M I.p1

326317

327318p2 ::

328319 ( Num e,

329− CountableDimsN n m,

330− FLN e m n,

331− FLN e n n,

320+ CountableDimensionsN n m,

321+ FromListsN e m n,

322+ FromListsN e n n,

332323 TrivialE m n

333324 ) =>

334325 Matrix e (m + n) n

@@ -338,9 +329,9 @@ p2 = M I.p2

338329

339330i1 ::

340331 ( Num e,

341− CountableDimsN n rows,

342− FLN e n rows,

343− FLN e rows rows,

332+ CountableDimensionsN n rows,

333+ FromListsN e n rows,

334+ FromListsN e rows rows,

344335 TrivialE rows n

345336 ) =>

346337 Matrix e rows (rows + n)

@@ -348,9 +339,9 @@ i1 = tr p1

348339

349340i2 ::

350341 ( Num e,

351− CountableDimsN rows m,

352− FLN e m rows,

353− FLN e rows rows,

342+ CountableDimensionsN rows m,

343+ FromListsN e m rows,

344+ FromListsN e rows rows,

354345 TrivialE m rows

355346 ) =>

356347 Matrix e rows (m + rows)

@@ -364,16 +355,16 @@ rows (M m) = I.rows m

364355columns :: (CountableN cols) => Matrix e cols rows -> Int

365356columns (M m) = I.columns m

366357

358+-- | Coproduct Bifunctor

367359infixl 5 -|-

368360

369−-- | Coproduct Bifunctor (Direct sum)

370361(-|-) ::

371362 ( Num e,

372− CountableDimsN j k,

373− FLN e k k,

374− FLN e j k,

375− FLN e k j,

376− FLN e j j,

363+ CountableDimensionsN j k,

364+ FromListsN e k k,

365+ FromListsN e j k,

366+ FromListsN e k j,

367+ FromListsN e j j,

377368 TrivialE n m,

378369 TrivialE k j

379370 ) =>

@@ -382,42 +373,40 @@ infixl 5 -|-

382373 Matrix e (n + m) (k + j)

383374(-|-) (M a) (M b) = M ((I.-|-) a b)

384375

385−-- | Khatri Rao Product first projection

386−fstM ::

376+-- | Khatri Rao Product and projections

377+kp1 ::

387378 forall e m k .

388379 ( Num e,

389− CountableDimsN m k,

380+ CountableDimensionsN m k,

390381 CountableN (m * k),

391− FLN e (m * k) m,

382+ FromListsN e (m * k) m,

392383 TrivialP m k

393384 ) => Matrix e (m * k) m

394−fstM = M (I.fstM @e @(I.FromNat m) @(I.FromNat k))

385+kp1 = M (I.kp1 @e @(I.FromNat m) @(I.FromNat k))

395386

396−-- | Khatri Rao Product second projection

397−sndM ::

387+kp2 ::

398388 forall e m k.

399389 ( Num e,

400− CountableDimsN k m,

401− FLN e (m * k) k,

390+ CountableDimensionsN k m,

391+ FromListsN e (m * k) k,

402392 CountableN (m * k),

403393 TrivialP m k

404394 ) => Matrix e (m * k) k

405−sndM = M (I.sndM @e @(I.FromNat m) @(I.FromNat k))

395+kp2 = M (I.kp2 @e @(I.FromNat m) @(I.FromNat k))

406396

407−-- | Khatri Rao Product

408−kr ::

397+khatri ::

409398 forall e cols a b.

410399 ( Num e,

411− CountableDimsN a b,

400+ CountableDimensionsN a b,

412401 CountableN (a * b),

413− FLN e (a * b) a,

414− FLN e (a * b) b,

402+ FromListsN e (a * b) a,

403+ FromListsN e (a * b) b,

415404 TrivialP a b

416405 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a * b)

417−kr a b =

418− let fstM' = fstM @e @a @b

419− sndM' = sndM @e @a @b

420− in comp (tr fstM') a * comp (tr sndM') b

406+khatri a b =

407+ let kp1' = kp1 @e @a @b

408+ kp2' = kp2 @e @a @b

409+ in comp (tr kp1') a * comp (tr kp2') b

421410

422411-- | Product Bifunctor (Kronecker)

423412infixl 4 ><

@@ -425,28 +414,28 @@ infixl 4 ><

425414(><) ::

426415 forall e m p n q.

427416 ( Num e,

428− CountableDimsN m n,

429− CountableDimsN p q,

430− CountableDimsN (m * n) (p * q),

431− FLN e (m * n) m,

432− FLN e (m * n) n,

433− FLN e (p * q) p,

434− FLN e (p * q) q,

417+ CountableDimensionsN m n,

418+ CountableDimensionsN p q,

419+ CountableDimensionsN (m * n) (p * q),

420+ FromListsN e (m * n) m,

421+ FromListsN e (m * n) n,

422+ FromListsN e (p * q) p,

423+ FromListsN e (p * q) q,

435424 TrivialP m n,

436425 TrivialP p q

437426 ) => Matrix e m p -> Matrix e n q -> Matrix e (m * n) (p * q)

438427(><) a b =

439− let fstM' = fstM @e @m @n

440− sndM' = sndM @e @m @n

441− in kr (comp a fstM') (comp b sndM')

428+ let kp1' = kp1 @e @m @n

429+ kp2' = kp2 @e @m @n

430+ in khatri (comp a kp1') (comp b kp2')

442431

443−-- | Matrix abide Join Fork

444−abideJF :: Matrix e cols rows -> Matrix e cols rows

445−abideJF (M m) = M (I.abideJF m)

432+-- | Matrix abide Junc Split

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

434+abideJS (M m) = M (I.abideJS m)

446435

447−-- | Matrix abide Fork Join

448−abideFJ :: Matrix e cols rows -> Matrix e cols rows

449−abideFJ (M m) = M (I.abideFJ m)

436+-- | Matrix abide Split Junc

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

438+abideSJ (M m) = M (I.abideSJ m)

450439

451440-- | Matrix transposition

452441tr :: Matrix e cols rows -> Matrix e rows cols

@@ -455,7 +444,7 @@ tr (M m) = M (I.tr m)

455444-- Selective 'select' operator

456445select ::

457446 ( Num e,

458− FLN e rows1 rows1,

447+ FromListsN e rows1 rows1,

459448 CountableN rows1,

460449 I.FromNat rows2 ~ I.FromNat rows1,

461450 I.FromNat cols1 ~ I.FromNat cols2,

@@ -468,9 +457,9 @@ select (M m) (M y) = M (I.select m y)

468457cond ::

469458 ( I.FromNat (I.Count (I.FromNat cols)) ~ I.FromNat cols,

470459 CountableN cols,

471− I.FL () (I.FromNat cols),

472− I.FL (I.FromNat cols) (),

473− FLN e cols cols,

460+ I.FromLists e () (I.FromNat cols),

461+ I.FromLists e (I.FromNat cols) (),

462+ FromListsN e cols cols,

474463 Liftable e a Bool

475464 )

476465 =>

@@ -479,12 +468,8 @@ cond p (M a) (M b) = M (I.cond p a b)

479468

480469-- Pretty print

481470

482−pretty :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> String

471+pretty :: (CountableDimensionsN cols rows, Show e) => Matrix e cols rows -> String

483472pretty (M m) = I.pretty m

484473

485−prettyPrint :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> IO ()

474+prettyPrint :: (CountableDimensionsN cols rows, Show e) => Matrix e cols rows -> IO ()

486475prettyPrint (M m) = I.prettyPrint m

487−

488−-- | Zip two matrices with a given binary function

489−zipWithM :: (e -> f -> g) -> Matrix e cols rows -> Matrix f cols rows -> Matrix g cols rows

490−zipWithM f (M a) (M b) = M (I.zipWithM f a b)

src/LAoP/Matrix/Type.hs+180−224

@@ -1,11 +1,11 @@

11{-# LANGUAGE ConstraintKinds #-}

2−{-# LANGUAGE TypeFamilies #-}

32{-# LANGUAGE AllowAmbiguousTypes #-}

43{-# LANGUAGE DataKinds #-}

54{-# LANGUAGE DerivingVia #-}

65{-# LANGUAGE FlexibleContexts #-}

76{-# LANGUAGE FlexibleInstances #-}

87{-# LANGUAGE GADTs #-}

8+{-# LANGUAGE KindSignatures #-}

99{-# LANGUAGE MultiParamTypeClasses #-}

1010{-# LANGUAGE NoStarIsType #-}

1111{-# LANGUAGE RankNTypes #-}

@@ -58,10 +58,10 @@ module LAoP.Matrix.Type

5858

5959 -- * Constraint type aliases

6060 Countable,

61− CountableDims,

61+ CountableDimensions,

6262 CountableN,

63− CountableDimsN,

64− FLN,

63+ CountableDimensionsN,

64+ FromListsN,

6565 Liftable,

6666 Trivial,

6767 TrivialP,

@@ -71,9 +71,10 @@ module LAoP.Matrix.Type

7171 One,

7272

7373 -- * Primitives

74+ empty,

7475 one,

75− join,

76− fork,

76+ junc,

77+ split,

7778

7879 -- * Auxiliary type families

7980 I.FromNat,

@@ -85,7 +86,6 @@ module LAoP.Matrix.Type

8586 fromLists,

8687 toLists,

8788 toList,

88− matrixBuilder',

8989 matrixBuilder,

9090 row,

9191 col,

@@ -104,8 +104,8 @@ module LAoP.Matrix.Type

104104 multM,

105105

106106 -- * Selective equivalent instance function

107− selectM,

108−

107+ selectM,

108+

109109 -- * Monad equivalent instance function

110110 returnM,

111111 bindM,

@@ -113,34 +113,25 @@ module LAoP.Matrix.Type

113113 -- * Misc

114114 -- ** Get dimensions

115115 columns,

116− columns',

117116 rows,

118− rows',

119117

120118 -- ** Matrix Transposition

121119 tr,

122120

123− -- ** Scalar multiplication/division of matrices

124− (.|),

125− (./),

126−

127121 -- ** McCarthy's Conditional

128122 cond,

129123

130124 -- ** Matrix "abiding"

131− abideJF,

132− abideFJ,

133−

134− -- ** Zip Matrices

135− zipWithM,

125+ abideJS,

126+ abideSJ,

136127

137128 -- * Biproduct approach

138− -- ** Fork

129+ -- ** Split

139130 (===),

140131 -- *** Projections

141132 p1,

142133 p2,

143− -- ** Join

134+ -- ** Junc

144135 (|||),

145136 -- *** Injections

146137 i1,

@@ -154,11 +145,11 @@ module LAoP.Matrix.Type

154145 -- | Note that given the restrictions imposed it is not possible to

155146 -- implement the standard type classes present in standard Haskell.

156147 -- *** Matrix pairing projections

157− fstM,

158− sndM,

148+ kp1,

149+ kp2,

159150

160151 -- *** Matrix pairing

161− kr,

152+ khatri,

162153

163154 -- * Matrix composition and lifting

164155

@@ -166,10 +157,10 @@ module LAoP.Matrix.Type

166157

167158 -- | Note that given the restrictions imposed it is not possible to

168159 -- implement the standard type classes present in standard Haskell.

169− iden,

160+ identity,

170161 comp,

171− fromF',

172162 fromF,

163+ fromF',

173164

174165 -- * Relation

175166 toRel,

@@ -183,44 +174,46 @@ where

183174import Data.Void

184175import Data.Proxy

185176import Data.Kind

186−import GHC.TypeLits

177+import GHC.TypeLits

187178import Control.DeepSeq

188179import LAoP.Utils

180+import qualified Control.Category as C

189181import qualified LAoP.Matrix.Internal as I

190−import Prelude hiding (id, (.))

191182

192183newtype Matrix e (cols :: Type) (rows :: Type) = M (I.Matrix e (I.Normalize cols) (I.Normalize rows))

193184 deriving (Show, Num, Eq, Ord, NFData) via (I.Matrix e (I.Normalize cols) (I.Normalize rows))

194185

195186-- | Constraint type synonyms to keep the type signatures less convoluted

196−type Countable a = KnownNat (I.Count a)

197−type CountableDims a b = (Countable a, Countable b)

198−type CountableN a = KnownNat (I.Count (I.Normalize a))

199−type CountableDimsN a b = (CountableN a, CountableN b)

200−type FLN a b = I.FromLists (I.Normalize a) (I.Normalize b)

201−type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)

202−type Trivial a = I.Normalize (I.Normalize a) ~ I.Normalize (I.Normalize (I.Normalize a))

203−type Trivial2 a = I.Normalize a ~ I.Normalize (I.Normalize a)

204−type Trivial3 a = I.FromNat (I.Count (I.Normalize (I.Normalize a))) ~ I.Normalize (I.Normalize a)

205−type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)

206−

207−-- | It is possible to implement a constrained version of the category type

208−-- class.

209−instance (Num e) => Category (Matrix e) where

210− type Object (Matrix e) a = (FLN a a, CountableN a)

211− id = iden

212− (.) = comp

187+type Countable a = KnownNat (I.Count a)

188+type CountableDimensions a b = (Countable a, Countable b)

189+type CountableN a = KnownNat (I.Count (I.Normalize a))

190+type CountableDimensionsN a b = (CountableN a, CountableN b)

191+type FromListsN e a b = I.FromLists e (I.Normalize a) (I.Normalize b)

192+type Liftable e a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num e, Ord e)

193+type Trivial a = I.Normalize (I.Normalize a) ~ I.Normalize (I.Normalize (I.Normalize a))

194+type Trivial2 a = I.Normalize a ~ I.Normalize (I.Normalize a)

195+type Trivial3 a = I.FromNat (I.Count (I.Normalize (I.Normalize a))) ~ I.Normalize (I.Normalize a)

196+type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)

197+

198+-- | It isn't possible to implement the 'id' function so it's

199+-- implementation is 'undefined'. However 'comp' can be and this partial

200+-- class implementation exists just to make the code more readable.

201+--

202+-- Please use 'identity' instead.

203+instance (Num e) => C.Category (Matrix e) where

204+ id = undefined

205+ (.) = comp

213206

214207-- | Bifunctor equivalent function

215208bimapM ::

216209 ( Liftable e a b,

217210 Liftable e c d,

218− CountableDimsN a c,

219− CountableDimsN b d,

220− FLN d c,

221− FLN b a

211+ CountableDimensionsN a c,

212+ CountableDimensionsN b d,

213+ FromListsN e d c,

214+ FromListsN e b a

222215 ) => (a -> b) -> (c -> d) -> Matrix e a c -> Matrix e b d

223−bimapM f g m = fromF g . m . tr (fromF f)

216+bimapM f g m = fromF' g `comp` m `comp` tr (fromF' f)

224217

225218-- | Zero type alias

226219type Zero = Void

@@ -230,74 +223,78 @@ type One = ()

230223

231224-- Primitives

232225

226+-- | Empty matrix constructor

227+empty :: Matrix e Zero Zero

228+empty = M I.Empty

229+

233230-- | Unit matrix constructor

234231one :: e -> Matrix e One One

235232one = M . I.One

236233

237−-- | Matrix 'Join' constructor

238−join ::

234+-- | Matrix 'Junc' constructor

235+junc ::

239236 Matrix e a rows ->

240237 Matrix e b rows ->

241238 Matrix e (Either a b) rows

242−join (M a) (M b) = M (I.Join a b)

239+junc (M a) (M b) = M (I.Junc a b)

243240

244241infixl 3 |||

245−-- | Matrix 'Join' constructor

242+-- | Matrix 'Junc' constructor

246243(|||) ::

247244 Matrix e a rows ->

248245 Matrix e b rows ->

249246 Matrix e (Either a b) rows

250−(|||) = join

247+(|||) = junc

251248

252−-- | Matrix 'Fork' constructor

253−fork ::

249+-- | Matrix 'Split' constructor

250+split ::

254251 Matrix e cols a ->

255252 Matrix e cols b ->

256253 Matrix e cols (Either a b)

257−fork (M a) (M b) = M (I.Fork a b)

254+split (M a) (M b) = M (I.Split a b)

258255

259256infixl 2 ===

260−-- | Matrix 'Fork' constructor

257+-- | Matrix 'Split' constructor

261258(===) ::

262259 Matrix e cols a ->

263260 Matrix e cols b ->

264261 Matrix e cols (Either a b)

265−(===) = fork

262+(===) = split

266263

267264-- Functor hierarchy

268265

269266-- | Functor instance equivalent function

270−fmapM ::

267+fmapM ::

271268 ( Liftable e a b,

272− CountableDimsN a b,

273− FLN b a

269+ CountableDimensionsN a b,

270+ FromListsN e b a

274271 )

275272 =>

276273 (a -> b) -> Matrix e c a -> Matrix e c b

277−fmapM f m = fromF f . m

274+fmapM f m = fromF' f `comp` m

278275

279276-- | Applicative instance equivalent 'unit' function,

280277unitM :: (Num e) => Matrix e () ()

281278unitM = one 1

282279

283280-- | Applicative instance equivalent 'unit' function,

284−multM ::

285− ( CountableDimsN a b,

281+multM ::

282+ ( CountableDimensionsN a b,

286283 CountableN (a, b),

287284 Num e,

288− FLN (a, b) a,

289− FLN (a, b) b,

285+ FromListsN e (a, b) a,

286+ FromListsN e (a, b) b,

290287 TrivialP a b

291288 ) => Matrix e c a -> Matrix e c b -> Matrix e c (a, b)

292−multM = kr

289+multM = khatri

293290

294291-- | Monad instance equivalent 'return' function,

295−returnM ::

296− forall e a .

292+returnM ::

293+ forall e a .

297294 ( Num e,

298295 Enum e,

299296 Enum a,

300− FLN () a,

297+ FromListsN e () a,

301298 Countable a

302299 ) => a -> Matrix e One a

303300returnM a = col l

@@ -314,64 +311,51 @@ bindM = flip comp

314311

315312-- | Build a matrix out of a list of list of elements. Throws a runtime

316313-- error if the dimensions do not match.

317−fromLists :: (FLN cols rows) => [[e]] -> Matrix e cols rows

314+fromLists :: (FromListsN e cols rows) => [[e]] -> Matrix e cols rows

318315fromLists = M . I.fromLists

319316

320317-- | Matrix builder function. Constructs a matrix provided with

321−-- a construction function that operates with indices.

322−matrixBuilder' ::

323− (FLN cols rows, CountableDimsN cols rows )

324− => ((Int, Int) -> e) -> Matrix e cols rows

325−matrixBuilder' = M . I.matrixBuilder'

326−

327−-- | Matrix builder function. Constructs a matrix provided with

328−-- a construction function that operates with arbitrary types.

318+-- a construction function.

329319matrixBuilder ::

330− ( FLN a b,

331− Enum a,

332− Enum b,

333− Bounded a,

334− Bounded b,

335− Eq a,

336− Countable b

337− ) => ((a, b) -> e) -> Matrix e a b

338−matrixBuilder f = M (I.matrixBuilder f)

320+ (FromListsN e cols rows, CountableDimensionsN cols rows )

321+ => ((Int, Int) -> e) -> Matrix e cols rows

322+matrixBuilder = M . I.matrixBuilder

339323

340324-- | Constructs a column vector matrix

341−col :: (FLN () rows) => [e] -> Matrix e One rows

325+col :: (FromListsN e () rows) => [e] -> Matrix e One rows

342326col = M . I.col

343327

344328-- | Constructs a row vector matrix

345−row :: (FLN cols ()) => [e] -> Matrix e cols One

329+row :: (FromListsN e cols ()) => [e] -> Matrix e cols One

346330row = M . I.row

347331

348332-- | Lifts functions to matrices with arbitrary dimensions.

349333--

350334-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of

351335-- types @a@ or @b@ allows.

352−fromF' ::

336+fromF ::

353337 ( Liftable e a b,

354− CountableDimsN cols rows,

355− FLN rows cols

338+ CountableDimensionsN cols rows,

339+ FromListsN e rows cols

356340 ) =>

357341 (a -> b) -> Matrix e cols rows

358−fromF' = M . I.fromF'

342+fromF = M . I.fromF

359343

360344-- | Lifts functions to matrices with dimensions matching @a@ and @b@

361345-- cardinality's.

362−fromF ::

346+fromF' ::

363347 ( Liftable e a b,

364− CountableDimsN a b,

365− FLN b a

348+ CountableDimensionsN a b,

349+ FromListsN e b a

366350 ) =>

367351 (a -> b) -> Matrix e a b

368−fromF = M . I.fromF

352+fromF' = M . I.fromF'

369353

370354-- | Lifts relation functions to Boolean Matrix

371355toRel ::

372356 ( Liftable (Natural 0 1) a b,

373− CountableDims a b,

374− FLN b a

357+ CountableDimensionsN a b,

358+ FromListsN (Natural 0 1) b a

375359 ) => (a -> b -> Bool) -> Matrix (Natural 0 1) a b

376360toRel = M . I.toRel

377361

@@ -389,7 +373,7 @@ toList (M m) = I.toList m

389373

390374-- | The zero matrix. A matrix wholly filled with zeros.

391375zeros ::

392− (Num e, FLN cols rows, CountableDimsN cols rows)

376+ (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)

393377 => Matrix e cols rows

394378zeros = M I.zeros

395379

@@ -399,7 +383,7 @@ zeros = M I.zeros

399383--

400384-- Also known as T (Top) matrix.

401385ones ::

402− (Num e, FLN cols rows, CountableDimsN cols rows)

386+ (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)

403387 => Matrix e cols rows

404388ones = M I.ones

405389

@@ -408,7 +392,7 @@ ones = M I.ones

408392-- | The constant matrix constructor. A matrix wholly filled with a given

409393-- value.

410394constant ::

411− (Num e, FLN cols rows, CountableDimsN cols rows)

395+ (Num e, FromListsN e cols rows, CountableDimensionsN cols rows)

412396 => e -> Matrix e cols rows

413397constant = M . I.constant

414398

@@ -417,30 +401,30 @@ constant = M . I.constant

417401-- | The T (Top) row vector matrix.

418402bang ::

419403 forall e cols.

420− (Num e, Enum e, FLN cols (), CountableN cols) =>

404+ (Num e, Enum e, FromListsN e cols (), CountableN cols) =>

421405 Matrix e cols One

422406bang = M I.bang

423407

424408-- | Point constant relation

425−point ::

409+point ::

426410 ( Bounded a,

427411 Enum a,

428412 Eq a,

429413 Num e,

430414 Ord e,

431415 CountableN a,

432− FLN a One

416+ FromListsN e a One

433417 ) => a -> Matrix e One a

434−point = fromF . const

418+point = fromF' . const

435419

436−-- iden Matrix

420+-- Identity Matrix

437421

438−-- | iden matrix

439−iden ::

440− (Num e, FLN a a, CountableN a) =>

422+-- | Identity matrix

423+identity ::

424+ (Num e, FromListsN e a a, CountableN a) =>

441425 Matrix e a a

442−iden = M I.iden

443−{-# NOINLINE iden #-}

426+identity = M I.identity

427+{-# NOINLINE identity #-}

444428

445429-- Matrix composition (MMM)

446430

@@ -451,31 +435,17 @@ iden = M I.iden

451435comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

452436comp (M a) (M b) = M (I.comp a b)

453437{-# NOINLINE comp #-}

454−{-# RULES

455− "comp/iden1" forall m. comp m iden = m ;

456− "comp/iden2" forall m. comp iden m = m

438+{-# RULES

439+ "comp/identity1" forall m. comp m identity = m ;

440+ "comp/identity2" forall m. comp identity m = m

457441#-}

458442

459−-- Scalar multiplication of matrices

460−

461−infixl 7 .|

462−-- | Scalar multiplication of matrices.

463−(.|) :: Num e => e -> Matrix e cols rows -> Matrix e cols rows

464−(.|) e (M m) = M (e I..| m)

465−

466−-- Scalar division of matrices

467−

468−infixl 7 ./

469−-- | Scalar multiplication of matrices.

470−(./) :: Fractional e => Matrix e cols rows -> e -> Matrix e cols rows

471−(./) (M m) e = M (m I../ e)

472−

473443-- | Biproduct first component projection

474444p1 ::

475445 ( Num e,

476− CountableDimsN n m,

477− FLN n m,

478− FLN m m

446+ CountableDimensionsN n m,

447+ FromListsN e n m,

448+ FromListsN e m m

479449 ) =>

480450 Matrix e (Either m n) m

481451p1 = M I.p1

@@ -483,9 +453,9 @@ p1 = M I.p1

483453-- | Biproduct second component projection

484454p2 ::

485455 ( Num e,

486− CountableDimsN n m,

487− FLN m n,

488− FLN n n

456+ CountableDimensionsN n m,

457+ FromListsN e m n,

458+ FromListsN e n n

489459 ) =>

490460 Matrix e (Either m n) n

491461p2 = M I.p2

@@ -495,9 +465,9 @@ p2 = M I.p2

495465-- | Biproduct first component injection

496466i1 ::

497467 ( Num e,

498− CountableDimsN n m,

499− FLN n m,

500− FLN m m

468+ CountableDimensionsN n m,

469+ FromListsN e n m,

470+ FromListsN e m m

501471 ) =>

502472 Matrix e m (Either m n)

503473i1 = tr p1

@@ -505,9 +475,9 @@ i1 = tr p1

505475-- | Biproduct second component injection

506476i2 ::

507477 ( Num e,

508− CountableDimsN n m,

509− FLN m n,

510− FLN n n

478+ CountableDimensionsN n m,

479+ FromListsN e m n,

480+ FromListsN e n n

511481 ) =>

512482 Matrix e n (Either m n)

513483i2 = tr p2

@@ -516,34 +486,24 @@ i2 = tr p2

516486

517487-- | Obtain the number of rows.

518488--

519−-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

520−-- dimensions in constant time. For a version that doesn't require the

521−-- constraint see 'rows''.

489+-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

490+-- dimensions in constant time.

491+--

492+-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in

493+-- exchange for performance.

522494rows :: (CountableN rows) => Matrix e cols rows -> Int

523495rows (M m) = I.rows m

524496

525−-- | Obtain the number of rows in an inefficient manner, but without any

526−-- constraints.

527−--

528−-- For a more efficient version see 'rows'.

529−rows' :: Matrix e cols rows -> Int

530−rows' (M m) = I.rows' m

531−

532497-- | Obtain the number of columns.

498+--

499+-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

500+-- dimensions in constant time.

533501--

534−-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

535−-- dimensions in constant time. For a version that doesn't require the

536−-- constraint see 'columns''.

502+-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in

503+-- exchange for performance.

537504columns :: (CountableN cols) => Matrix e cols rows -> Int

538505columns (M m) = I.columns m

539506

540−-- | Obtain the number of columns in an inefficient manner, but without any

541−-- constraints.

542−--

543−-- For a more efficient version see 'columns'.

544−columns' :: Matrix e cols rows -> Int

545−columns' (M m) = I.columns' m

546−

547507-- Coproduct Bifunctor

548508

549509infixl 5 -|-

@@ -551,11 +511,11 @@ infixl 5 -|-

551511-- | Matrix coproduct functor also known as matrix direct sum.

552512(-|-) ::

553513 ( Num e,

554− CountableDimsN j k,

555− FLN k k,

556− FLN j k,

557− FLN k j,

558− FLN j j

514+ CountableDimensionsN j k,

515+ FromListsN e k k,

516+ FromListsN e j k,

517+ FromListsN e k j,

518+ FromListsN e j j

559519 ) =>

560520 Matrix e n k ->

561521 Matrix e m j ->

@@ -565,98 +525,98 @@ infixl 5 -|-

565525-- Khatri Rao Product and projections

566526

567527-- | Khatri Rao product first component projection matrix.

568−fstM ::

528+kp1 ::

569529 forall e m k .

570530 ( Num e,

571− CountableDimsN m k,

531+ CountableDimensionsN m k,

572532 CountableN (m, k),

573− FLN (m, k) m,

533+ FromListsN e (m, k) m,

574534 TrivialP m k

575535 ) => Matrix e (m, k) m

576−fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))

536+kp1 = M (I.kp1 @e @(I.Normalize m) @(I.Normalize k))

577537

578538-- | Khatri Rao product second component projection matrix.

579−sndM ::

539+kp2 ::

580540 forall e m k.

581541 ( Num e,

582− CountableDimsN k m,

542+ CountableDimensionsN k m,

583543 CountableN (m, k),

584− FLN (m, k) k,

544+ FromListsN e (m, k) k,

585545 TrivialP m k

586546 ) => Matrix e (m, k) k

587−sndM = M (I.sndM @e @(I.Normalize m) @(I.Normalize k))

547+kp2 = M (I.kp2 @e @(I.Normalize m) @(I.Normalize k))

588548

589549-- | Khatri Rao Matrix product also known as matrix pairing.

590550--

591551-- NOTE: That this is not a true categorical product, see for instance:

592−--

552+--

593553-- @

594−-- | fstM . kr a b == a

595−-- kr a b ==> |

596−-- | sndM . kr a b == b

554+-- | kp1 `comp` khatri a b == a

555+-- khatri a b ==> |

556+-- | kp2 `comp` khatri a b == b

597557-- @

598558--

599559-- __Emphasis__ on the implication symbol.

600−kr ::

560+khatri ::

601561 forall e cols a b.

602562 ( Num e,

603− CountableDimsN a b,

563+ CountableDimensionsN a b,

604564 CountableN (a, b),

605− FLN (a, b) a,

606− FLN (a, b) b,

565+ FromListsN e (a, b) a,

566+ FromListsN e (a, b) b,

607567 TrivialP a b

608568 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a, b)

609−kr a b =

610− let fstM' = fstM @e @a @b

611− sndM' = sndM @e @a @b

612− in comp (tr fstM') a * comp (tr sndM') b

569+khatri a b =

570+ let kp1' = kp1 @e @a @b

571+ kp2' = kp2 @e @a @b

572+ in comp (tr kp1') a * comp (tr kp2') b

613573

614574-- Product Bifunctor (Kronecker)

615575

616576infixl 4 ><

617577

618−-- | Matrix product functor also known as Kronecker product

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

619579(><) ::

620580 forall e m p n q.

621581 ( Num e,

622− CountableDimsN m n,

623− CountableDimsN p q,

624− CountableDimsN (m, n) (p, q),

625− FLN (m, n) m,

626− FLN (m, n) n,

627− FLN (p, q) p,

628− FLN (p, q) q,

582+ CountableDimensionsN m n,

583+ CountableDimensionsN p q,

584+ CountableDimensionsN (m, n) (p, q),

585+ FromListsN e (m, n) m,

586+ FromListsN e (m, n) n,

587+ FromListsN e (p, q) p,

588+ FromListsN e (p, q) q,

629589 TrivialP m n,

630590 TrivialP p q

631591 ) => Matrix e m p -> Matrix e n q -> Matrix e (m, n) (p, q)

632592(><) a b =

633− let fstM' = fstM @e @m @n

634− sndM' = sndM @e @m @n

635− in kr (comp a fstM') (comp b sndM')

593+ let kp1' = kp1 @e @m @n

594+ kp2' = kp2 @e @m @n

595+ in khatri (comp a kp1') (comp b kp2')

636596

637−-- Matrix abide Join Fork

597+-- Matrix abide Junc Split

638598

639−-- | Matrix "abiding" followin the 'Join'-'Fork' abide law.

640−--

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

600+--

641601-- Law:

642602--

643603-- @

644−-- 'Join' ('Fork' a c) ('Fork' b d) == 'Fork' ('Join' a b) ('Join' c d)

604+-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)

645605-- @

646−abideJF :: Matrix e cols rows -> Matrix e cols rows

647−abideJF (M m) = M (I.abideJF m)

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

607+abideJS (M m) = M (I.abideJS m)

648608

649−-- Matrix abide Fork Join

609+-- Matrix abide Split Junc

650610

651−-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.

652−--

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

612+--

653613-- Law:

654614--

655615-- @

656−-- 'Fork' ('Join' a b) ('Join' c d) == 'Join' ('Fork' a c) ('Fork' b d)

616+-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)

657617-- @

658−abideFJ :: Matrix e cols rows -> Matrix e cols rows

659−abideFJ (M m) = M (I.abideFJ m)

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

619+abideSJ (M m) = M (I.abideSJ m)

660620

661621-- Matrix transposition

662622

@@ -668,9 +628,9 @@ tr (M m) = M (I.tr m)

668628

669629-- | Selective functors 'select' operator equivalent inspired by the

670630-- ArrowMonad solution presented in the paper.

671−selectM ::

631+selectM ::

672632 ( Num e,

673− FLN b b,

633+ FromListsN e b b,

674634 CountableN b

675635 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b

676636selectM (M m) (M y) = M (I.select m y)

@@ -683,9 +643,9 @@ cond ::

683643 Trivial2 a,

684644 Trivial3 a,

685645 CountableN a,

686− FLN () a,

687− FLN a (),

688− FLN a a,

646+ FromListsN e () a,

647+ FromListsN e a (),

648+ FromListsN e a a,

689649 Liftable e a Bool

690650 )

691651 =>

@@ -695,13 +655,9 @@ cond p (M a) (M b) = M (I.cond p a b)

695655-- Pretty print

696656

697657-- | Matrix pretty printer

698−pretty :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> String

658+pretty :: (CountableDimensionsN cols rows, Show e) => Matrix e cols rows -> String

699659pretty (M m) = I.pretty m

700660

701661-- | Matrix pretty printer

702−prettyPrint :: (CountableDimsN cols rows, Show e) => Matrix e cols rows -> IO ()

662+prettyPrint :: (CountableDimensionsN cols rows, Show e) => Matrix e cols rows -> IO ()

703663prettyPrint (M m) = I.prettyPrint m

704−

705−-- | Zip two matrices with a given binary function

706−zipWithM :: (e -> f -> g) -> Matrix e a b -> Matrix f a b -> Matrix g a b

707−zipWithM f (M a) (M b) = M (I.zipWithM f a b)

src/LAoP/Relation.hs+9−8

@@ -32,19 +32,20 @@ module LAoP.Relation

3232

3333 -- * Constraint type synonyms

3434 Countable,

35− CountableDims,

35+ CountableDimensions,

3636 CountableN,

37− CountableDimsN,

38− FLN,

37+ CountableDimensionsN,

38+ FromListsN,

3939 Liftable,

4040 Trivial,

4141 TrivialP,

4242

4343 -- * Primitives

44+ empty,

4445 one,

45− join,

46+ junc,

4647 (|||),

47− fork,

48+ split,

4849 (===),

4950

5051 -- * Auxiliary type families

@@ -107,8 +108,8 @@ module LAoP.Relation

107108 splitR,

108109

109110 -- ** Projections

110− fstR,

111− sndR,

111+ p1,

112+ p2,

112113 -- ** Bifunctor

113114 (><),

114115 -- * Relational coproduct

@@ -147,7 +148,7 @@ module LAoP.Relation

147148 cond,

148149

149150 -- * Relational composition and lifting

150− iden,

151+ identity,

151152 comp,

152153 fromF,

153154 fromF',

src/LAoP/Relation/Internal.hs+234−245

@@ -1,4 +1,3 @@

1−{-# LANGUAGE TypeFamilies #-}

21{-# LANGUAGE ConstraintKinds #-}

32{-# LANGUAGE GADTs #-}

43{-# LANGUAGE UndecidableInstances #-}

@@ -43,19 +42,20 @@ module LAoP.Relation.Internal

4342

4443 -- * Constraint type synonyms

4544 Countable,

46− CountableDims,

45+ CountableDimensions,

4746 CountableN,

48− CountableDimsN,

49− FLN,

47+ CountableDimensionsN,

48+ FromListsN,

5049 Liftable,

5150 Trivial,

5251 TrivialP,

5352

5453 -- * Primitives

54+ empty,

5555 one,

56− join,

56+ junc,

5757 (|||),

58− fork,

58+ split,

5959 (===),

6060

6161 -- * Auxiliary type families

@@ -66,15 +66,14 @@ module LAoP.Relation.Internal

6666 -- * Matrix construction and conversion

6767 I.FromLists,

6868 fromLists,

69− fromF',

7069 fromF,

70+ fromF',

7171 toRel,

7272 toLists,

7373 toList,

7474 toBool,

7575 pt,

7676 belongs,

77− relationBuilder',

7877 relationBuilder,

7978 zeros,

8079 ones,

@@ -119,8 +118,8 @@ module LAoP.Relation.Internal

119118 splitR,

120119

121120 -- ** Projections

122− fstR,

123− sndR,

121+ p1,

122+ p2,

124123 -- ** Bifunctor

125124 (><),

126125 -- * Relational coproduct

@@ -159,10 +158,10 @@ module LAoP.Relation.Internal

159158 cond,

160159

161160 -- * Relational composition and lifting

162− iden,

161+ identity,

163162 comp,

164− fromF',

165163 fromF,

164+ fromF',

166165

167166 -- ** Relational application

168167 pointAp,

@@ -178,9 +177,9 @@ import Data.Void

178177import qualified LAoP.Matrix.Internal as I

179178import LAoP.Utils.Internal

180179import Control.DeepSeq

180+import qualified Control.Category as C

181181import Data.Bool

182182import GHC.TypeLits

183−import Prelude hiding (id, (.))

184183

185184-- | Boolean type synonym for working with boolean matrices

186185type Boolean = Natural 0 1

@@ -193,30 +192,32 @@ newtype Relation a b = R (I.Matrix Boolean (I.Normalize a) (I.Normalize b))

193192deriving instance (Read (I.Matrix Boolean (I.Normalize a) (I.Normalize b))) => Read (Relation a b)

194193

195194-- | Constraint type synonyms to keep the type signatures less convoluted

196−type Countable a = KnownNat (I.Count a)

197−type CountableDims a b = (Countable a, Countable b)

198−type CountableN a = KnownNat (I.Count (I.Normalize a))

199−type CountableDimsN a b = (CountableN a, CountableN b)

200−type FLN a b = I.FromLists (I.Normalize a) (I.Normalize b)

201−type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Boolean, Ord Boolean)

202−type Trivial a = I.Normalize a ~ I.Normalize (I.Normalize a)

203−type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)

204−

205−-- | It is possible to implement a constrained version of the category type

206−-- class.

207−instance Category Relation where

208− type Object Relation a = (FLN a a, CountableN a)

209− id = iden

210− (.) = comp

195+type Countable a = KnownNat (I.Count a)

196+type CountableDimensions a b = (Countable a, Countable b)

197+type CountableN a = KnownNat (I.Count (I.Normalize a))

198+type CountableDimensionsN a b = (CountableN a, CountableN b)

199+type FromListsN a b = I.FromLists Boolean (I.Normalize a) (I.Normalize b)

200+type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Boolean, Ord Boolean)

201+type Trivial a = I.Normalize a ~ I.Normalize (I.Normalize a)

202+type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a, I.Normalize b)

203+

204+-- | It isn't possible to implement the 'id' function so it's

205+-- implementation is 'undefined'. However 'comp' can be and this partial

206+-- class implementation exists just to make the code more readable.

207+--

208+-- Please use 'identity' instead.

209+instance C.Category Relation where

210+ id = undefined

211+ (.) = comp

211212

212213instance Num (Relation a b) where

213− -- | Matrix addition becomes Boolean matrix disjointion

214+ -- | Matrix addition becomes Boolean matrix disjunction

214215 (R a) + (R b) = R (I.orM a b)

215216

216217 -- | Matrix subtraction becomes Relational subtraction

217218 (R a) - (R b) = R (I.subM a b)

218219

219− -- | Matrix multiplication becomes Boolean matrix conjointion

220+ -- | Matrix multiplication becomes Boolean matrix conjunction

220221 (R a) * (R b) = R (I.andM a b)

221222

222223 -- | Matrix negation becomes Boolean matrix negation

@@ -228,92 +229,83 @@ type One = ()

228229

229230-- Primitives

230231

232+-- | Empty matrix constructor

233+empty :: Relation Zero Zero

234+empty = R I.Empty

235+

231236-- | Unit matrix constructor

232237one :: Boolean -> Relation One One

233238one = R . I.One

234239

235−-- | Boolean Matrix 'Join' constructor, also known as relational coproduct.

240+-- | Boolean Matrix 'Junc' constructor, also known as relational coproduct.

236241--

237242-- See 'eitherR'.

238−join :: Relation a c -> Relation b c -> Relation (Either a b) c

239−join (R a) (R b) = R (I.Join a b)

243+junc :: Relation a c -> Relation b c -> Relation (Either a b) c

244+junc (R a) (R b) = R (I.Junc a b)

240245

241246infixl 3 |||

242−-- | Boolean Matrix 'Join' constructor

247+-- | Boolean Matrix 'Junc' constructor

243248--

244249-- See 'eitherR'.

245250(|||) ::

246251 Relation a c ->

247252 Relation b c ->

248253 Relation (Either a b) c

249−(|||) = join

254+(|||) = junc

250255

251−-- | Boolean Matrix 'Fork' constructor, also known as relational product.

252−fork :: Relation c a -> Relation c b -> Relation c (Either a b)

253−fork (R a) (R b) = R (I.Fork a b)

256+-- | Boolean Matrix 'Split' constructor, also known as relational product.

257+split :: Relation c a -> Relation c b -> Relation c (Either a b)

258+split (R a) (R b) = R (I.Split a b)

254259

255260infixl 2 ===

256−-- | Boolean Matrix 'Fork' constructor

261+-- | Boolean Matrix 'Split' constructor

257262(===) ::

258263 Relation c a ->

259264 Relation c b ->

260265 Relation c (Either a b)

261−(===) = fork

266+(===) = split

262267

263268-- Construction

264269

265270-- | Build a matrix out of a list of list of elements. Throws a runtime

266271-- error if the dimensions do not match.

267−fromLists :: (FLN a b) => [[Boolean]] -> Relation a b

272+fromLists :: (FromListsN a b) => [[Boolean]] -> Relation a b

268273fromLists = R . I.fromLists

269274

270−-- | Relation builder function. Constructs a relation provided with

271−-- a construction function that operates with indices.

272−relationBuilder' ::

273− (FLN a b, CountableDimsN a b) =>

274− ((Int, Int) -> Boolean) -> Relation a b

275−relationBuilder' = R . I.matrixBuilder'

276−

277−-- | Relation builder function. Constructs a relation provided with

278−-- a construction function that operates with arbitrary types.

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

276+-- a construction function.

279277relationBuilder ::

280− ( FLN a b,

281− Enum a,

282− Enum b,

283− Bounded a,

284− Bounded b,

285− Eq a,

286− CountableDims a b

287− ) => ((a, b) -> Boolean) -> Relation a b

278+ (FromListsN a b, CountableDimensionsN a b) =>

279+ ((Int, Int) -> Boolean) -> Relation a b

288280relationBuilder = R . I.matrixBuilder

289281

290282-- | Lifts functions to matrices with arbitrary dimensions.

291283--

292284-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of

293285-- types @a@ or @b@ allows.

294−fromF' ::

286+fromF ::

295287 ( Liftable a b,

296− CountableDimsN c d,

297− FLN d c

288+ CountableDimensionsN c d,

289+ FromListsN d c

298290 )

299291 => (a -> b) -> Relation c d

300−fromF' f = R (I.fromFRel' f)

292+fromF f = R (I.fromFRel f)

301293

302294-- | Lifts functions to matrices with dimensions matching @a@ and @b@

303295-- cardinality's.

304−fromF ::

296+fromF' ::

305297 ( Liftable a b,

306− CountableDimsN a b,

307− FLN b a

298+ CountableDimensionsN a b,

299+ FromListsN b a

308300 )

309301 => (a -> b) -> Relation a b

310−fromF f = R (I.fromFRel f)

302+fromF' f = R (I.fromFRel' f)

311303

312304-- | Lifts relation functions to 'Relation'

313305toRel ::

314306 ( Liftable a b,

315− CountableDims a b,

316− FLN b a

307+ CountableDimensionsN a b,

308+ FromListsN b a

317309 )

318310 => (a -> b -> Bool) -> Relation a b

319311toRel = R . I.toRel

@@ -322,9 +314,9 @@ toRel = R . I.toRel

322314fromRel ::

323315 ( Liftable a b,

324316 Eq a,

325− CountableDimsN a b,

326− FLN a One,

327− FLN b One

317+ CountableDimensionsN a b,

318+ FromListsN a One,

319+ FromListsN b One

328320 )

329321 => Relation a b -> (a -> b -> Bool)

330322fromRel r a b = pointApBool a b r

@@ -348,12 +340,12 @@ toBool r = case toList r of

348340-- | Power transpose.

349341--

350342-- Maps a relation to a set valued function.

351−pt ::

343+pt ::

352344 ( Liftable a b,

353345 Eq a,

354− CountableDimsN a b,

355− FLN a One,

356− FLN b One

346+ CountableDimensionsN a b,

347+ FromListsN a One,

348+ FromListsN b One

357349 )

358350 => Relation a b -> (a -> List b)

359351pt r a =

@@ -365,8 +357,8 @@ belongs ::

365357 ( Bounded a,

366358 Enum a,

367359 Eq a,

368− CountableDims (List a) a,

369− FLN a (List a)

360+ CountableDimensionsN (List a) a,

361+ FromListsN a (List a)

370362 )

371363 => Relation (List a) a

372364belongs = toRel elemR

@@ -378,16 +370,16 @@ belongs = toRel elemR

378370-- | The zero relation. A relation where no element of type @a@ relates

379371-- with elements of type @b@.

380372--

381−-- Also known as ⊥ (Bottom) Relation.

373+-- Also known as ⊥ (Bottom) Relation or empty Relation.

382374--

383375-- @

384−-- r `.` ⊥ == ⊥ `.` r == ⊥

376+-- r ``comp`` ⊥ == ⊥ ``comp`` r == ⊥

385377-- ⊥ ``sse`` R && R ``sse`` T == True

386378-- @

387379zeros ::

388− (FLN a b, CountableDimsN a b) =>

380+ (FromListsN a b, CountableDimensionsN a b) =>

389381 Relation a b

390−zeros = relationBuilder' (const (nat 0))

382+zeros = relationBuilder (const (nat 0))

391383

392384-- Ones Matrix

393385

@@ -400,43 +392,43 @@ zeros = relationBuilder' (const (nat 0))

400392-- ⊥ ``sse`` R && R ``sse`` T == True

401393-- @

402394ones ::

403− (FLN a b, CountableDimsN a b) =>

395+ (FromListsN a b, CountableDimensionsN a b) =>

404396 Relation a b

405−ones = relationBuilder' (const (nat 1))

397+ones = relationBuilder (const (nat 1))

406398

407399-- Bang Matrix

408400

409401-- | The T (Top) row vector relation.

410402bang ::

411− (FLN a One, CountableN a) =>

403+ (FromListsN a One, CountableN a) =>

412404 Relation a One

413405bang = ones

414406

415407-- | Point constant relation

416−point ::

408+point ::

417409 ( Bounded a,

418410 Enum a,

419411 Eq a,

420412 CountableN a,

421− FLN a One

413+ FromListsN a One

422414 ) => a -> Relation One a

423−point = fromF . const

415+point = fromF' . const

424416

425−-- iden Matrix

417+-- Identity Matrix

426418

427−-- | iden matrix

419+-- | Identity matrix

428420--

429421-- @

430−-- 'iden' `.` r == r == r `.` 'iden'

422+-- 'identity' ``comp`` r == r == r ``comp`` 'identity'

431423-- @

432−iden ::

433− (FLN a a, CountableN a) => Relation a a

434−iden = relationBuilder' (bool (nat 0) (nat 1) . uncurry (==))

424+identity ::

425+ (FromListsN a a, CountableN a) => Relation a a

426+identity = relationBuilder (bool (nat 0) (nat 1) . uncurry (==))

435427

436428-- | Relational composition

437429--

438430-- @

439−-- r `.` (s `.` p) = (r `.` s) `.` p

431+-- r ``comp`` (s ``comp`` p) = (r ``comp`` s) ``comp`` p

440432-- @

441433comp :: Relation b c -> Relation a b -> Relation a c

442434comp (R a) (R b) = R (I.compRel a b)

@@ -484,7 +476,7 @@ shrunkBy r s = r `intersection` divR s (conv r)

484476-- r ``overriddenBy`` r == r

485477-- @

486478overriddenBy ::

487− ( FLN b b,

479+ ( FromListsN b b,

488480 CountableN b

489481 ) => Relation a b -> Relation a b -> Relation a b

490482overriddenBy r s = s `union` r `intersection` divR zeros (conv s)

@@ -496,11 +488,11 @@ overriddenBy r s = s `union` r `intersection` divR zeros (conv s)

496488pointAp ::

497489 ( Liftable a b,

498490 Eq a,

499− CountableDimsN a b,

500− FLN a One,

501− FLN b One

491+ CountableDimensionsN a b,

492+ FromListsN a One,

493+ FromListsN b One

502494 ) => a -> b -> Relation a b -> Relation One One

503−pointAp a b r = conv (point b) . r . point a

495+pointAp a b r = conv (point b) `comp` r `comp` point a

504496

505497-- | Relational application

506498--

@@ -508,11 +500,11 @@ pointAp a b r = conv (point b) . r . point a

508500pointApBool ::

509501 ( Liftable a b,

510502 Eq a,

511− CountableDimsN a b,

512− FLN a One,

513− FLN b One

503+ CountableDimensionsN a b,

504+ FromListsN a One,

505+ FromListsN b One

514506 ) => a -> b -> Relation a b -> Bool

515−pointApBool a b r = toBool $ conv (point b) . r . point a

507+pointApBool a b r = toBool $ conv (point b) `comp` r `comp` point a

516508

517509-- | Relational converse

518510--

@@ -538,7 +530,7 @@ iff r s = r == s

538530

539531-- | Relational intersection

540532--

541−-- Lifts pointwise conjointion.

533+-- Lifts pointwise conjunction.

542534--

543535-- @

544536-- (r ``intersection`` s) ``intersection`` t == r ``intersection`` (s ``intersection`` t)

@@ -549,13 +541,13 @@ intersection a b = a * b

549541

550542-- | Relational union

551543--

552−-- Lifts pointwise disjointion.

544+-- Lifts pointwise disjunction.

553545--

554546-- @

555547-- (r ``union`` s) ``union`` t == r `'union' (s ``union`` t)

556548-- r ``union`` s ``sse`` x == r ``sse`` x && s ``sse`` x

557−-- r `.` (s ``union`` t) == (r `.` s) ``union`` (r `.` t)

558−-- (s ``union`` t) `.` r == (s `.` r) ``union`` (t `.` r)

549+-- r ``comp`` (s ``union`` t) == (r ``comp`` s) ``union`` (r ``comp`` t)

550+-- (s ``union`` t) ``comp`` r == (s ``comp`` r) ``union`` (t ``comp`` r)

559551-- @

560552union :: Relation a b -> Relation a b -> Relation a b

561553union a b = a + b

@@ -563,46 +555,46 @@ union a b = a + b

563555-- | Relation Kernel

564556--

565557-- @

566−-- 'ker' r == 'conv' r `.` r

558+-- 'ker' r == 'conv' r ``comp`` r

567559-- 'ker' r == 'img' ('conv' r)

568560-- @

569561ker :: Relation a b -> Relation a a

570−ker r = conv r . r

562+ker r = conv r `comp` r

571563

572564-- | Relation Image

573565--

574566-- @

575−-- 'img' r == r `.` conv r

567+-- 'img' r == r ``comp`` conv r

576568-- 'img' r == 'ker' ('conv' r)

577569-- @

578570img :: Relation a b -> Relation b b

579−img r = r . conv r

571+img r = r `comp` conv r

580572

581573-- | Function division. Special case of 'divS'.

582574--

583575-- NOTE: _This is only valid_ if @f@ and @g@ are 'function's, i.e. 'simple' and

584576-- 'entire'.

585577--

586−-- @'divisionF' f g == 'conv' g `.` f@

578+-- @'divisionF' f g == 'conv' g ``comp`` f@

587579divisionF :: Relation a c -> Relation b c -> Relation a b

588−divisionF f g = conv g . f

580+divisionF f g = conv g `comp` f

589581

590582-- Taxonomy of binary relations

591583

592584-- | A 'Relation' @r@ is 'simple' 'iff' @'coreflexive' ('img' r)@

593−simple :: (CountableN b, FLN b b) => Relation a b -> Bool

585+simple :: (CountableN b, FromListsN b b) => Relation a b -> Bool

594586simple = coreflexive . img

595587

596588-- | A 'Relation' @r@ is 'injective' 'iff' @'coreflexive' ('ker' r)@

597−injective :: (CountableN a, FLN a a) => Relation a b -> Bool

589+injective :: (CountableN a, FromListsN a a) => Relation a b -> Bool

598590injective = coreflexive . ker

599591

600592-- | A 'Relation' @r@ is 'entire' 'iff' @'reflexive' ('ker' r)@

601−entire :: (CountableN a, FLN a a) => Relation a b -> Bool

593+entire :: (CountableN a, FromListsN a a) => Relation a b -> Bool

602594entire = reflexive . ker

603595

604596-- | A 'Relation' @r@ is 'surjective' 'iff' @'reflexive' ('img' r)@

605−surjective :: (CountableN b, FLN b b) => Relation a b -> Bool

597+surjective :: (CountableN b, FromListsN b b) => Relation a b -> Bool

606598surjective = reflexive . img

607599

608600-- | A 'Relation' @r@ is a 'function' 'iff' @'simple' r && 'entire' r@

@@ -611,13 +603,13 @@ surjective = reflexive . img

611603-- relations:

612604--

613605-- @

614−-- f `.` r ``sse`` s == r ``sse`` f `.` s

615−-- r `.` f ``sse`` s == r ``sse`` s `.` f

606+-- f ``comp`` r ``sse`` s == r ``sse`` f ``comp`` s

607+-- r ``comp`` f ``sse`` s == r ``sse`` s ``comp`` f

616608-- @

617609function ::

618− ( CountableDimsN a b,

619− FLN a a,

620− FLN b b

610+ ( CountableDimensionsN a b,

611+ FromListsN a a,

612+ FromListsN b b

621613 )

622614 => Relation a b -> Bool

623615function r = simple r && entire r

@@ -625,7 +617,7 @@ function r = simple r && entire r

625617-- | A 'Relation' @r@ is a 'representation' 'iff' @'injective' r && 'entire' r@

626618representation ::

627619 ( CountableN a,

628− FLN a a

620+ FromListsN a a

629621 )

630622 => Relation a b -> Bool

631623representation r = injective r && entire r

@@ -633,91 +625,91 @@ representation r = injective r && entire r

633625-- | A 'Relation' @r@ is an 'abstraction' 'iff' @'surjective' r && 'simple' r@

634626abstraction ::

635627 ( CountableN b,

636− FLN b b

628+ FromListsN b b

637629 )

638630 => Relation a b -> Bool

639631abstraction r = surjective r && simple r

640632

641633-- | A 'Relation' @r@ is a 'surjection' 'iff' @'function' r && 'abstraction' r@

642634surjection ::

643− ( CountableDimsN a b,

644− FLN a a,

645− FLN b b

635+ ( CountableDimensionsN a b,

636+ FromListsN a a,

637+ FromListsN b b

646638 )

647639 => Relation a b -> Bool

648640surjection r = function r && abstraction r

649641

650642-- | A 'Relation' @r@ is a 'injection' 'iff' @'function' r && 'representation' r@

651643injection ::

652− ( CountableDimsN a b,

653− FLN a a,

654− FLN b b

644+ ( CountableDimensionsN a b,

645+ FromListsN a a,

646+ FromListsN b b

655647 )

656648 => Relation a b -> Bool

657649injection r = function r && representation r

658650

659651-- | A 'Relation' @r@ is an 'bijection' 'iff' @'injection' r && 'surjection' r@

660652bijection ::

661− ( CountableDimsN a b,

662− FLN b b,

663− FLN a a

653+ ( CountableDimensionsN a b,

654+ FromListsN b b,

655+ FromListsN a a

664656 ) => Relation a b -> Bool

665657bijection r = injection r && surjection r

666658

667659-- Properties of relations

668660

669−-- | A 'Relation' @r@ is 'reflexive' 'iff' @'id' ``sse`` r@

670−reflexive :: (CountableN a, FLN a a) => Relation a a -> Bool

671−reflexive r = id <= r

661+-- | A 'Relation' @r@ is 'reflexive' 'iff' @'identity' ``sse`` r@

662+reflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool

663+reflexive r = identity <= r

672664

673−-- | A 'Relation' @r@ is 'coreflexive' 'iff' @r ``sse`` 'id'@

674−coreflexive :: (CountableN a, FLN a a) => Relation a a -> Bool

675−coreflexive r = r <= id

665+-- | A 'Relation' @r@ is 'coreflexive' 'iff' @r ``sse`` 'identity'@

666+coreflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool

667+coreflexive r = r <= identity

676668

677−-- | A 'Relation' @r@ is 'transitive' 'iff' @(r `.` r) ``sse`` r@

669+-- | A 'Relation' @r@ is 'transitive' 'iff' @(r ``comp`` r) ``sse`` r@

678670transitive :: Relation a a -> Bool

679−transitive r = (r . r) `sse` r

671+transitive r = (r `comp` r) `sse` r

680672

681673-- | A 'Relation' @r@ is 'symmetric' 'iff' @r == 'conv' r@

682674symmetric :: Relation a a -> Bool

683675symmetric r = r == conv r

684676

685−-- | A 'Relation' @r@ is anti-symmetric 'iff' @(r ``intersection`` 'conv' r) ``sse`` 'id'@

686−antiSymmetric :: (CountableN a, FLN a a) => Relation a a -> Bool

687−antiSymmetric r = (r `intersection` conv r) `sse` id

677+-- | A 'Relation' @r@ is anti-symmetric 'iff' @(r ``intersection`` 'conv' r) ``sse`` 'identity'@

678+antiSymmetric :: (CountableN a, FromListsN a a) => Relation a a -> Bool

679+antiSymmetric r = (r `intersection` conv r) `sse` identity

688680

689−-- | A 'Relation' @r@ is 'irreflexive' 'iff' @(r ``intersection`` 'id') == 'zeros'@

690−irreflexive :: (CountableN a, FLN a a) => Relation a a -> Bool

691−irreflexive r = (r `intersection` id) == zeros

681+-- | A 'Relation' @r@ is 'irreflexive' 'iff' @(r ``intersection`` 'identity') == 'zeros'@

682+irreflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool

683+irreflexive r = (r `intersection` identity) == zeros

692684

693685-- | A 'Relation' @r@ is 'connected' 'iff' @(r ``union`` 'conv' r) == 'ones'@

694−connected :: (CountableN a, FLN a a) => Relation a a -> Bool

686+connected :: (CountableN a, FromListsN a a) => Relation a a -> Bool

695687connected r = (r `union` conv r) == ones

696688

697689-- | A 'Relation' @r@ is a 'preorder' 'iff' @'reflexive' r && 'transitive' r@

698−preorder :: (CountableN a, FLN a a) => Relation a a -> Bool

690+preorder :: (CountableN a, FromListsN a a) => Relation a a -> Bool

699691preorder r = reflexive r && transitive r

700692

701693-- | A 'Relation' @r@ is a partial-order 'iff' @'antiSymmetric' r && 'preorder' r@

702−partialOrder :: (CountableN a, FLN a a) => Relation a a -> Bool

694+partialOrder :: (CountableN a, FromListsN a a) => Relation a a -> Bool

703695partialOrder r = antiSymmetric r && preorder r

704696

705697-- | A 'Relation' @r@ is a linear-order 'iff' @'connected' r && 'partialOrder' r@

706−linearOrder :: (CountableN a, FLN a a) => Relation a a -> Bool

698+linearOrder :: (CountableN a, FromListsN a a) => Relation a a -> Bool

707699linearOrder r = connected r && partialOrder r

708700

709701-- | A 'Relation' @r@ is an 'equivalence' 'iff' @'symmetric' r && 'preorder' r@

710−equivalence :: (CountableN a, FLN a a) => Relation a a -> Bool

702+equivalence :: (CountableN a, FromListsN a a) => Relation a a -> Bool

711703equivalence r = symmetric r && preorder r

712704

713705-- | A 'Relation' @r@ is a partial-equivalence 'iff' @'partialOrder' r && 'equivalence' r@

714−partialEquivalence :: (CountableN a, FLN a a) => Relation a a -> Bool

706+partialEquivalence :: (CountableN a, FromListsN a a) => Relation a a -> Bool

715707partialEquivalence r = partialOrder r && equivalence r

716708

717709-- | A 'Relation' @r@ is 'difunctional' or regular wherever

718−-- @r `.` 'conv' r `.` r == r@

710+-- @r ``comp`` 'conv' r ``comp`` r == r@

719711difunctional :: Relation a b -> Bool

720−difunctional r = r . conv r . r == r

712+difunctional r = r `comp` conv r `comp` r == r

721713

722714-- Relational pairing

723715

@@ -726,61 +718,61 @@ difunctional r = r . conv r . r == r

726718-- NOTE: That this is not a true categorical product, see for instance:

727719--

728720-- @

729−-- | 'fstR' `.` 'splitR' a b ``sse`` a

721+-- | 'p1' ``comp`` 'splitR' a b ``sse`` a

730722-- 'splitR' a b <=> |

731−-- | 'sndR' `.` 'splitR' a b ``sse`` b

723+-- | 'p2' ``comp`` 'splitR' a b ``sse`` b

732724-- @

733725--

734726-- __Emphasis__ on the 'sse'.

735727--

736728-- @

737−-- 'splitR' r s `.` f == 'splitR' (r `.` f) (s `.` f)

738−-- (R '><' S) `.` 'splitR' p q == 'splitR' (r `.` p) (s `.` q)

739−-- 'conv' ('splitR' r s) `.` 'splitR' x y == ('conv' r `.` x) ``intersection`` ('conv' s `.` y)

729+-- 'splitR' r s ``comp`` f == 'splitR' (r ``comp`` f) (s ``comp`` f)

730+-- (R '><' S) ``comp`` 'splitR' p q == 'splitR' (r ``comp`` p) (s ``comp`` q)

731+-- 'conv' ('splitR' r s) ``comp`` 'splitR' x y == ('conv' r ``comp`` x) ``intersection`` ('conv' s ``comp`` y)

740732-- @

741733--

742734-- @

743735-- 'eitherR' ('splitR' r s) ('splitR' t v) == 'splitR' ('eitherR' r t) ('eitherR' s v)

744736-- @

745737splitR ::

746− ( CountableDimsN a b,

738+ ( CountableDimensionsN a b,

747739 CountableN (a, b),

748− FLN (a, b) a,

749− FLN (a, b) b,

740+ FromListsN (a, b) a,

741+ FromListsN (a, b) b,

750742 TrivialP a b

751743 )

752744 => Relation c a -> Relation c b -> Relation c (a, b)

753−splitR (R f) (R g) = R (I.kr f g)

745+splitR (R f) (R g) = R (I.khatri f g)

754746

755747-- | Relational pairing first component projection

756748--

757749-- @

758−-- 'fstR' `.` 'splitR' r s ``sse`` r

750+-- 'p1' ``comp`` 'splitR' r s ``sse`` r

759751-- @

760−fstR ::

752+p1 ::

761753 forall a b .

762− ( CountableDimsN a b,

754+ ( CountableDimensionsN a b,

763755 CountableN (a, b),

764− FLN (a, b) a,

756+ FromListsN (a, b) a,

765757 TrivialP a b

766758 )

767759 => Relation (a, b) a

768−fstR = R (I.fstM @Boolean @(I.Normalize a) @(I.Normalize b))

760+p1 = R (I.kp1 @Boolean @(I.Normalize a) @(I.Normalize b))

769761

770762-- | Relational pairing second component projection

771763--

772764-- @

773−-- 'sndR' `.` 'splitR' r s ``sse`` s

765+-- 'p2' ``comp`` 'splitR' r s ``sse`` s

774766-- @

775−sndR ::

767+p2 ::

776768 forall a b .

777− ( CountableDimsN a b,

769+ ( CountableDimensionsN a b,

778770 CountableN (a, b),

779− FLN (a, b) b,

771+ FromListsN (a, b) b,

780772 TrivialP a b

781773 )

782774 => Relation (a, b) b

783−sndR = R (I.sndM @Boolean @(I.Normalize a) @(I.Normalize b))

775+p2 = R (I.kp2 @Boolean @(I.Normalize a) @(I.Normalize b))

784776

785777-- Relational pairing functor

786778

@@ -788,17 +780,17 @@ infixl 4 ><

788780-- | Relational pairing functor

789781--

790782-- @

791−-- r '><' s == 'splitR' (r `.` fstR) (s `.` sndR)

792−-- (r '><' s) `.` (p '><' q) == (r `.` p) '><' (s `.` q)

783+-- r '><' s == 'splitR' (r ``comp`` p1) (s ``comp`` p2)

784+-- (r '><' s) ``comp`` (p '><' q) == (r ``comp`` p) '><' (s ``comp`` q)

793785-- @

794786(><) ::

795− ( CountableDimsN a b,

796− CountableDimsN c d,

797− CountableDimsN (a, c) (b, d),

798− FLN (a, c) a,

799− FLN (a, c) c,

800− FLN (b, d) b,

801− FLN (b, d) d,

787+ ( CountableDimensionsN a b,

788+ CountableDimensionsN c d,

789+ CountableDimensionsN (a, c) (b, d),

790+ FromListsN (a, c) a,

791+ FromListsN (a, c) c,

792+ FromListsN (b, d) b,

793+ FromListsN (b, d) d,

802794 TrivialP a c,

803795 TrivialP b d

804796 )

@@ -810,31 +802,31 @@ infixl 4 ><

810802-- | Relational coproduct.

811803--

812804-- @

813−-- | 'eitherR' a b `.` 'i1' == a

805+-- | 'eitherR' a b ``comp`` 'i1' == a

814806-- 'eitherR' a b <=> |

815−-- | 'eitherR' a b `.` 'i2' == b

807+-- | 'eitherR' a b ``comp`` 'i2' == b

816808-- @

817809--

818810-- @

819−-- 'eitherR' r s `.` 'conv' ('eitherR' t u) == (r `.` 'conv' t) ``union`` (s `.` 'conv' u)

811+-- 'eitherR' r s ``comp`` 'conv' ('eitherR' t u) == (r ``comp`` 'conv' t) ``union`` (s ``comp`` 'conv' u)

820812-- @

821813--

822814-- @

823815-- 'eitherR' ('splitR' r s) ('splitR' t v) == 'splitR' ('eitherR' r t) ('eitherR' s v)

824816-- @

825817eitherR :: Relation a c -> Relation b c -> Relation (Either a b) c

826−eitherR = join

818+eitherR = junc

827819

828820-- | Relational coproduct first component injection

829821--

830822-- @

831−-- 'img' 'i1' ``union`` 'img' 'i2' == 'id'

832−-- 'i1' `.` 'i2' = 'zeros'

823+-- 'img' 'i1' ``union`` 'img' 'i2' == 'identity'

824+-- 'i1' ``comp`` 'i2' = 'zeros'

833825-- @

834826i1 ::

835− ( CountableDimsN a b,

836− FLN b a,

837− FLN a a

827+ ( CountableDimensionsN a b,

828+ FromListsN b a,

829+ FromListsN a a

838830 )

839831 => Relation a (Either a b)

840832i1 = R I.i1

@@ -842,13 +834,13 @@ i1 = R I.i1

842834-- | Relational coproduct second component injection

843835--

844836-- @

845−-- 'img' 'i1' ``union`` 'img' 'i2' == 'id'

846−-- 'i1' `.` 'i2' = 'zeros'

837+-- 'img' 'i1' ``union`` 'img' 'i2' == 'identity'

838+-- 'i1' ``comp`` 'i2' = 'zeros'

847839-- @

848840i2 ::

849− ( CountableDimsN a b,

850− FLN a b,

851− FLN b b

841+ ( CountableDimensionsN a b,

842+ FromListsN a b,

843+ FromListsN b b

852844 )

853845 => Relation b (Either a b)

854846i2 = R I.i2

@@ -858,14 +850,14 @@ infixl 5 -|-

858850-- | Relational coproduct functor.

859851--

860852-- @

861−-- r '-|-' s == 'eitherR' ('i1' `.` r) ('i2' `.` s)

853+-- r '-|-' s == 'eitherR' ('i1' ``comp`` r) ('i2' ``comp`` s)

862854-- @

863855(-|-) ::

864− ( CountableDimsN b d,

865− FLN b b,

866− FLN d b,

867− FLN b d,

868− FLN d d

856+ ( CountableDimensionsN b d,

857+ FromListsN b b,

858+ FromListsN d b,

859+ FromListsN b d,

860+ FromListsN d d

869861 )

870862 => Relation a b -> Relation c d -> Relation (Either a c) (Either b d)

871863(-|-) (R a) (R b) = R ((I.-|-) a b)

@@ -878,20 +870,20 @@ infixl 5 -|-

878870-- 'trans'/'untrans';

879871-- more-over, where each particular attribute is placed (input/output) is irrelevant.

880872trans ::

881− ( CountableDimsN a b,

873+ ( CountableDimensionsN a b,

882874 CountableN c,

883− CountableDimsN (a, b) (c, b),

884− FLN (c, b) c,

885− FLN (c, b) b,

886− FLN (a, b) a,

887− FLN (a, b) b,

875+ CountableDimensionsN (a, b) (c, b),

876+ FromListsN (c, b) c,

877+ FromListsN (c, b) b,

878+ FromListsN (a, b) a,

879+ FromListsN (a, b) b,

888880 Trivial (a, b),

889881 Trivial (c, b),

890882 TrivialP a b,

891883 TrivialP c b

892884 )

893885 => Relation (a, b) c -> Relation a (c, b)

894−trans r = splitR r sndR . conv fstR

886+trans r = splitR r p2 `comp` conv p1

895887

896888-- | Relational 'untrans'

897889--

@@ -899,110 +891,107 @@ trans r = splitR r sndR . conv fstR

899891-- 'trans'/'untrans';

900892-- more-over, where each particular attribute is placed (input/output) is irrelevant.

901893untrans ::

902− ( CountableDimsN a b,

894+ ( CountableDimensionsN a b,

903895 CountableN c,

904− CountableDimsN (a, b) (c, b),

905− FLN (c, b) c,

906− FLN (c, b) b,

907− FLN (a, b) b,

908− FLN (a, b) a,

896+ CountableDimensionsN (a, b) (c, b),

897+ FromListsN (c, b) c,

898+ FromListsN (c, b) b,

899+ FromListsN (a, b) b,

900+ FromListsN (a, b) a,

909901 Trivial (a, b),

910902 Trivial (c, b),

911903 TrivialP a b,

912904 TrivialP c b

913905 )

914906 => Relation a (c, b) -> Relation (a, b) c

915−untrans s = fstR . conv (splitR (conv s) sndR)

907+untrans s = p1 `comp` conv (splitR (conv s) p2)

916908

917909-- | Transforms predicate @p@ into a correflexive relation.

918910--

919911-- @

920−-- 'predR' ('const' True) == 'id'

912+-- 'predR' ('const' True) == 'identity'

921913-- 'predR' ('const' False) == 'zeros'

922914-- @

923915--

924916-- @

925−-- 'predR' q `.` 'predR' p == 'predR' q ``union`` 'predR' p

917+-- 'predR' q ``comp`` 'predR' p == 'predR' q ``union`` 'predR' p

926918-- @

927919predR ::

928920 ( Bounded a,

929921 Enum a,

930− Countable a,

931922 CountableN a,

932− FLN a a,

933− FLN Bool a

923+ FromListsN a a,

924+ FromListsN Bool a

934925 )

935926 => Relation a Bool -> Relation a a

936−predR p = id `intersection` divisionF (fromF (const True)) p

927+predR p = identity `intersection` divisionF (fromF' (const True)) p

937928

938929-- | Equalizes functions @f@ and @g@.

939930-- That is, @'equalizer' f g@ is the largest coreflexive

940931-- that restricts @g@ so that @f@ and @g@ yield the same outputs.

941932--

942933-- @

943−-- 'equalizer' r r == 'id'

934+-- 'equalizer' r r == 'identity'

944935-- 'equalizer' ('point' True) ('point' False) == 'zeros'

945936-- @

946937equalizer ::

947938 ( CountableN a,

948− FLN a a

939+ FromListsN a a

949940 )

950941 => Relation a b -> Relation a b -> Relation a a

951−equalizer f g = id `intersection` divisionF f g

942+equalizer f g = identity `intersection` divisionF f g

952943

953944-- | Relational conditional guard.

954945--

955946-- @

956−-- 'guard' p = 'i2' ``overriddenBy`` 'i1' `.` 'predR' p

947+-- 'guard' p = 'i2' ``overriddenBy`` 'i1' ``comp`` 'predR' p

957948-- @

958−guard ::

949+guard ::

959950 ( Bounded b,

960951 Enum b,

961952 CountableN b,

962− Countable b,

963− FLN b b,

964− FLN Bool b

953+ FromListsN b b,

954+ FromListsN Bool b

965955 ) => Relation b Bool -> Relation b (Either b b)

966956guard p = conv (eitherR (predR p) (predR (negate p)))

967957

968958-- | Relational McCarthy's conditional.

969−cond ::

959+cond ::

970960 ( Bounded b,

971961 Enum b,

972− Countable b,

973962 CountableN b,

974− FLN b b,

975− FLN Bool b

976− )

963+ FromListsN b b,

964+ FromListsN Bool b

965+ )

977966 => Relation b Bool -> Relation b c -> Relation b c -> Relation b c

978−cond p r s = eitherR r s . guard p

967+cond p r s = eitherR r s `comp` guard p

979968

980969-- | Relational domain.

981970--

982971-- For injective relations, 'domain' and 'ker'nel coincide,

983−-- since @'ker' r ``sse`` 'id'@ in such situations.

972+-- since @'ker' r ``sse`` 'identity'@ in such situations.

984973domain ::

985974 ( CountableN a,

986− FLN a a

975+ FromListsN a a

987976 ) => Relation a b -> Relation a a

988−domain r = ker r `intersection` id

977+domain r = ker r `intersection` identity

989978

990979-- | Relational range.

991980--

992981-- For functions, 'range' and 'img' (image) coincide,

993−-- since @'img' f ``sse`` id@ for any @f@.

982+-- since @'img' f ``sse`` 'identity'@ for any @f@.

994983range ::

995984 ( CountableN b,

996− FLN b b

985+ FromListsN b b

997986 ) => Relation a b -> Relation b b

998−range r = img r `intersection` id

987+range r = img r `intersection` identity

999988

1000989-- Relation pretty print

1001990

1002991-- | Relation pretty printing

1003−pretty :: (CountableDimsN a b) => Relation a b -> String

992+pretty :: (CountableDimensionsN a b) => Relation a b -> String

1004993pretty (R a) = I.pretty a

1005994

1006995-- | Relation pretty printing

1007−prettyPrint :: (CountableDimsN a b) => Relation a b -> IO ()

996+prettyPrint :: (CountableDimensionsN a b) => Relation a b -> IO ()

1008997prettyPrint (R a) = I.prettyPrint a

src/LAoP/Utils.hs+1−4

@@ -96,10 +96,7 @@ module LAoP.Utils

9696 coerceNat3,

9797

9898 -- * List data type

99− List (..),

100−

101− -- * Category type-class

102− Category(..)

99+ List (..)

103100 )

104101where

105102

src/LAoP/Utils/Internal.hs+2−28

@@ -1,9 +1,9 @@

1−{-# LANGUAGE TypeFamilies #-}

21{-# LANGUAGE DeriveGeneric #-}

32{-# LANGUAGE TypeApplications #-}

43{-# LANGUAGE DataKinds #-}

54{-# LANGUAGE FlexibleInstances #-}

65{-# LANGUAGE GeneralizedNewtypeDeriving #-}

6+{-# LANGUAGE KindSignatures #-}

77{-# LANGUAGE ScopedTypeVariables #-}

99module LAoP.Utils.Internal

@@ -19,10 +19,7 @@ module LAoP.Utils.Internal

1919 coerceNat3,

2020

2121 -- * 'List' data type

22− List (..),

23−

24− -- * Category type class

25− Category(..)

22+ List (..)

2623 )

2724where

2825

@@ -33,9 +30,6 @@ import Data.Maybe

3330import GHC.TypeLits

3431import Control.DeepSeq

3532import GHC.Generics

36−import Data.Kind

37−import Prelude hiding (id, (.))

38−import qualified Prelude

3933

4034-- | Wrapper around 'Int's that have a restrictive semantic associated.

4135-- A value of type @'Natural' n m@ can only be instanciated with some 'Int'

@@ -174,23 +168,3 @@ instance

174168 fromEnum (L x) =

175169 let as = [minBound .. maxBound]

176170 in fromMaybe (error "Does not exist") $ elemIndex x (powerset as)

177−

178−-- | Constrained category instance

179−class Category k where

180− type Object k o :: Constraint

181− type Object k o = ()

182− id :: Object k a => k a a

183− (.) :: k b c -> k a b -> k a c

184−

185−{-# RULES

186−"identity/left" forall p .

187− id . p = p

188−"identity/right" forall p .

189− p . id = p

190−"association" forall p q r .

191− (p . q) . r = p . (q . r)

192− #-}

193−

194−instance Category (->) where

195− id = Prelude.id

196− (.) = (Prelude..)

stack-8.8.3.yamldeleted−1

@@ -1 +0,0 @@

1−resolver: lts-15.5

stack.yaml+66−1

@@ -1 +1,66 @@

1−resolver: lts-14.3

1+# This file was automatically generated by 'stack init'

2+#

3+# Some commonly used options have been documented as comments in this file.

4+# For advanced use and comprehensive documentation of the format, please see:

5+# https://docs.haskellstack.org/en/stable/yaml_configuration/

7+# Resolver to choose a 'specific' stackage snapshot or a compiler version.

8+# A snapshot resolver dictates the compiler version and the set of packages

9+# to be used for project dependencies. For example:

10+#

11+# resolver: lts-3.5

12+# resolver: nightly-2015-09-21

13+# resolver: ghc-7.10.2

14+#

15+# The location of a snapshot can be provided as a file or url. Stack assumes

16+# a snapshot provided as a file might change, whereas a url resource does not.

17+#

18+# resolver: ./custom-snapshot.yaml

19+# resolver: https://example.com/snapshots/2018-01-01.yaml

20+resolver: lts-14.18

21+

22+# User packages to be built.

23+# Various formats can be used as shown in the example below.

24+#

25+# packages:

26+# - some-directory

27+# - https://example.com/foo/bar/baz-0.0.2.tar.gz

28+# subdirs:

29+# - auto-update

30+# - wai

31+packages:

32+- .

33+# Dependency packages to be pulled from upstream that are not in the resolver.

34+# These entries can reference officially published versions as well as

35+# forks / in-progress versions pinned to a git hash. For example:

36+#

37+# extra-deps:

38+# - acme-missiles-0.3

39+# - git: https://github.com/commercialhaskell/stack.git

40+# commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a

41+#

42+# extra-deps: []

43+

44+# Override default flag values for local packages and extra-deps

45+# flags: {}

46+

47+# Extra package databases containing global packages

48+# extra-package-dbs: []

49+

50+# Control whether we use the GHC we find on the path

51+# system-ghc: true

52+#

53+# Require a specific version of stack, using version ranges

54+# require-stack-version: -any # Default

55+# require-stack-version: ">=2.1"

56+#

57+# Override the architecture used by stack, especially useful on Windows

58+# arch: i386

59+# arch: x86_64

60+#

61+# Extra directories used by stack for building

62+# extra-include-dirs: [/path/to/dir]

63+# extra-lib-dirs: [/path/to/dir]

64+#

65+# Allow a newer minor version of GHC than the snapshot specifies

66+# compiler-check: newer-minor

stack.yaml.lock+4−4

@@ -6,7 +6,7 @@

66packages: []

77snapshots:

88- completed:

9− size: 523878

10− url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/14/3.yaml

11− sha256: 470c46c27746a48c7c50f829efc0cf00112787a7804ee4ac7a27754658f6d92c

12− original: lts-14.3

9+ size: 524789

10+ url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/14/18.yaml

11+ sha256: 646be71223e08234131c6989912e6011e01b9767bc447b6d466a35e14360bdf2

12+ original: lts-14.18

test/Examples/Quantum.hsdeleted−31

@@ -1,31 +0,0 @@

1−{-# LANGUAGE StandaloneDeriving #-}

2−module Examples.Quantum where

3−

4−import LAoP.Utils

5−import LAoP.Matrix.Type

6−import Data.Complex

7−import Prelude hiding (id, (.))

8−

9−deriving instance Ord a => Ord (Complex a)

10−

11−xor :: (Bool, Bool) -> Bool

12−xor (False, b) = b

13−xor (True, b) = not b

14−

15−ker :: Num e => Matrix e a b -> Matrix e a a

16−ker m = tr m . m

17−

18−cnot :: Matrix (Complex Double) (Bool, Bool) (Bool, Bool)

19−cnot = kr fstM (fromF xor)

20−

21−ccnot :: (Num e, Ord e) => Matrix e ((Bool, Bool), Bool) ((Bool, Bool), Bool)

22−ccnot = kr fstM (fromF f)

23− where

24− f = xor . tp (uncurry (&&)) id

25− tp f g (a,b) = (f a, g b)

26−

27−had :: Matrix (Complex Double) Bool Bool

28−had = (1/sqrt 2) .| fromLists [[1, 1], [1, -1]]

29−

30−bell :: Matrix (Complex Double) (Bool, Bool) (Bool, Bool)

31−bell = cnot . (had >< iden)

test/Spec.hs+1−7

@@ -1,8 +1,2 @@

1−module Main (main) where

2−

3−import qualified Examples.Readme as RD

4−

51main :: IO ()

6−main = do

7− putStrLn ("Testing if README works" :: String)

8− RD.exec

2+main = putStrLn "Test suite not yet implemented"