c115295...master · laop

.ghc.environment.x86_64-linux-8.6.5deleted−17

since splitsnapshots

unifiedsplit

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

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

.ghc.environment.x86_64-linux-8.8.3deleted−17

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

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-8.8.3/package.db

10−package-db dist-docs.Q1TJPL/packagedb/ghc-8.8.3

11−package-id laop-0.1.0.7-inplace

12−package-id base-4.13.0.0

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-0.5.4.0

.github/workflows/ci.ymlnew file+43

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

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+54−2

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

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

1.stack-work/

25.stack-work/

2−laop.cabal

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]

3−*~

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

.travis.ymlnew file+47

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

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.mdnew file+17

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

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.mddeleted−3

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

1−# Changelog for laop

2−

3−## Unreleased changes

LICENSE+17−26

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

1+MIT License

2

4

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

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

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

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

7

11

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

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

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

13+copies or substantial portions of the Software.

10

14

11− * Redistributions in binary form must reproduce the above

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

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

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

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

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

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

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

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

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

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

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

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

21+SOFTWARE.

README.md+34−30

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

1# laop - Linear Algebra of Programming library

2

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+

3The LAoP discipline generalises relations and functions treating them as

9The LAoP discipline generalises relations and functions treating them as

4Boolean matrices and in turn consider these as arrows.

10Boolean matrices and in turn consider these as arrows.

5

11

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

10This module offers many of the combinators mentioned in the work of

16This module offers many of the combinators mentioned in the work of

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

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

12

18

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

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

14−

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).

16

20

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

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

18

22

19## Features

23## Features

20

24

21−This library offers:

25+This library offers 3 main matrix programming modules:

22−

26+

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

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

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

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

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

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

26− around the internal matrix data type.

30+

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

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

28− around the internal matrix data type.

32+distributions.

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

33+

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

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

31− AoP and Relational Calculus/Algebra.

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

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

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

33− make it easier to deal with sample space.

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

34−

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

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

39+and transformation functions.

36−

40+

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

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.

38−- Statically typed dimensions;

42+

39−- Polymorphic data type dimensions;

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

40−- Polymorphic matrix content;

44+

41−- Awesome dimension type inference;

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

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

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.

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

47+

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

48+## Known issues

45−

49+

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.

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).

47

51

48## Notes

52## Notes

49

53

Setup.hsdeleted−2

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

1−import Distribution.Simple

2−main = defaultMain

app/Main.hsdeleted−7

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

1−module Main where

2−

3−import Examples

4−import Benchmarks

5−

6−main :: IO ()

7−main = benchmark

appveyor.ymlnew file+34

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

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

app/Benchmarks.hs → benchmark/Main.hsrenamed+3−6

@@ -8,10 +8,7 @@

8{-# LANGUAGE AllowAmbiguousTypes #-}

9{-# LANGUAGE ScopedTypeVariables #-}

10

11−module Benchmarks

12− ( benchmark

13− )

14− where

11+module Main (main) where

15

12

16import LAoP.Dist.Internal

13import LAoP.Dist.Internal

17import LAoP.Utils

14import LAoP.Utils

@@ -147,8 +144,8 @@ setupEnv2 = do

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

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

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

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

149

146

150−benchmark :: IO ()

147+main :: IO ()

151−benchmark = defaultMain [

148+main = defaultMain [

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

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

153 bgroup "10x10" [

150 bgroup "10x10" [

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

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

hackage.shdeleted−10

@@ -1,10 +0,0 @@

1−#!/bin/sh

2−set -e

3−

4−dir=$(mktemp -d dist-docs.XXXXXX)

5−trap 'rm -r "$dir"' EXIT

6−

7−# assumes cabal 2.4 or later

8−cabal v2-haddock --builddir="$dir" --haddock-for-hackage --enable-doc

9−

10−cabal upload -d $dir/*-docs.tar.gz --publish

laop.cabal+82−72

@@ -1,79 +1,89 @@

1−cabal-version: 1.12

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

2

20

3−-- This file has been generated from package.yaml by hpack version 0.31.2.

21+source-repository head

4−--

22+ type: git

5−-- see: https://github.com/sol/hpack

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

6−--

7−-- hash: c53e5ac8b0734f570fcea8d217d84e401323172c60a00eee9d60ffbaef505191

8

24

9−name: laop

25+common common-options

10−version: 0.1.0.7

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

11−description: Please see the README on GitHub at <https://github.com/xxxx/laop#readme>

27+ deepseq

12−category: Data

28+

13−homepage: https://github.com/xxxx/laop#readme

29+ ghc-options: -Wall

14−bug-reports: https://github.com/xxxx/laop/issues

30+ -Wcompat

15−author: Armando Santos

31+ -Widentities

16−maintainer: armandoifsantos@gmail.com

32+ -Wincomplete-uni-patterns

17−copyright: MIT

33+ -Wincomplete-record-updates

18−license: BSD3

34+ if impl(ghc >= 8.0)

19−license-file: LICENSE

35+ ghc-options: -Wredundant-constraints

20−build-type: Simple

36+ if impl(ghc >= 8.2)

21−extra-source-files:

37+ ghc-options: -fhide-source-paths

22− README.md

38+ if impl(ghc >= 8.4)

23− ChangeLog.md

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

40+ -Wpartial-fields

41+ if impl(ghc >= 8.8)

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

24

43

25−source-repository head

44+ default-language: Haskell2010

26− type: git

27− location: https://github.com/xxxx/laop

28

45

29library

46library

47+ import: common-options

48+ hs-source-dirs: src

30− exposed-modules:

49+ exposed-modules: LAoP.Dist

31− LAoP.Dist

32− LAoP.Dist.Internal

50+ LAoP.Dist.Internal

33− LAoP.Matrix.Internal

51+ LAoP.Matrix.Internal

34− LAoP.Matrix.Nat

52+ LAoP.Matrix.Nat

35− LAoP.Matrix.Type

53+ LAoP.Matrix.Type

36− LAoP.Relation

54+ LAoP.Relation

37− LAoP.Relation.Internal

55+ LAoP.Relation.Internal

38− LAoP.Utils

56+ LAoP.Utils

39− LAoP.Utils.Internal

57+ LAoP.Utils.Internal

40− other-modules:

41− Paths_laop

42− hs-source-dirs:

43− src

44− build-depends:

45− base >=4.7 && <5

46− , deepseq

47− default-language: Haskell2010

48−

49−executable laop-exe

50− main-is: Main.hs

51− other-modules:

52− Benchmarks

53− Examples

54− Spreadsheets

55− Paths_laop

56− hs-source-dirs:

57− app

58− ghc-options: -threaded -rtsopts -with-rtsopts=-N2 -funfolding-use-threshold=16 -fexcess-precision -optc-O3 -optc-ffast-math

59− build-depends:

60− QuickCheck

61− , base >=4.7 && <5

62− , criterion

63− , deepseq

64− , laop

65− default-language: Haskell2010

66

58

67test-suite laop-test

59test-suite laop-test

60+ import: common-options

68− type: exitcode-stdio-1.0

61+ type: exitcode-stdio-1.0

69− main-is: Spec.hs

62+ hs-source-dirs: test

70− other-modules:

63+ other-modules: Examples.Readme

71− Paths_laop

64+ main-is: Spec.hs

72− hs-source-dirs:

65+ build-depends: laop

73− test

74− ghc-options: -threaded -rtsopts -with-rtsopts=-N

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

75− build-depends:

79+ build-depends: criterion

76− base >=4.7 && <5

80+ , QuickCheck

77− , deepseq

81+ , deepseq

78− , laop

82+ , laop

79− default-language: Haskell2010

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.yamldeleted−57

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

1−name: laop

2−version: 0.1.0.7

3−github: "bolt12/laop"

4−license: BSD3

5−author: "Armando Santos"

6−maintainer: "armandoifsantos@gmail.com"

7−copyright: "MIT"

8−

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

src/LAoP/Matrix/Internal.hs+54−87

@@ -30,7 +30,7 @@

30-- motivation behind the library, the underlying theory, and implementation details.

31--

32-- This module offers many of the combinators mentioned in the work of

33−-- Macedo (2012) and Oliveira (2012).

33+-- Macedo (2012) and Oliveira (2012).

34--

35-- This is an Internal module and it is no supposed to be imported.

36--

@@ -43,8 +43,8 @@ module LAoP.Matrix.Internal

43 --

44 -- There exists two type families that make it easier to write

45 -- matrix dimensions: 'FromNat' and 'Count'. This approach

46− -- leads to a very straightforward implementation

46+ -- leads to a very straightforward implementation

47− -- of LAoP combinators.

47+ -- of LAoP combinators.

48

49 -- * Type safe matrix representation

50 Matrix (..),

@@ -86,7 +86,9 @@ module LAoP.Matrix.Internal

86 -- * Misc

87 -- ** Get dimensions

88 columns,

89+ columns',

89 rows,

90 rows,

91+ rows',

90

92

91 -- ** Matrix Transposition

93 -- ** Matrix Transposition

92 tr,

94 tr,

@@ -174,6 +176,7 @@ import Data.Kind

174import Data.List

176import Data.List

175import Data.Maybe

177import Data.Maybe

176import Data.Proxy

178import Data.Proxy

179+import Data.Typeable

177import Data.Void

180import Data.Void

178import GHC.TypeLits

181import GHC.TypeLits

179import Data.Type.Equality

182import Data.Type.Equality

@@ -240,7 +243,7 @@ type Trivial a = FromNat (Count a) ~ a

240-- class.

243-- class.

241instance (Num e) => Category (Matrix e) where

244instance (Num e) => Category (Matrix e) where

242 type Object (Matrix e) a = (FL a a, Countable a)

245 type Object (Matrix e) a = (FL a a, Countable a)

243− id = iden

246+ id = iden

244 (.) = comp

247 (.) = comp

245

248

246instance NFData e => NFData (Matrix e cols rows) where

249instance NFData e => NFData (Matrix e cols rows) where

@@ -256,7 +259,6 @@ instance Eq e => Eq (Matrix e cols rows) where

256 x@(Join _ _) == y@(Fork _ _) = abideJF x == y

259 x@(Join _ _) == y@(Fork _ _) = abideJF x == y

257

260

258instance Num e => Num (Matrix e cols rows) where

261instance Num e => Num (Matrix e cols rows) where

259−

260 a + b = zipWithM (+) a b

262 a + b = zipWithM (+) a b

261

263

262 a - b = zipWithM (-) a b

264 a - b = zipWithM (-) a b

@@ -315,31 +317,34 @@ class FromLists cols rows where

315 -- error if the dimensions do not match.

317 -- error if the dimensions do not match.

316 fromLists :: [[e]] -> Matrix e cols rows

318 fromLists :: [[e]] -> Matrix e cols rows

317

319

318−instance {-# OVERLAPPING #-} FromLists () () where

320+instance FromLists () () where

319 fromLists [[e]] = One e

321 fromLists [[e]] = One e

320 fromLists _ = error "Wrong dimensions"

322 fromLists _ = error "Wrong dimensions"

321

323

322−instance {-# OVERLAPPING #-} (FromLists cols ()) => FromLists (Either () cols) () where

324+instance (FromLists cols ()) => FromLists (Either () cols) () where

323 fromLists [h : t] = Join (One h) (fromLists [t])

325 fromLists [h : t] = Join (One h) (fromLists [t])

324 fromLists _ = error "Wrong dimensions"

326 fromLists _ = error "Wrong dimensions"

325

327

328+instance {-# OVERLAPPABLE #-}

326−instance {-# OVERLAPPABLE #-} (FromLists a (), FromLists b (), Countable a) => FromLists (Either a b) () where

329+ (FromLists a (), FromLists b (), Countable a) => FromLists (Either a b) () where

327 fromLists [l] =

330 fromLists [l] =

328 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

331 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

329 in Join (fromLists [take rowsA l]) (fromLists [drop rowsA l])

332 in Join (fromLists [take rowsA l]) (fromLists [drop rowsA l])

330 fromLists _ = error "Wrong dimensions"

333 fromLists _ = error "Wrong dimensions"

331

334

332−instance {-# OVERLAPPING #-} (FromLists () rows) => FromLists () (Either () rows) where

335+instance (FromLists () rows) => FromLists () (Either () rows) where

333 fromLists ([h] : t) = Fork (One h) (fromLists t)

336 fromLists ([h] : t) = Fork (One h) (fromLists t)

334 fromLists _ = error "Wrong dimensions"

337 fromLists _ = error "Wrong dimensions"

335

338

339+instance {-# OVERLAPPABLE #-}

336−instance {-# OVERLAPPABLE #-} (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where

340+ (FromLists () a, FromLists () b, Countable a) => FromLists () (Either a b) where

337− fromLists l@([_] : _) =

341+ fromLists l@([_] : _) =

338 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

342 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

339 in Fork (fromLists (take rowsA l)) (fromLists (drop rowsA l))

343 in Fork (fromLists (take rowsA l)) (fromLists (drop rowsA l))

340 fromLists _ = error "Wrong dimensions"

344 fromLists _ = error "Wrong dimensions"

341

345

342−instance {-# OVERLAPPABLE #-} (FromLists (Either a b) c, FromLists (Either a b) d, Countable c) => FromLists (Either a b) (Either c d) where

346+instance (FromLists (Either a b) c, FromLists (Either a b) d, Countable c)

347+ => FromLists (Either a b) (Either c d) where

343 fromLists l@(h : t) =

348 fromLists l@(h : t) =

344 let lh = length h

349 let lh = length h

345 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))

350 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))

@@ -366,16 +371,15 @@ matrixBuilder' f =

366matrixBuilder ::

371matrixBuilder ::

367 forall e a b.

372 forall e a b.

368 ( FLN a b,

373 ( FLN a b,

369− CountableN b,

370 Enum a,

374 Enum a,

371 Enum b,

375 Enum b,

372 Bounded a,

376 Bounded a,

373 Bounded b,

377 Bounded b,

374 Eq a,

378 Eq a,

375− CountableDimsN a b

379+ Countable b

376 ) => ((a, b) -> e) -> Matrix e (Normalize a) (Normalize b)

380 ) => ((a, b) -> e) -> Matrix e (Normalize a) (Normalize b)

377matrixBuilder f =

381matrixBuilder f =

378− let r = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))

382+ let r = fromInteger $ natVal (Proxy :: Proxy (Count b))

379 positions = [(a, b) | a <- [minBound .. maxBound], b <- [minBound .. maxBound]]

383 positions = [(a, b) | a <- [minBound .. maxBound], b <- [minBound .. maxBound]]

380 in fromLists . map (map f) . transpose . buildList r $ positions

384 in fromLists . map (map f) . transpose . buildList r $ positions

381 where

385 where

@@ -431,24 +435,7 @@ fromF ::

431 ) =>

435 ) =>

432 (a -> b) ->

436 (a -> b) ->

433 Matrix e (Normalize a) (Normalize b)

437 Matrix e (Normalize a) (Normalize b)

434−fromF f =

438+fromF = fromF'

435− let minA = minBound @a

436− maxA = maxBound @a

437− minB = minBound @b

438− maxB = maxBound @b

439− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))

440− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))

441− elementsA = take ccols [minA .. maxA]

442− elementsB = take rrows [minB .. maxB]

443− combinations = (,) <$> elementsA <*> elementsB

444− combAp = map snd . sort . map (\(a, b) -> if f a == b

445− then ((fromEnum a, fromEnum b), 1)

446− else ((fromEnum a, fromEnum b), 0)) $ combinations

447− mList = buildList combAp rrows

448− in tr $ fromLists mList

449− where

450− buildList [] _ = []

451− buildList l r = take r l : buildList (drop r l) r

452

439

453-- Conversion

440-- Conversion

454

441

@@ -510,7 +497,7 @@ comp (Join a b) (Fork c d) = comp a c + comp b d -- Divide-and-conquer l

510comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law

497comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law

511comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law

498comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law

512{-# NOINLINE comp #-}

499{-# NOINLINE comp #-}

513−{-# RULES

500+{-# RULES

514 "comp/iden1" forall m. comp m iden = m ;

501 "comp/iden1" forall m. comp m iden = m ;

515 "comp/iden2" forall m. comp iden m = m

502 "comp/iden2" forall m. comp iden m = m

516#-}

503#-}

@@ -557,24 +544,38 @@ i2 = tr p2

557

544

558-- | Obtain the number of rows.

545-- | Obtain the number of rows.

559--

546--

560−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

547+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

561−-- dimensions in constant time.

548+-- dimensions in constant time. For a version that doesn't require the

562−--

549+-- constraint see 'rows''.

563−-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in

564−-- exchange for performance.

565rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int

550rows :: forall e cols rows. (Countable rows) => Matrix e cols rows -> Int

566rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))

551rows _ = fromInteger $ natVal (Proxy :: Proxy (Count rows))

567

552

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+

568-- | Obtain the number of columns.

562-- | Obtain the number of columns.

569−--

570−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

571−-- dimensions in constant time.

572--

563--

573−-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in

564+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

574−-- exchange for performance.

565+-- dimensions in constant time. For a version that doesn't require the

566+-- constraint see 'columns''.

575columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int

567columns :: forall e cols rows. (Countable cols) => Matrix e cols rows -> Int

576columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))

568columns _ = fromInteger $ natVal (Proxy :: Proxy (Count cols))

577

569

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+

578-- Coproduct Bifunctor

579-- Coproduct Bifunctor

579

580

580infixl 5 -|-

581infixl 5 -|-

@@ -629,7 +630,7 @@ sndM = matrixBuilder' f

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

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

630--

631--

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

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

632−--

633+--

633-- @

634-- @

634-- | fstM . kr a b == a

635-- | fstM . kr a b == a

635-- kr a b ==> |

636-- kr a b ==> |

@@ -665,7 +666,7 @@ infixl 4 ><

665 FL (Normalize (m, n)) n,

666 FL (Normalize (m, n)) n,

666 FL (Normalize (p, q)) p,

667 FL (Normalize (p, q)) p,

667 FL (Normalize (p, q)) q

668 FL (Normalize (p, q)) q

668− )

669+ )

669 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))

670 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))

670(><) a b =

671(><) a b =

671 let fstM' = fstM @e @m @n

672 let fstM' = fstM @e @m @n

@@ -930,24 +931,7 @@ fromFRel' ::

930 ) =>

931 ) =>

931 (a -> b) ->

932 (a -> b) ->

932 Relation cols rows

933 Relation cols rows

933−fromFRel' f =

934+fromFRel' = fromF'

934− let minA = minBound @a

935− maxA = maxBound @a

936− minB = minBound @b

937− maxB = maxBound @b

938− ccols = fromInteger $ natVal (Proxy :: Proxy (Count cols))

939− rrows = fromInteger $ natVal (Proxy :: Proxy (Count rows))

940− elementsA = take ccols [minA .. maxA]

941− elementsB = take rrows [minB .. maxB]

942− combinations = (,) <$> elementsA <*> elementsB

943− combAp = map snd . sort . map (\(a, b) -> if f a == b

944− then ((fromEnum a, fromEnum b), nat 1)

945− else ((fromEnum a, fromEnum b), nat 0)) $ combinations

946− mList = buildList combAp rrows

947− in tr $ fromLists mList

948− where

949− buildList [] _ = []

950− buildList l r = take r l : buildList (drop r l) r

951

935

952-- | Lifts functions to relations with dimensions matching @a@ and @b@

936-- | Lifts functions to relations with dimensions matching @a@ and @b@

953-- cardinality's.

937-- cardinality's.

@@ -955,28 +939,11 @@ fromFRel ::

955 forall a b.

939 forall a b.

956 ( Liftable Boolean a b,

940 ( Liftable Boolean a b,

957 CountableDimsN a b,

941 CountableDimsN a b,

958− FL (Normalize b) (Normalize a)

942+ FLN b a

959 ) =>

943 ) =>

960 (a -> b) ->

944 (a -> b) ->

961 Relation (Normalize a) (Normalize b)

945 Relation (Normalize a) (Normalize b)

962−fromFRel f =

946+fromFRel = fromFRel'

963− let minA = minBound @a

964− maxA = maxBound @a

965− minB = minBound @b

966− maxB = maxBound @b

967− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))

968− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))

969− elementsA = take ccols [minA .. maxA]

970− elementsB = take rrows [minB .. maxB]

971− combinations = (,) <$> elementsA <*> elementsB

972− combAp = map snd . sort . map (\(a, b) -> if f a == b

973− then ((fromEnum a, fromEnum b), nat 1)

974− else ((fromEnum a, fromEnum b), nat 0)) $ combinations

975− mList = buildList combAp rrows

976− in tr $ fromLists mList

977− where

978− buildList [] _ = []

979− buildList l r = take r l : buildList (drop r l) r

980

947

981-- | Lifts a relation function to a Boolean Matrix

948-- | Lifts a relation function to a Boolean Matrix

982toRel ::

949toRel ::

@@ -986,17 +953,17 @@ toRel ::

986 Enum a,

953 Enum a,

987 Enum b,

954 Enum b,

988 Eq b,

955 Eq b,

989− CountableDimsN a b,

956+ CountableDims a b,

990 FLN b a

957 FLN b a

991− )

958+ )

992 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)

959 => (a -> b -> Bool) -> Relation (Normalize a) (Normalize b)

993toRel f =

960toRel f =

994 let minA = minBound @a

961 let minA = minBound @a

995 maxA = maxBound @a

962 maxA = maxBound @a

996 minB = minBound @b

963 minB = minBound @b

997 maxB = maxBound @b

964 maxB = maxBound @b

998− ccols = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize a)))

965+ ccols = fromInteger $ natVal (Proxy :: Proxy (Count a))

999− rrows = fromInteger $ natVal (Proxy :: Proxy (Count (Normalize b)))

966+ rrows = fromInteger $ natVal (Proxy :: Proxy (Count b))

1000 elementsA = take ccols [minA .. maxA]

967 elementsA = take ccols [minA .. maxA]

1001 elementsB = take rrows [minB .. maxB]

968 elementsB = take rrows [minB .. maxB]

1002 combinations = (,) <$> elementsA <*> elementsB

969 combinations = (,) <$> elementsA <*> elementsB

src/LAoP/Matrix/Type.hs+42−30

@@ -104,8 +104,8 @@ module LAoP.Matrix.Type

104 multM,

105

106 -- * Selective equivalent instance function

107− selectM,

107+ selectM,

108−

108+

109 -- * Monad equivalent instance function

110 returnM,

111 bindM,

@@ -113,7 +113,9 @@ module LAoP.Matrix.Type

113 -- * Misc

114 -- ** Get dimensions

115 columns,

116+ columns',

116 rows,

117 rows,

118+ rows',

117

119

118 -- ** Matrix Transposition

120 -- ** Matrix Transposition

119 tr,

121 tr,

@@ -265,7 +267,7 @@ infixl 2 ===

265-- Functor hierarchy

267-- Functor hierarchy

266

268

267-- | Functor instance equivalent function

269-- | Functor instance equivalent function

268−fmapM ::

270+fmapM ::

269 ( Liftable e a b,

271 ( Liftable e a b,

270 CountableDimsN a b,

272 CountableDimsN a b,

271 FLN b a

273 FLN b a

@@ -279,7 +281,7 @@ unitM :: (Num e) => Matrix e () ()

279unitM = one 1

281unitM = one 1

280

282

281-- | Applicative instance equivalent 'unit' function,

283-- | Applicative instance equivalent 'unit' function,

282−multM ::

284+multM ::

283 ( CountableDimsN a b,

285 ( CountableDimsN a b,

284 CountableN (a, b),

286 CountableN (a, b),

285 Num e,

287 Num e,

@@ -290,8 +292,8 @@ multM ::

290multM = kr

292multM = kr

291

293

292-- | Monad instance equivalent 'return' function,

294-- | Monad instance equivalent 'return' function,

293−returnM ::

295+returnM ::

294− forall e a .

296+ forall e a .

295 ( Num e,

297 ( Num e,

296 Enum e,

298 Enum e,

297 Enum a,

299 Enum a,

@@ -331,7 +333,7 @@ matrixBuilder ::

331 Bounded a,

333 Bounded a,

332 Bounded b,

334 Bounded b,

333 Eq a,

335 Eq a,

334− CountableDimsN a b

336+ Countable b

335 ) => ((a, b) -> e) -> Matrix e a b

337 ) => ((a, b) -> e) -> Matrix e a b

336matrixBuilder f = M (I.matrixBuilder f)

338matrixBuilder f = M (I.matrixBuilder f)

337

339

@@ -368,7 +370,7 @@ fromF = M . I.fromF

368-- | Lifts relation functions to Boolean Matrix

370-- | Lifts relation functions to Boolean Matrix

369toRel ::

371toRel ::

370 ( Liftable (Natural 0 1) a b,

372 ( Liftable (Natural 0 1) a b,

371− CountableDimsN a b,

373+ CountableDims a b,

372 FLN b a

374 FLN b a

373 ) => (a -> b -> Bool) -> Matrix (Natural 0 1) a b

375 ) => (a -> b -> Bool) -> Matrix (Natural 0 1) a b

374toRel = M . I.toRel

376toRel = M . I.toRel

@@ -387,7 +389,7 @@ toList (M m) = I.toList m

387

389

388-- | The zero matrix. A matrix wholly filled with zeros.

390-- | The zero matrix. A matrix wholly filled with zeros.

389zeros ::

391zeros ::

390− (Num e, FLN cols rows, CountableDimsN cols rows)

392+ (Num e, FLN cols rows, CountableDimsN cols rows)

391 => Matrix e cols rows

393 => Matrix e cols rows

392zeros = M I.zeros

394zeros = M I.zeros

393

395

@@ -397,7 +399,7 @@ zeros = M I.zeros

397--

399--

398-- Also known as T (Top) matrix.

400-- Also known as T (Top) matrix.

399ones ::

401ones ::

400− (Num e, FLN cols rows, CountableDimsN cols rows)

402+ (Num e, FLN cols rows, CountableDimsN cols rows)

401 => Matrix e cols rows

403 => Matrix e cols rows

402ones = M I.ones

404ones = M I.ones

403

405

@@ -406,7 +408,7 @@ ones = M I.ones

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

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

407-- value.

409-- value.

408constant ::

410constant ::

409− (Num e, FLN cols rows, CountableDimsN cols rows)

411+ (Num e, FLN cols rows, CountableDimsN cols rows)

410 => e -> Matrix e cols rows

412 => e -> Matrix e cols rows

411constant = M . I.constant

413constant = M . I.constant

412

414

@@ -420,7 +422,7 @@ bang ::

420bang = M I.bang

422bang = M I.bang

421

423

422-- | Point constant relation

424-- | Point constant relation

423−point ::

425+point ::

424 ( Bounded a,

426 ( Bounded a,

425 Enum a,

427 Enum a,

426 Eq a,

428 Eq a,

@@ -449,7 +451,7 @@ iden = M I.iden

449comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

451comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

450comp (M a) (M b) = M (I.comp a b)

452comp (M a) (M b) = M (I.comp a b)

451{-# NOINLINE comp #-}

453{-# NOINLINE comp #-}

452−{-# RULES

454+{-# RULES

453 "comp/iden1" forall m. comp m iden = m ;

455 "comp/iden1" forall m. comp m iden = m ;

454 "comp/iden2" forall m. comp iden m = m

456 "comp/iden2" forall m. comp iden m = m

455#-}

457#-}

@@ -514,24 +516,34 @@ i2 = tr p2

514

516

515-- | Obtain the number of rows.

517-- | Obtain the number of rows.

516--

518--

517−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

519+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

518−-- dimensions in constant time.

520+-- dimensions in constant time. For a version that doesn't require the

519−--

521+-- constraint see 'rows''.

520−-- TODO: A 'rows' function that does not need the 'KnownNat' constraint in

521−-- exchange for performance.

522rows :: (CountableN rows) => Matrix e cols rows -> Int

523rows (M m) = I.rows m

524

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+

525-- | Obtain the number of columns.

532-- | Obtain the number of columns.

526−--

527−-- NOTE: The 'KnownNat' constaint is needed in order to obtain the

528−-- dimensions in constant time.

529--

533--

530−-- TODO: A 'columns' function that does not need the 'KnownNat' constraint in

534+-- NOTE: The 'KnownNat' constraint is needed in order to obtain the

531−-- exchange for performance.

535+-- dimensions in constant time. For a version that doesn't require the

536+-- constraint see 'columns''.

532columns :: (CountableN cols) => Matrix e cols rows -> Int

537columns :: (CountableN cols) => Matrix e cols rows -> Int

533columns (M m) = I.columns m

538columns (M m) = I.columns m

534

539

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+

535-- Coproduct Bifunctor

547-- Coproduct Bifunctor

536

548

537infixl 5 -|-

549infixl 5 -|-

@@ -553,7 +565,7 @@ infixl 5 -|-

553-- Khatri Rao Product and projections

565-- Khatri Rao Product and projections

554

566

555-- | Khatri Rao product first component projection matrix.

567-- | Khatri Rao product first component projection matrix.

556−fstM ::

568+fstM ::

557 forall e m k .

569 forall e m k .

558 ( Num e,

570 ( Num e,

559 CountableDimsN m k,

571 CountableDimsN m k,

@@ -564,7 +576,7 @@ fstM ::

564fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))

576fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))

565

577

566-- | Khatri Rao product second component projection matrix.

578-- | Khatri Rao product second component projection matrix.

567−sndM ::

579+sndM ::

568 forall e m k.

580 forall e m k.

569 ( Num e,

581 ( Num e,

570 CountableDimsN k m,

582 CountableDimsN k m,

@@ -577,9 +589,9 @@ sndM = M (I.sndM @e @(I.Normalize m) @(I.Normalize k))

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

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

578--

590--

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

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

580−--

592+--

581-- @

593-- @

582−-- | fstM . kr a b == a

594+-- | fstM . kr a b == a

583-- kr a b ==> |

595-- kr a b ==> |

584-- | sndM . kr a b == b

596-- | sndM . kr a b == b

585-- @

597-- @

@@ -625,7 +637,7 @@ infixl 4 ><

625-- Matrix abide Join Fork

637-- Matrix abide Join Fork

626

638

627-- | Matrix "abiding" followin the 'Join'-'Fork' abide law.

639-- | Matrix "abiding" followin the 'Join'-'Fork' abide law.

628−--

640+--

629-- Law:

641-- Law:

630--

642--

631-- @

643-- @

@@ -637,7 +649,7 @@ abideJF (M m) = M (I.abideJF m)

637-- Matrix abide Fork Join

649-- Matrix abide Fork Join

638

650

639-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.

651-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.

640−--

652+--

641-- Law:

653-- Law:

642--

654--

643-- @

655-- @

@@ -656,7 +668,7 @@ tr (M m) = M (I.tr m)

656

668

657-- | Selective functors 'select' operator equivalent inspired by the

669-- | Selective functors 'select' operator equivalent inspired by the

658-- ArrowMonad solution presented in the paper.

670-- ArrowMonad solution presented in the paper.

659−selectM ::

671+selectM ::

660 ( Num e,

672 ( Num e,

661 FLN b b,

673 FLN b b,

662 CountableN b

674 CountableN b

src/LAoP/Relation/Internal.hs+12−9

@@ -283,7 +283,7 @@ relationBuilder ::

283 Bounded a,

284 Bounded b,

285 Eq a,

286− CountableDimsN a b

286+ CountableDims a b

287 ) => ((a, b) -> Boolean) -> Relation a b

288relationBuilder = R . I.matrixBuilder

289

@@ -301,7 +301,7 @@ fromF' f = R (I.fromFRel' f)

301

302-- | Lifts functions to matrices with dimensions matching @a@ and @b@

303-- cardinality's.

304−fromF ::

304+fromF ::

305 ( Liftable a b,

306 CountableDimsN a b,

307 FLN b a

@@ -312,7 +312,7 @@ fromF f = R (I.fromFRel f)

312-- | Lifts relation functions to 'Relation'

313toRel ::

314 ( Liftable a b,

315− CountableDimsN a b,

315+ CountableDims a b,

316 FLN b a

317 )

318 => (a -> b -> Bool) -> Relation a b

@@ -348,7 +348,7 @@ toBool r = case toList r of

348-- | Power transpose.

349--

350-- Maps a relation to a set valued function.

351−pt ::

351+pt ::

352 ( Liftable a b,

353 Eq a,

354 CountableDimsN a b,

@@ -365,7 +365,7 @@ belongs ::

365 ( Bounded a,

366 Enum a,

367 Eq a,

368− CountableDimsN (List a) a,

368+ CountableDims (List a) a,

369 FLN a (List a)

370 )

371 => Relation (List a) a

@@ -413,7 +413,7 @@ bang ::

413bang = ones

414

415-- | Point constant relation

416−point ::

416+point ::

417 ( Bounded a,

418 Enum a,

419 Eq a,

@@ -927,6 +927,7 @@ untrans s = fstR . conv (splitR (conv s) sndR)

927predR ::

928 ( Bounded a,

929 Enum a,

930+ Countable a,

930 CountableN a,

931 CountableN a,

931 FLN a a,

932 FLN a a,

932 FLN Bool a

933 FLN Bool a

@@ -954,23 +955,25 @@ equalizer f g = id `intersection` divisionF f g

954-- @

955-- @

955-- 'guard' p = 'i2' ``overriddenBy`` 'i1' `.` 'predR' p

956-- 'guard' p = 'i2' ``overriddenBy`` 'i1' `.` 'predR' p

956-- @

957-- @

957−guard ::

958+guard ::

958 ( Bounded b,

959 ( Bounded b,

959 Enum b,

960 Enum b,

960 CountableN b,

961 CountableN b,

962+ Countable b,

961 FLN b b,

963 FLN b b,

962 FLN Bool b

964 FLN Bool b

963 ) => Relation b Bool -> Relation b (Either b b)

965 ) => Relation b Bool -> Relation b (Either b b)

964guard p = conv (eitherR (predR p) (predR (negate p)))

966guard p = conv (eitherR (predR p) (predR (negate p)))

965

967

966-- | Relational McCarthy's conditional.

968-- | Relational McCarthy's conditional.

967−cond ::

969+cond ::

968 ( Bounded b,

970 ( Bounded b,

969 Enum b,

971 Enum b,

972+ Countable b,

970 CountableN b,

973 CountableN b,

971 FLN b b,

974 FLN b b,

972 FLN Bool b

975 FLN Bool b

973− )

976+ )

974 => Relation b Bool -> Relation b c -> Relation b c -> Relation b c

977 => Relation b Bool -> Relation b c -> Relation b c -> Relation b c

975cond p r s = eitherR r s . guard p

978cond p r s = eitherR r s . guard p

976

979

stack-8.8.3.yamlnew file+1

@@ -0,0 +1 @@

1+resolver: lts-15.5

stack.yaml+1−66

@@ -1,66 +1 @@

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/

6−

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

1+resolver: lts-14.3

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 @@

6packages: []

7snapshots:

8- completed:

9− size: 524789

9+ size: 523878

10− url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/14/18.yaml

10+ url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/14/3.yaml

11− sha256: 646be71223e08234131c6989912e6011e01b9767bc447b6d466a35e14360bdf2

11+ sha256: 470c46c27746a48c7c50f829efc0cf00112787a7804ee4ac7a27754658f6d92c

12− original: lts-14.18

12+ original: lts-14.3

app/Quantum.hs → test/Examples/Quantum.hsrenamed+2−2

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

1{-# LANGUAGE StandaloneDeriving #-}

2−module Quantum where

2+module Examples.Quantum where

3

4import LAoP.Utils

5import LAoP.Matrix.Type

@@ -21,7 +21,7 @@ cnot = kr fstM (fromF xor)

21ccnot :: (Num e, Ord e) => Matrix e ((Bool, Bool), Bool) ((Bool, Bool), Bool)

22ccnot = kr fstM (fromF f)

23 where

24− f = xor . (tp (uncurry (&&)) id)

24+ f = xor . tp (uncurry (&&)) id

25 tp f g (a,b) = (f a, g b)

26

27had :: Matrix (Complex Double) Bool Bool

app/Examples.hs → test/Examples/Readme.hsrenamed+1−2

@@ -1,11 +1,10 @@

1{-# LANGUAGE GADTs #-}

2{-# LANGUAGE DeriveGeneric #-}

3{-# LANGUAGE FlexibleContexts #-}

4−{-# LANGUAGE TypeOperators #-}

5{-# LANGUAGE TypeApplications #-}

4{-# LANGUAGE TypeApplications #-}

6{-# LANGUAGE DataKinds #-}

5{-# LANGUAGE DataKinds #-}

7

6

8−module Examples

7+module Examples.Readme

9 ( exec

8 ( exec

10 )

9 )

11 where

10 where

app/Spreadsheets.hs → test/Examples/Spreadsheets.hsrenamed+1−2

@@ -1,7 +1,6 @@

1{-# LANGUAGE DeriveGeneric #-}

2

3−module Spreadsheets

3+module Examples.Spreadsheets

4− where

5

4

6import LAoP.Utils

5import LAoP.Utils

7import LAoP.Matrix.Type

6import LAoP.Matrix.Type

test/Spec.hs+7−1

@@ -1,2 +1,8 @@

1+module Main (main) where

2+

3+import qualified Examples.Readme as RD

4+

1main :: IO ()

5main :: IO ()

2−main = putStrLn "Test suite not yet implemented"

6+main = do

7+ putStrLn ("Testing if README works" :: String)

8+ RD.exec