FiniteCategoriesGraphViz (empty) → 0.1.0.0
raw patch · 6 files changed
+1356/−0 lines, 6 filesdep +FiniteCategoriesdep +FiniteCategoriesGraphVizdep +WeakSets
Dependencies added: FiniteCategories, FiniteCategoriesGraphViz, WeakSets, base, containers, directory, fgl, filepath, graphviz, process, random, text
Files
- CHANGELOG.md +5/−0
- FiniteCategoriesGraphViz.cabal +112/−0
- LICENSE +674/−0
- Readme.md +55/−0
- src/Math/IO/FiniteCategories/ExportGraphViz.hs +487/−0
- test/RunAllExamples.hs +23/−0
+ CHANGELOG.md view
@@ -0,0 +1,5 @@+# Revision history for FiniteCategoriesGraphViz + +## 0.1.0.0 -- 2023-09-26 + +* First version.
+ FiniteCategoriesGraphViz.cabal view
@@ -0,0 +1,112 @@+cabal-version: 3.0 + +-- Initial package description 'FiniteCategoriesGaphViz.cabal' generated by +-- 'cabal init'. For further documentation, see: +-- http://haskell.org/cabal/users-guide/ +-- +-- The name of the package. +name: FiniteCategoriesGraphViz + +-- The package version. +-- See the Haskell package versioning policy (PVP) for standards +-- guiding when and how versions should be incremented. +-- https://pvp.haskell.org +-- PVP summary: +-+------- breaking API changes +-- | | +----- non-breaking API additions +-- | | | +--- code changes with no API change +version: 0.1.0.0 + +-- A short (one-line) description of the package. +synopsis: Transform objects of the package FiniteCategories into graphs using GraphViz. + + +-- A longer description of the package. +description: A way to visualize finite categories of the package FiniteCategories thanks to GraphViz. See FiniteCategories for examples of categories. + +-- URL for the project homepage or repository. +homepage: https://gitlab.utc.fr/gsabbagh/FiniteCategoriesGraphViz + +-- A URL where users can report bugs. +-- bug-reports: + +-- The license under which the package is released. +license: GPL-3.0-or-later + +-- The file containing the license text. +license-file: LICENSE + +-- The package author(s). +author: Guillaume Sabbagh + +-- An email address to which users can send suggestions, bug reports, and patches. +maintainer: guillaumesabbagh@protonmail.com + +-- A copyright notice. +-- copyright: +category: Maths, Data + +-- Extra files to be distributed with the package, such as examples or a README. +extra-source-files: + Readme.md + +extra-doc-files: + CHANGELOG.md + +library + -- Modules exported by the library. + exposed-modules: Math.IO.FiniteCategories.ExportGraphViz, + + + -- Modules included in this library but not exported. + -- other-modules: + + -- LANGUAGE extensions used by modules in this package. + other-extensions: MultiParamTypeClasses, FunctionalDependencies, UndecidableInstances, FlexibleInstances + + -- Other library packages from which modules are imported. + build-depends: base >= 4.18.0.0 && < 4.19, + containers >= 0.6.4 && < 0.7, + directory >= 1.3.6 && < 1.4, + filepath >= 1.4.2 && < 1.5, + fgl >= 5.8.0 && < 5.9, + graphviz >= 2999.20.1 && < 2999.21, + text >= 1.0 && < 2.2, + process >= 1.6.11 && < 1.7, + random >= 1.2.1 && < 1.3, + WeakSets >= 1.4.0.1 && < 1.4.0.2, + FiniteCategories >= 0.3.0.1 && < 0.4.0.0, + + -- Directories containing source files. + hs-source-dirs: src + + -- Base language which the package is written in. + default-language: Haskell2010 + +test-suite FiniteCategories-test + -- Base language which the package is written in. + default-language: Haskell2010 + + -- The interface type and version of the test suite. + type: exitcode-stdio-1.0 + + -- Directories containing source files. + hs-source-dirs: test + + -- The entrypoint to the test suite. + main-is: RunAllExamples.hs + + + -- Test dependencies. + build-depends: FiniteCategoriesGraphViz, + base >= 4.18.0.0 && < 4.19, + containers >= 0.6.4 && < 0.7, + directory >= 1.3.6 && < 1.4, + filepath >= 1.4.2 && < 1.5, + fgl >= 5.8.0 && < 5.9, + graphviz >= 2999.20.1 && < 2999.21, + text >= 1.0 && < 2.2, + process >= 1.6.11 && < 1.7, + random >= 1.2.1 && < 1.3, + WeakSets >= 1.4.0.0 && < 1.4.0.2, + FiniteCategories >= 0.3.0.1 && < 0.4.0.0, + -- other-modules:
+ LICENSE view
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+ Readme.md view
@@ -0,0 +1,55 @@+# FiniteCategoriesGraphViz + +The goal of this project is to represent small finite categories in order to make usual constructions automatically on them (e.g. (co)limits, (co)completion, adjunctions, etc.) + +## Table of Contents +1. [General Info](#general-info) +2. [Technologies](#technologies) +3. [Installation](#installation) +4. [Collaboration](#collaboration) +5. [Examples](#examples) + +## General Info + +This package provides tools to export categories of the FiniteCategories using GraphViz. See the package [FiniteCategories](https://hackage.haskell.org/package/FiniteCategories) on hackage. + +## Technologies + +The project uses GraphViz for visualizing the categories created. + +## Installation + +To use the graphviz exports, you must first install graphviz (see [graphviz website](https://graphviz.org/download/)) and make sure that Graphviz folder is in the path (dot should be a callable program from your terminal, if you are on Windows see [this tutorial](https://stackoverflow.com/questions/44272416/how-to-add-a-folder-to-path-environment-variable-in-windows-10-with-screensho#44272417) and if you are on unix see [this tutorial]( https://unix.stackexchange.com/questions/26047/how-to-correctly-add-a-path-to-path)). + +Then you can call the functions `catToPdf`, `diagToPdf`, `diag2ToPdf`, `natToPdf`. + +## Collaboration + +All contributions are appreciated! Contact me by email for any information. + +## Usage + +To run all examples of the project, clone the repository and run in a terminal from the repository the following command : + +```cabal test``` + +You can then find the graphviz output in the folder `OutputGraphViz/`. + + +## Examples + +A category exported with graphviz looks like the following image : + + + +A diagram on this category selecting two objects C and D is represented next : + + + +A cone on this diagram follows, the apex of the cone is in green, its legs are in yellow and the diagram is in blue : + + + +The limiting cone is represented below, it is the product of the two objects C and D. + +
+ src/Math/IO/FiniteCategories/ExportGraphViz.hs view
@@ -0,0 +1,487 @@+{-# LANGUAGE MonadComprehensions #-} + +{-| Module : FiniteCategoriesGraphViz +Description : Visualize finite categories with GraphViz. +Copyright : Guillaume Sabbagh 2022 +License : GPL-3 +Maintainer : guillaumesabbagh@protonmail.com +Stability : experimental +Portability : portable + +This module is a way of exporting finite categories with GraphViz. + +Every function assumes that the 'FiniteCategory' is a 'FiniteCategory', if you want to export a category without implementing an instantiation of 'FiniteCategory', you can instantiate 'FiniteCategory' with the default functions 'defaultGenAr' and 'defaultDecompose'. +-} + +module Math.IO.FiniteCategories.ExportGraphViz +( + -- * Visualize categories + categoryToGraph, + catToDot, + catToPdf, + genToDot, + genToPdf, + categoryToGraphFormat, + catToDotFormat, + catToPdfFormat, + -- * Visualize diagrams + diagToDotCluster, + diagToPdfCluster, + diagToDot, + diagToPdf, + diagToDot2, + diagToPdf2, + diagToDot2Format, + diagToPdf2Format, + -- * Visualize natural transformations + natToDot, + natToPdf, + natToDotFormat, + natToPdfFormat, +) +where + import Math.FiniteCategory + import Math.FiniteCategories + import Math.IO.PrettyPrint + + import qualified Data.Text.Lazy as L (pack, Text) + import qualified Data.Text.Lazy.IO as IO (putStrLn, writeFile) + import Data.Graph.Inductive.Graph (mkGraph, Node, Edge, LNode, LEdge) + import Data.Graph.Inductive.PatriciaTree (Gr) + import Data.GraphViz (graphToDot, nonClusteredParams, fmtNode, fmtEdge, GraphvizParams(..), NodeCluster(..), blankParams,GraphID( Num ), Number(..)) + import Data.GraphViz.Attributes.Complete (Label(StrLabel), Attribute(Label)) + import Data.GraphViz.Attributes (X11Color(..), color) + import Data.GraphViz.Printing (renderDot, toDot) + import Data.Maybe (fromJust) + import Data.List (elemIndex,intercalate) + import Data.WeakSet.Safe + import qualified Data.WeakSet as Set + import Data.WeakMap.Safe + + import System.Process (callCommand) + import System.Directory (createDirectoryIfMissing) + import System.FilePath.Posix (takeDirectory) + + + + -- | Write lazy text to a file specified by a path, if the path leads to non existing directories, it creates the directories. Credits to wisn : https://stackoverflow.com/a/58685979 + createAndWriteFile :: FilePath -> L.Text -> IO () + createAndWriteFile path content = do + createDirectoryIfMissing True $ takeDirectory path + IO.writeFile path content + + -- | Transform an object of a category into a pure node. + objToNode :: (Eq o, FiniteCategory c m o) => c -> o -> Node + objToNode c o + | index == Nothing = error("Call objToNod on an object not in the category.") + | otherwise = i + where + Just i = index + index = elemIndex o (setToList.ob $ c) + + -- | Transform an object of a category into a labeled node. + objToLNode :: (Eq o, PrettyPrint o, FiniteCategory c m o) => c -> o -> LNode String + objToLNode c o = (objToNode c o, pprint o) + + -- | Transform an object of a category into a labeled node, using a custom function. + objToLNodeFormat :: (Eq o, FiniteCategory c m o) => c -> (o -> String) -> o -> LNode String + objToLNodeFormat c formatObj o = (objToNode c o, formatObj o) + + -- | Transform a morphism of a category into a pure edge. + arToEdge :: (Eq o, Morphism m o, FiniteCategory c m o) => c -> m -> Edge + arToEdge c m = ((objToNode c). source $ m, (objToNode c). target $ m) + + -- | Transform a morphism of a category into a labeled edge. + arToLEdge :: (Eq o, PrettyPrint o, PrettyPrint m, Morphism m o, FiniteCategory c m o) => c -> m -> LEdge String + arToLEdge c m = ((objToNode c). source $ m, (objToNode c). target $ m, pprint m) + + -- | Transform a morphism of a category into a labeled edge using a custom function. + arToLEdgeFormat :: (Eq o, Morphism m o, FiniteCategory c m o) => c -> (m -> String) -> m -> LEdge String + arToLEdgeFormat c formatMorph m = ((objToNode c). source $ m, (objToNode c). target $ m, formatMorph m) + + -- | Transform a category into an underlying inductive graph. + categoryToGraph :: (Eq o, PrettyPrint o, PrettyPrint m, Morphism m o, FiniteCategory c m o) => c -> Gr String String + categoryToGraph c = mkGraph (setToList (objToLNode c <$> (ob c))) (setToList (arToLEdge c <$> (arrows c))) + + -- | Transform a category into an underlying inductive graph using formatting functions. + categoryToGraphFormat :: (Eq o, Morphism m o, FiniteCategory c m o) => c -> (o -> String) -> (m -> String) -> Gr String String + categoryToGraphFormat c formatObj formatMorph = mkGraph (setToList (objToLNodeFormat c formatObj <$> (ob c))) (setToList (arToLEdgeFormat c formatMorph <$> (arrows c))) + + -- | Transform a dot representation of a graph into a pdf file. + dotToPdf :: IO () -> String -> IO () + dotToPdf dot path = dot >> callCommand ("dot "++path++" -o "++path++".pdf -T pdf") + + -- | Export a category with GraphViz. If the category is too large, use `genToDot` instead. + -- + -- The black arrows are generating arrows, grey one are generated arrows. + catToDot :: (Eq o, PrettyPrint o, PrettyPrint m, Morphism m o, FiniteCategory c m o) => c -> String -> IO () + catToDot c path = createAndWriteFile path $ renderDot $ toDot dot_file where + dot_file = graphToDot nonClusteredParams { fmtNode= \(n,label)-> [Label (StrLabel (L.pack label))], + fmtEdge= \(n1,n2,label)-> [Label (StrLabel (L.pack label)), + if label `isIn` generatorsLabels then color Black else color Gray80]} (categoryToGraph c) + generators = genArrows c + generatorsLabels = pprint <$> generators + + -- | Export a category with GraphViz, format the objects and the morphisms. If the category is too large, use `genToDot` instead. + -- + -- The black arrows are generating arrows, grey one are generated arrows. + catToDotFormat :: (Eq o, Morphism m o, FiniteCategory c m o) => c -> (o -> String) -> (m -> String) -> String -> IO () + catToDotFormat c formatObj formatMorph path = createAndWriteFile path $ renderDot $ toDot dot_file where + dot_file = graphToDot nonClusteredParams { fmtNode= \(n,label)-> [Label (StrLabel (L.pack label))], + fmtEdge= \(n1,n2,label)-> [Label (StrLabel (L.pack label)), + if label `isIn` generatorsLabels then color Black else color Gray80]} (categoryToGraphFormat c formatObj formatMorph) + generators = genArrows c + generatorsLabels = formatMorph <$> generators + + + -- | Export a category with GraphViz. If the category is too large, use `genToPdf` instead. + -- + -- The black arrows are generating arrows, grey one are generated arrows. + catToPdf :: (Eq o, PrettyPrint o, PrettyPrint m, Morphism m o, FiniteCategory c m o) => c -> String -> IO () + catToPdf c path = dotToPdf (catToDot c path) path + + -- | Export a category with GraphViz and format objects and arrows. If the category is too large, use `genToPdf` instead. + -- + -- The black arrows are generating arrows, grey one are generated arrows. + catToPdfFormat :: (Eq o, Morphism m o, FiniteCategory c m o) => c -> (o -> String) -> (m -> String) -> String -> IO () + catToPdfFormat c formatObj formatMorph path = dotToPdf (catToDotFormat c formatObj formatMorph path) path + + -- | Transforms a category into an inductive graph. + categoryToGeneratorGraph :: (Eq o, PrettyPrint o, PrettyPrint m, Morphism m o, FiniteCategory c m o) => c -> Gr String String + categoryToGeneratorGraph c = mkGraph (setToList (objToLNode c <$> (ob c))) (setToList (arToLEdge c <$> (genArrows c))) + + -- | Export the generator of a category with GraphViz. Use this when the category is too large to be fully exported. + genToDot :: (Eq o, PrettyPrint o, PrettyPrint m, Morphism m o, FiniteCategory c m o) => c -> String -> IO () + genToDot c path = createAndWriteFile path $ renderDot $ toDot dot_file where + dot_file = graphToDot nonClusteredParams { fmtNode= \(n,label)-> [Label (StrLabel (L.pack label))], + fmtEdge= \(n1,n2,label)-> [Label (StrLabel (L.pack label))]} (categoryToGeneratorGraph c) + + -- | Export the generator of a category with GraphViz. Use this when the category is to large to be fully exported. + genToPdf :: (Eq o, PrettyPrint o, PrettyPrint m, Morphism m o, FiniteCategory c m o) => c -> String -> IO () + genToPdf c path = dotToPdf (genToDot c path) path + + + -- __________________________________ + -- __________________________________ + -- + -- Diagram representation with cluster of objects mapped together + -- __________________________________ + -- __________________________________ + + + + -- | If the node is pair, then it is part of the source category, else it is part of the target category. + diagObjToNodeCluster :: (Eq o, FiniteCategory c m o) => c -> Bool -> o -> Node + diagObjToNodeCluster c b o + | index == Nothing = error("Call diagObjToNod on an object not in the category.") + | otherwise = if b then 2*i else 2*i+1 + where + Just i = index + index = elemIndex o (setToList (ob c)) + + diagObjToLNodeCluster :: (Eq o, PrettyPrint o, FiniteCategory c m o) => c -> Bool -> o -> LNode String + diagObjToLNodeCluster c b o = (diagObjToNodeCluster c b o, pprint o) + + diagArToEdgeCluster :: (Eq o, Morphism m o, FiniteCategory c m o) => c -> Bool -> m -> Edge + diagArToEdgeCluster c b m = ((diagObjToNodeCluster c b). source $ m, (diagObjToNodeCluster c b). target $ m) + + diagArToLEdgeCluster :: (Eq o, PrettyPrint o, PrettyPrint m, Morphism m o, FiniteCategory c m o) => c -> Bool -> m -> LEdge String + diagArToLEdgeCluster c b m = ((diagObjToNodeCluster c b). source $ m, (diagObjToNodeCluster c b). target $ m, pprint m) + + diagToGraphCluster :: (Eq c1, Eq o1, PrettyPrint o1, PrettyPrint m1, Morphism m1 o1, FiniteCategory c1 m1 o1, + Eq c2, Eq o2, PrettyPrint o2, PrettyPrint m2, Morphism m2 o2, FiniteCategory c2 m2 o2) => + Diagram c1 m1 o1 c2 m2 o2 -> Gr String String + diagToGraphCluster f = mkGraph (setToList ((diagObjToLNodeCluster (src f) True <$> (ob (src f))))++(setToList (diagObjToLNodeCluster (tgt f) False <$> (ob (tgt f))))) (setToList ((diagArToLEdgeCluster (src f) True <$> (genArrows (src f))))++(setToList (diagArToLEdgeCluster (tgt f) False <$> (genArrows (tgt f))))) + + -- | Export a functor with GraphViz such that the source category is in green, the target in blue, the objects mapped together are in the same cluster. + diagToDotCluster :: (Eq c1, Eq o1, PrettyPrint o1, PrettyPrint m1, Morphism m1 o1, FiniteCategory c1 m1 o1, + Eq c2, Eq o2, PrettyPrint o2, PrettyPrint m2, Morphism m2 o2, FiniteCategory c2 m2 o2) => + Diagram c1 m1 o1 c2 m2 o2 -> String -> IO () + diagToDotCluster f@Diagram{src=s,tgt=t,omap=om,mmap=fm} path = createAndWriteFile path $ renderDot $ toDot dot_file where + dot_file = graphToDot Params { + isDirected = True + ,globalAttributes = [] + ,clusterBy = (\(n,nl) -> if (n `mod` 2) == 0 then (C ((fromJust (elemIndex (om |!| ((setToList (ob s)) !! (n `div` 2))) (setToList (ob t))))) $ N (n,nl)) else (C (fromJust (elemIndex ((setToList (ob t)) !! (n `div` 2)) (setToList (ob t)))) $ N (n,nl))) + ,isDotCluster = const True + ,clusterID = Num . Int + ,fmtCluster = const [] + ,fmtNode = \(n,label)-> [Label (StrLabel (L.pack label)), if (n `mod` 2) == 0 then color Green else color Blue] + ,fmtEdge= \(n1,n2,label)-> [Label (StrLabel (L.pack label))] + } (diagToGraphCluster f) + + -- | Export a functor as a pdf with GraphViz such that the source category is in green, the target in blue, the objects mapped together are in the same cluster. + diagToPdfCluster :: (Eq c1, Eq o1, PrettyPrint o1, PrettyPrint m1, Morphism m1 o1, FiniteCategory c1 m1 o1, + Eq c2, Eq o2, PrettyPrint o2, PrettyPrint m2, Morphism m2 o2, FiniteCategory c2 m2 o2) => + Diagram c1 m1 o1 c2 m2 o2 -> String -> IO () + diagToPdfCluster f path = dotToPdf (diagToDotCluster f path) path + + + -- __________________________________ + -- __________________________________ + -- + -- Diagram representation with arrows between arrows + -- __________________________________ + -- __________________________________ + + indexAr :: (Morphism m o, FiniteCategory c m o, Eq o, Eq m) => c -> m -> Int + indexAr c m + | isIn m (arrows c) = fromJust $ elemIndex m (setToList (arrows c)) + | otherwise = error "indexAr of arrow not in category" + + indexOb :: (FiniteCategory c m o, Eq o) => c -> o -> Int + indexOb c o + | isIn o (ob c) = fromJust $ elemIndex o (setToList (ob c)) + | otherwise = error "indexOb of object not in category" + + -- | If the node%4 == 0, then it is part of the source category, else if node%4 == 1 it is part of the target category. + diagObjToNode :: (Eq o, FiniteCategory c m o) => c -> Bool -> o -> Node + diagObjToNode c b o + | index == Nothing = error("Call diagObjToNode on an object not in the category.") + | otherwise = if b then 4*i else 4*i+1 + where + Just i = index + index = elemIndex o (setToList (ob c)) + + diagObjToLNode :: (Eq o, PrettyPrint o, FiniteCategory c m o) => c -> Bool -> o -> LNode String + diagObjToLNode c b o = (diagObjToNode c b o, pprint o) + + -- Creates the invisible node associated to an arrow of the source category if the boolean is True, of the target category if the boolean is False. + invisNodeSrc :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2) => + (Diagram c1 m1 o1 c2 m2 o2) -> m1 -> LNode String + invisNodeSrc f@Diagram{src=s,tgt=t,mmap=_,omap=_} m = (4*(indexAr s m)+2, pprint m) + + invisNodeTgt :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2) => + (Diagram c1 m1 o1 c2 m2 o2) -> m2 -> LNode String + invisNodeTgt f@Diagram{src=s,tgt=t,mmap=_,omap=_} m = (4*(indexAr t m)+3, pprint m) + + diagArToLEdges :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2) => + (Diagram c1 m1 o1 c2 m2 o2) -> Either m1 m2 -> [LEdge String] + diagArToLEdges f@Diagram{src=s,tgt=t,omap=_,mmap=_} (Left m) = [((diagObjToNode s True). source $ m, fst.(invisNodeSrc f) $ m, ""),(fst.(invisNodeSrc f) $ m,(diagObjToNode s True). target $ m, "")] + diagArToLEdges f@Diagram{src=s,tgt=t,omap=_,mmap=_} (Right m) = [((diagObjToNode t False). source $ m, fst.(invisNodeTgt f) $ m, ""),(fst.(invisNodeTgt f) $ m,(diagObjToNode t False). target $ m, "")] + + linkArrows :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2) => + (Diagram c1 m1 o1 c2 m2 o2) -> [LEdge String] + linkArrows f@Diagram{src=s,tgt=t,omap=_,mmap=fm} = (\m->(fst(invisNodeSrc f m),fst(invisNodeTgt f (fm |!| m)),"")) <$> (setToList (arrows s)) + + linkObjects :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2) => + (Diagram c1 m1 o1 c2 m2 o2) -> [LEdge String] + linkObjects f@Diagram{src=s,tgt=t,omap=om,mmap=_} = (\o->(diagObjToNode s True o,diagObjToNode t False (om |!| o),"")) <$> (setToList (ob s)) + + diagToGraph :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2, PrettyPrint o2) => + (Diagram c1 m1 o1 c2 m2 o2) -> Gr String String + diagToGraph f = mkGraph ((diagObjToLNode (src f) True <$> (setToList (ob (src f))))++(diagObjToLNode (tgt f) False <$> (setToList (ob (tgt f))))++((invisNodeSrc f) <$> (setToList (arrows (src f))))++((invisNodeTgt f) <$> (setToList (arrows (tgt f))))) + ((Prelude.concat ((diagArToLEdges f <$> (Left <$> (setToList (arrows (src f)))))++(diagArToLEdges f <$> (Right <$> (setToList (arrows (tgt f)))))))++(linkArrows f)++(linkObjects f)) + + -- | Export a diagram with GraphViz such that the source category is in green, the target in blue, each morphism is represented by a node. + diagToDot :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2, PrettyPrint o2) => + (Diagram c1 m1 o1 c2 m2 o2) -> String -> IO () + diagToDot f@Diagram{src=s,tgt=t,omap=om,mmap=fm} path = createAndWriteFile path $ renderDot $ toDot dot_file where + dot_file = graphToDot Params { + isDirected = True + ,globalAttributes = [] + ,clusterBy = (\(n,nl) -> case () of + _ | (n `mod` 2) == 0 -> (C 0 $ N (n,nl)) + | (n `mod` 2) == 1 -> (C 1 $ N (n,nl))) + ,isDotCluster = const True + ,clusterID = Num . Int + ,fmtCluster = const [] + ,fmtNode = \(n,label)-> [Label (StrLabel (L.pack label)), fmtColorN n] + ,fmtEdge= \e@(n1,n2,label)-> [Label (StrLabel (L.pack label)), fmtColorE e] + } (diagToGraph f) + where + fmtColorN n | n `mod` 4 == 0 = color Green + | n `mod` 4 == 1 = color Blue + | n `mod` 4 == 2 = color Red + | n `mod` 4 == 3 = color Pink + fmtColorE (s,t,_) | s `mod ` 4 == 0 = if t `mod` 2 == 1 then color Red else color Green + | t `mod ` 4 == 0 = color Green + | s `mod ` 4 == 1 = color Blue + | t `mod ` 4 == 1 = color Blue + | otherwise = color Black + + -- | Export a diagram as a pdf with GraphViz such that the source category is in green, the target in blue, each morphism is represented by a node. + diagToPdf :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2, PrettyPrint o2) => + (Diagram c1 m1 o1 c2 m2 o2) -> String -> IO () + diagToPdf f path = dotToPdf (diagToDot f path) path + + + -- __________________________________ + -- __________________________________ + -- + -- Diagram representation as a selection of the target category + -- __________________________________ + -- __________________________________ + + -- | Export a diagram with GraphViz such that a node or an arrow is in orange if it is the target of the functor. + diagToDot2 :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2, PrettyPrint o2) => + (Diagram c1 m1 o1 c2 m2 o2) -> String -> IO () + diagToDot2 f@Diagram{src=s,tgt=t,omap=om,mmap=fm} path = createAndWriteFile path $ renderDot $ toDot dot_file where + dot_file = graphToDot nonClusteredParams { fmtNode= \(n,label)-> [Label (StrLabel (L.pack label)), colorNode n], + fmtEdge= \(n1,n2,label)-> [Label (StrLabel (L.pack label)), colorEdge label]} (categoryToGraph t) + where + colorNode n = case () of + _ | countPredN == 0 -> color Black + | countPredN == 1 -> color Orange + | countPredN == 2 -> color Orange1 + | countPredN == 3 -> color Orange2 + | countPredN == 4 -> color Orange3 + | countPredN == 5 -> color Orange4 + | otherwise -> color OrangeRed4 + + where + countPredN = Prelude.length [1 | o <- (setToList (ob s)), (objToNode t (om |!| o)) == n] + colorEdge e = case () of + _ | countPredE == 0 -> color Black + | countPredE == 1 -> color Orange + | countPredE == 2 -> color Orange1 + | countPredE == 3 -> color Orange2 + | countPredE == 4 -> color Orange3 + | countPredE == 5 -> color Orange4 + | otherwise -> color OrangeRed4 + where + countPredE = Prelude.length [1 | m <- (setToList (arrows s)), (pprint (fm |!| m)) == e] + + -- | Export a diagram as a pdf with GraphViz such that a node or an arrow is in orange if it is the target of the functor. + diagToPdf2 :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2, PrettyPrint o2) => + (Diagram c1 m1 o1 c2 m2 o2) -> String -> IO () + diagToPdf2 f path = dotToPdf (diagToDot2 f path) path + + -- | Export a diagram with GraphViz such that a node or an arrow is in orange if it is the target of the functor. + -- + -- Allows to format the name of the objects and of the morphisms. + diagToDot2Format :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2, PrettyPrint o2) => + (Diagram c1 m1 o1 c2 m2 o2) -> (o2 -> String) -> (m2 -> String) -> String -> IO () + diagToDot2Format f@Diagram{src=s,tgt=t,omap=om,mmap=fm} formatObj formatMorph path = createAndWriteFile path $ renderDot $ toDot dot_file where + dot_file = graphToDot nonClusteredParams { fmtNode= \(n,label)-> [Label (StrLabel (L.pack label)), colorNode n], + fmtEdge= \(n1,n2,label)-> [Label (StrLabel (L.pack label)), colorEdge label]} (categoryToGraphFormat t formatObj formatMorph) + where + colorNode n = case () of + _ | countPredN == 0 -> color Black + | countPredN == 1 -> color Orange + | countPredN == 2 -> color Orange1 + | countPredN == 3 -> color Orange2 + | countPredN == 4 -> color Orange3 + | countPredN == 5 -> color Orange4 + | otherwise -> color OrangeRed4 + + where + countPredN = Prelude.length [1 | o <- (setToList (ob s)), (objToNode t (om |!| o)) == n] + colorEdge e = case () of + _ | countPredE == 0 -> color Black + | countPredE == 1 -> color Orange + | countPredE == 2 -> color Orange1 + | countPredE == 3 -> color Orange2 + | countPredE == 4 -> color Orange3 + | countPredE == 5 -> color Orange4 + | otherwise -> color OrangeRed4 + where + countPredE = Prelude.length [1 | m <- (setToList (arrows s)), (pprint (fm |!| m)) == e] + + -- | Export a diagram as a pdf with GraphViz such that a node or an arrow is in orange if it is the target of the functor. + -- + -- Allows to format the name of the objects and of the morphisms. + diagToPdf2Format :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, PrettyPrint m2, PrettyPrint o2) => + (Diagram c1 m1 o1 c2 m2 o2) -> (o2 -> String) -> (m2 -> String) -> String -> IO () + diagToPdf2Format f formatObj formatMorph path = dotToPdf (diagToDot2Format f formatObj formatMorph path) path + + + -- __________________________________ + -- __________________________________ + -- + -- Natural transformation representation as a translation in the target category. + -- __________________________________ + -- __________________________________ + + -- | Export a natural transformation with GraphViz such that the source diagram is in green, the target diagram is in blue and the translation is in yellow. + natToDot :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, Eq c1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, Eq c2, PrettyPrint m2, PrettyPrint o2) => + (NaturalTransformation c1 m1 o1 c2 m2 o2) -> String -> IO () + natToDot nt path = createAndWriteFile path $ renderDot $ toDot dot_file where + s = source nt + t = target nt + c = components nt + dot_file = graphToDot nonClusteredParams { fmtNode= \(n,label)-> [Label (StrLabel (L.pack label)), colorNode n], + fmtEdge= \(n1,n2,label)-> [Label (StrLabel (L.pack label)), colorEdge label]} (categoryToGraph (tgt s)) + where + colorNode n = case () of + _ | predNSrc && predNTgt -> color Turquoise + | predNSrc -> color Green + | predNTgt -> color Blue + | otherwise -> color Black + where + predNSrc = Set.or [(objToNode (tgt s) ((omap s) |!| o)) == n | o <- (ob (src s))] + predNTgt = Set.or [(objToNode (tgt t) ((omap t) |!| o)) == n | o <- (ob (src t))] + colorEdge e = case () of + _ | predESrc && predETgt && predENat -> color Beige + | predESrc && predETgt -> color Turquoise + | predESrc && predENat -> color Orange + | predETgt && predENat -> color LightBlue + | predESrc -> color Green + | predETgt -> color Blue + | predENat -> color Yellow + | otherwise -> color Black + where + predESrc = Set.foldr (||) False [(pprint ((mmap s) |!| m)) == e | m <- (arrows (src s))] + predETgt = Set.foldr (||) False [(pprint ((mmap t) |!| m)) == e | m <- (arrows (src t))] + predENat = Set.foldr (||) False [(pprint (c |!| o)) == e | o <- (ob (src s))] + + -- | Export a natural transformation as pdf with GraphViz such that the source diagram is in green, the target diagram is in blue and the translation is in yellow. + natToPdf :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, Eq c1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, Eq c2, PrettyPrint m2, PrettyPrint o2) => + (NaturalTransformation c1 m1 o1 c2 m2 o2) -> String -> IO () + natToPdf nt path = dotToPdf (natToDot nt path) path + + -- | Export a natural transformation with GraphViz such that the source diagram is in green, the target diagram is in blue and the translation is in yellow. + -- + -- Allows to format the name of the objects and of the morphisms. + natToDotFormat :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, Eq c1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, Eq c2, PrettyPrint m2, PrettyPrint o2) => + (NaturalTransformation c1 m1 o1 c2 m2 o2) -> (o2 -> String) -> (m2 -> String) -> String -> IO () + natToDotFormat nt formatObj formatMorph path = createAndWriteFile path $ renderDot $ toDot dot_file where + s = source nt + t = target nt + c = components nt + dot_file = graphToDot nonClusteredParams { fmtNode= \(n,label)-> [Label (StrLabel (L.pack label)), colorNode n], + fmtEdge= \(n1,n2,label)-> [Label (StrLabel (L.pack label)), colorEdge label]} (categoryToGraphFormat (tgt s) formatObj formatMorph) + where + colorNode n = case () of + _ | predNSrc && predNTgt -> color Turquoise + | predNSrc -> color Green + | predNTgt -> color Blue + | otherwise -> color Black + where + predNSrc = Set.or [(objToNode (tgt s) ((omap s) |!| o)) == n | o <- (ob (src s))] + predNTgt = Set.or [(objToNode (tgt t) ((omap t) |!| o)) == n | o <- (ob (src t))] + colorEdge e = case () of + _ | predESrc && predETgt && predENat -> color Beige + | predESrc && predETgt -> color Turquoise + | predESrc && predENat -> color Orange + | predETgt && predENat -> color LightBlue + | predESrc -> color Green + | predETgt -> color Blue + | predENat -> color Yellow + | otherwise -> color Black + where + predESrc = Set.foldr (||) False [(pprint ((mmap s) |!| m)) == e | m <- (arrows (src s))] + predETgt = Set.foldr (||) False [(pprint ((mmap t) |!| m)) == e | m <- (arrows (src t))] + predENat = Set.foldr (||) False [(pprint (c |!| o)) == e | o <- (ob (src s))] + + -- | Export a natural transformation as pdf with GraphViz such that the source diagram is in green, the target diagram is in blue and the translation is in yellow. + -- + -- Allows to format the name of the objects and of the morphisms. + natToPdfFormat :: (Morphism m1 o1, FiniteCategory c1 m1 o1, Eq o1, Eq m1, Eq c1, PrettyPrint m1, PrettyPrint o1, + Morphism m2 o2, FiniteCategory c2 m2 o2, Eq o2, Eq m2, Eq c2, PrettyPrint m2, PrettyPrint o2) => + (NaturalTransformation c1 m1 o1 c2 m2 o2) -> (o2 -> String) -> (m2 -> String) -> String -> IO () + natToPdfFormat nt formatObj formatMorph path = dotToPdf (natToDotFormat nt formatObj formatMorph path) path
+ test/RunAllExamples.hs view
@@ -0,0 +1,23 @@+{-| Module : FiniteCategoriesGraphViz +Description : Run all examples of the project. +Copyright : Guillaume Sabbagh 2022 +License : GPL-3 +Maintainer : guillaumesabbagh@protonmail.com +Stability : experimental +Portability : portable + +Run all examples of the project. See results in the folder OutputGraphViz. +-} + +module Main +( + main +) +where + import Math.FiniteCategories.CompositionGraph + import Math.IO.FiniteCategories.ExportGraphViz + + -- | Run all examples of the project. See results in the folder OutputGraphViz. + main = do + let Right cg = readCGString "A -f-> B\nB -g-> C\nC -h-> B\nB -g-> C -h-> B = <ID>\nC -h-> B -g-> C -h-> B -g-> C = C -h-> B -g-> C" + catToPdf cg "OutputGraphViz/CompositionGraph"