{-# LANGUAGE GADTs, RankNTypes, ViewPatterns #-} ----------------------------------------------------------------------------- -- | -- Module : Algebra.Graph.Test.Generic -- Copyright : (c) Andrey Mokhov 2016-2018 -- License : MIT (see the file LICENSE) -- Maintainer : andrey.mokhov@gmail.com -- Stability : experimental -- -- Generic graph API testing. ----------------------------------------------------------------------------- module Algebra.Graph.Test.Generic ( -- * Generic tests Testsuite, testsuite, HTestsuite, hTestsuite, testShow, testFromAdjacencyList, testBasicPrimitives, testToGraph, testIsSubgraphOf, testSize, testProperties, testAdjacencyList, testPreSet, testPostSet, testPostIntSet, testGraphFamilies, testTransformations, testDfsForest, testDfsForestFrom, testDfs, testTopSort, testIsTopSort, testSplitVertex, testBind, testSimplify ) where import Prelude () import Prelude.Compat import Control.Monad (when) import Data.Orphans () import Data.Foldable (toList) import Data.List (nub) import Data.Tree import Data.Tuple import Algebra.Graph.Class (Graph (..)) import Algebra.Graph.Test import Algebra.Graph.Test.API import Algebra.Graph.Relation (Relation) import qualified Data.Set as Set import qualified Data.IntSet as IntSet data Testsuite where Testsuite :: (Arbitrary g, Eq g, GraphAPI g, Num g, Show g, Vertex g ~ Int) => String -> (forall r. (g -> r) -> g -> r) -> Testsuite testsuite :: (Arbitrary g, Eq g, GraphAPI g, Num g, Show g, Vertex g ~ Int) => String -> g -> Testsuite testsuite prefix g = Testsuite prefix (\f x -> f (x `asTypeOf` g)) data HTestsuite where HTestsuite :: (Arbitrary g, Eq g, GraphAPI g, Num g, Show g, Vertex g ~ Int, g ~ f Int, Foldable f) => String -> (forall r. (g -> r) -> g -> r) -> HTestsuite hTestsuite :: (Arbitrary g, Eq g, GraphAPI g, Num g, Show g, Vertex g ~ Int, g ~ f Int, Foldable f) => String -> g -> HTestsuite hTestsuite prefix g = HTestsuite prefix (\f x -> f (x `asTypeOf` g)) testBasicPrimitives :: Testsuite -> IO () testBasicPrimitives = mconcat [ testEmpty , testVertex , testEdge , testOverlay , testConnect , testVertices , testEdges , testOverlays , testConnects ] testProperties :: Testsuite -> IO () testProperties = mconcat [ testIsEmpty , testHasVertex , testHasEdge , testVertexCount , testEdgeCount , testVertexList , testEdgeList , testVertexSet , testVertexIntSet , testEdgeSet ] testGraphFamilies :: Testsuite -> IO () testGraphFamilies = mconcat [ testPath , testCircuit , testClique , testBiclique , testStar , testStarTranspose , testTree , testForest ] testTransformations :: Testsuite -> IO () testTransformations = mconcat [ testRemoveVertex , testRemoveEdge , testReplaceVertex , testMergeVertices , testTranspose , testGmap , testInduce ] testShow :: Testsuite -> IO () testShow (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "Show ============" test "show (empty ) == \"empty\"" $ show % empty == "empty" test "show (1 ) == \"vertex 1\"" $ show % 1 == "vertex 1" test "show (1 + 2 ) == \"vertices [1,2]\"" $ show % (1 + 2) == "vertices [1,2]" test "show (1 * 2 ) == \"edge 1 2\"" $ show % (1 * 2) == "edge 1 2" test "show (1 * 2 * 3) == \"edges [(1,2),(1,3),(2,3)]\"" $ show % (1 * 2 * 3) == "edges [(1,2),(1,3),(2,3)]" test "show (1 * 2 + 3) == \"overlay (vertex 3) (edge 1 2)\"" $ show % (1 * 2 + 3) == "overlay (vertex 3) (edge 1 2)" testEmpty :: Testsuite -> IO () testEmpty (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "empty ============" test "isEmpty empty == True" $ isEmpty % empty == True test "hasVertex x empty == False" $ \x -> hasVertex x % empty == False test "vertexCount empty == 0" $ vertexCount % empty == 0 test "edgeCount empty == 0" $ edgeCount % empty == 0 testVertex :: Testsuite -> IO () testVertex (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "vertex ============" test "isEmpty (vertex x) == False" $ \x -> isEmpty % vertex x == False test "hasVertex x (vertex x) == True" $ \x -> hasVertex x % vertex x == True test "vertexCount (vertex x) == 1" $ \x -> vertexCount % vertex x == 1 test "edgeCount (vertex x) == 0" $ \x -> edgeCount % vertex x == 0 testEdge :: Testsuite -> IO () testEdge (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "edge ============" test "edge x y == connect (vertex x) (vertex y)" $ \x y -> edge x y == connect (vertex x) % vertex y test "hasEdge x y (edge x y) == True" $ \x y -> hasEdge x y % edge x y == True test "edgeCount (edge x y) == 1" $ \x y -> edgeCount % edge x y == 1 test "vertexCount (edge 1 1) == 1" $ vertexCount % edge 1 1 == 1 test "vertexCount (edge 1 2) == 2" $ vertexCount % edge 1 2 == 2 testOverlay :: Testsuite -> IO () testOverlay (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "overlay ============" test "isEmpty (overlay x y) == isEmpty x && isEmpty y" $ \x y -> isEmpty % overlay x y == (isEmpty x && isEmpty y) test "hasVertex z (overlay x y) == hasVertex z x || hasVertex z y" $ \x y z -> hasVertex z % overlay x y == (hasVertex z x || hasVertex z y) test "vertexCount (overlay x y) >= vertexCount x" $ \x y -> vertexCount % overlay x y >= vertexCount x test "vertexCount (overlay x y) <= vertexCount x + vertexCount y" $ \x y -> vertexCount % overlay x y <= vertexCount x + vertexCount y test "edgeCount (overlay x y) >= edgeCount x" $ \x y -> edgeCount % overlay x y >= edgeCount x test "edgeCount (overlay x y) <= edgeCount x + edgeCount y" $ \x y -> edgeCount % overlay x y <= edgeCount x + edgeCount y test "vertexCount (overlay 1 2) == 2" $ vertexCount % overlay 1 2 == 2 test "edgeCount (overlay 1 2) == 0" $ edgeCount % overlay 1 2 == 0 testConnect :: Testsuite -> IO () testConnect (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "connect ============" test "isEmpty (connect x y) == isEmpty x && isEmpty y" $ \x y -> isEmpty % connect x y == (isEmpty x && isEmpty y) test "hasVertex z (connect x y) == hasVertex z x || hasVertex z y" $ \x y z -> hasVertex z % connect x y == (hasVertex z x || hasVertex z y) test "vertexCount (connect x y) >= vertexCount x" $ \x y -> vertexCount % connect x y >= vertexCount x test "vertexCount (connect x y) <= vertexCount x + vertexCount y" $ \x y -> vertexCount % connect x y <= vertexCount x + vertexCount y test "edgeCount (connect x y) >= edgeCount x" $ \x y -> edgeCount % connect x y >= edgeCount x test "edgeCount (connect x y) >= edgeCount y" $ \x y -> edgeCount % connect x y >= edgeCount y test "edgeCount (connect x y) >= vertexCount x * vertexCount y" $ \x y -> edgeCount % connect x y >= vertexCount x * vertexCount y test "edgeCount (connect x y) <= vertexCount x * vertexCount y + edgeCount x + edgeCount y" $ \x y -> edgeCount % connect x y <= vertexCount x * vertexCount y + edgeCount x + edgeCount y test "vertexCount (connect 1 2) == 2" $ vertexCount % connect 1 2 == 2 test "edgeCount (connect 1 2) == 1" $ edgeCount % connect 1 2 == 1 testVertices :: Testsuite -> IO () testVertices (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "vertices ============" test "vertices [] == empty" $ vertices [] == id % empty test "vertices [x] == vertex x" $ \x -> vertices [x] == id % vertex x test "hasVertex x . vertices == elem x" $ \x xs -> hasVertex x % vertices xs == elem x xs test "vertexCount . vertices == length . nub" $ \xs -> vertexCount % vertices xs == (length . nubOrd) xs test "vertexSet . vertices == Set.fromList" $ \xs -> vertexSet % vertices xs == Set.fromList xs testEdges :: Testsuite -> IO () testEdges (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "edges ============" test "edges [] == empty" $ edges [] == id % empty test "edges [(x,y)] == edge x y" $ \x y -> edges [(x,y)] == id % edge x y test "edgeCount . edges == length . nub" $ \xs -> edgeCount % edges xs == (length . nubOrd) xs testOverlays :: Testsuite -> IO () testOverlays (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "overlays ============" test "overlays [] == empty" $ overlays [] == id % empty test "overlays [x] == x" $ \x -> overlays [x] == id % x test "overlays [x,y] == overlay x y" $ \x y -> overlays [x,y] == id % overlay x y test "overlays == foldr overlay empty" $ mapSize (min 10) $ \xs -> overlays xs == id % foldr overlay empty xs test "isEmpty . overlays == all isEmpty" $ mapSize (min 10) $ \xs -> isEmpty % overlays xs == all isEmpty xs testConnects :: Testsuite -> IO () testConnects (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "connects ============" test "connects [] == empty" $ connects [] == id % empty test "connects [x] == x" $ \x -> connects [x] == id % x test "connects [x,y] == connect x y" $ \x y -> connects [x,y] == id % connect x y test "connects == foldr connect empty" $ mapSize (min 10) $ \xs -> connects xs == id % foldr connect empty xs test "isEmpty . connects == all isEmpty" $ mapSize (min 10) $ \xs -> isEmpty % connects xs == all isEmpty xs testFromAdjacencyList :: Testsuite -> IO () testFromAdjacencyList (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "fromAdjacencyList ============" test "fromAdjacencyList [] == empty" $ fromAdjacencyList [] == id % empty test "fromAdjacencyList [(x, [])] == vertex x" $ \x -> fromAdjacencyList [(x, [])] == id % vertex x test "fromAdjacencyList [(x, [y])] == edge x y" $ \x y -> fromAdjacencyList [(x, [y])] == id % edge x y test "fromAdjacencyList . adjacencyList == id" $ \x -> (fromAdjacencyList . adjacencyList) % x == x test "overlay (fromAdjacencyList xs) (fromAdjacencyList ys) == fromAdjacencyList (xs ++ ys)" $ \xs ys -> overlay (fromAdjacencyList xs) % fromAdjacencyList ys == fromAdjacencyList (xs ++ ys) testToGraph :: HTestsuite -> IO () testToGraph (HTestsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "toGraph ============" test " toGraph (g :: Graph a ) :: Graph a == g" $ \g -> toGraph % g == g test "show (toGraph (1 * 2 :: Graph Int) :: Relation Int) == \"edge 1 2\"" $ show (toGraph % (1 * 2) :: Relation Int) == "edge 1 2" test "\ntoGraph == foldg empty vertex overlay connect" $ \x -> toGraph % x == id % foldg empty vertex overlay connect x putStrLn $ "\n============ " ++ prefix ++ "foldg ============" test "foldg empty vertex overlay connect == id" $ \x -> foldg empty vertex overlay connect x == id % x test "foldg empty vertex overlay (flip connect) == transpose" $ \x -> foldg empty vertex overlay (flip connect)x== transpose % x test "foldg [] return (++) (++) == toList" $ \x -> foldg [] return (++) (++) x == toList % x test "foldg 0 (const 1) (+) (+) == length" $ \x -> foldg 0 (const 1) (+) (+) x == length % x test "foldg 1 (const 1) (+) (+) == size" $ \x -> foldg 1 (const 1) (+) (+) x == size % x test "foldg True (const False) (&&) (&&) == isEmpty" $ \x -> foldg True (const False) (&&) (&&) x == isEmpty % x testIsSubgraphOf :: Testsuite -> IO () testIsSubgraphOf (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "isSubgraphOf ============" test "isSubgraphOf empty x == True" $ \x -> isSubgraphOf empty % x == True test "isSubgraphOf (vertex x) empty == False" $ \x -> isSubgraphOf (vertex x) % empty == False test "isSubgraphOf x (overlay x y) == True" $ \x y -> isSubgraphOf x % overlay x y == True test "isSubgraphOf (overlay x y) (connect x y) == True" $ \x y -> isSubgraphOf (overlay x y) % connect x y == True test "isSubgraphOf (path xs) (circuit xs) == True" $ \xs -> isSubgraphOf (path xs) % circuit xs == True testIsEmpty :: Testsuite -> IO () testIsEmpty (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "isEmpty ============" test "isEmpty empty == True" $ isEmpty % empty == True test "isEmpty (overlay empty empty) == True" $ isEmpty % overlay empty empty == True test "isEmpty (vertex x) == False" $ \x -> isEmpty % vertex x == False test "isEmpty (removeVertex x $ vertex x) == True" $ \x -> isEmpty (removeVertex x % vertex x) == True test "isEmpty (removeEdge x y $ edge x y) == False" $ \x y -> isEmpty (removeEdge x y % edge x y) == False testSize :: Testsuite -> IO () testSize (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "size ============" test "size empty == 1" $ size % empty == 1 test "size (vertex x) == 1" $ \x -> size % vertex x == 1 test "size (overlay x y) == size x + size y" $ \x y -> size % overlay x y == size x + size y test "size (connect x y) == size x + size y" $ \x y -> size % connect x y == size x + size y test "size x >= 1" $ \x -> size % x >= 1 test "size x >= vertexCount x" $ \x -> size % x >= vertexCount x testHasVertex :: Testsuite -> IO () testHasVertex (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "hasVertex ============" test "hasVertex x empty == False" $ \x -> hasVertex x % empty == False test "hasVertex x (vertex x) == True" $ \x -> hasVertex x % vertex x == True test "hasVertex 1 (vertex 2) == False" $ hasVertex 1 % vertex 2 == False test "hasVertex x . removeVertex x == const False" $ \x y -> (hasVertex x . removeVertex x) y == const False % y testHasEdge :: Testsuite -> IO () testHasEdge (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "hasEdge ============" test "hasEdge x y empty == False" $ \x y -> hasEdge x y % empty == False test "hasEdge x y (vertex z) == False" $ \x y z -> hasEdge x y % vertex z == False test "hasEdge x y (edge x y) == True" $ \x y -> hasEdge x y % edge x y == True test "hasEdge x y . removeEdge x y == const False" $ \x y z -> (hasEdge x y . removeEdge x y) z == const False % z test "hasEdge x y == elem (x,y) . edgeList" $ \x y z -> do (u, v) <- elements ((x, y) : edgeList z) return $ hasEdge u v z == elem (u, v) (edgeList % z) testVertexCount :: Testsuite -> IO () testVertexCount (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "vertexCount ============" test "vertexCount empty == 0" $ vertexCount % empty == 0 test "vertexCount (vertex x) == 1" $ \x -> vertexCount % vertex x == 1 test "vertexCount == length . vertexList" $ \x -> vertexCount % x == (length . vertexList) x testEdgeCount :: Testsuite -> IO () testEdgeCount (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "edgeCount ============" test "edgeCount empty == 0" $ edgeCount % empty == 0 test "edgeCount (vertex x) == 0" $ \x -> edgeCount % vertex x == 0 test "edgeCount (edge x y) == 1" $ \x y -> edgeCount % edge x y == 1 test "edgeCount == length . edgeList" $ \x -> edgeCount % x == (length . edgeList) x testVertexList :: Testsuite -> IO () testVertexList (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "vertexList ============" test "vertexList empty == []" $ vertexList % empty == [] test "vertexList (vertex x) == [x]" $ \x -> vertexList % vertex x == [x] test "vertexList . vertices == nub . sort" $ \xs -> vertexList % vertices xs == (nubOrd . sort) xs testEdgeList :: Testsuite -> IO () testEdgeList (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "edgeList ============" test "edgeList empty == []" $ edgeList % empty == [] test "edgeList (vertex x) == []" $ \x -> edgeList % vertex x == [] test "edgeList (edge x y) == [(x,y)]" $ \x y -> edgeList % edge x y == [(x,y)] test "edgeList (star 2 [3,1]) == [(2,1), (2,3)]" $ edgeList % star 2 [3,1] == [(2,1), (2,3)] test "edgeList . edges == nub . sort" $ \xs -> edgeList % edges xs == (nubOrd . sort) xs testAdjacencyList :: Testsuite -> IO () testAdjacencyList (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "adjacencyList ============" test "adjacencyList empty == []" $ adjacencyList % empty == [] test "adjacencyList (vertex x) == [(x, [])]" $ \x -> adjacencyList % vertex x == [(x, [])] test "adjacencyList (edge 1 2) == [(1, [2]), (2, [])]" $ adjacencyList % edge 1 2 == [(1, [2]), (2, [])] test "adjacencyList (star 2 [3,1]) == [(1, []), (2, [1,3]), (3, [])]" $ adjacencyList % star 2 [3,1] == [(1, []), (2, [1,3]), (3, [])] testVertexSet :: Testsuite -> IO () testVertexSet (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "vertexSet ============" test "vertexSet empty == Set.empty" $ vertexSet % empty == Set.empty test "vertexSet . vertex == Set.singleton" $ \x -> vertexSet % vertex x == Set.singleton x test "vertexSet . vertices == Set.fromList" $ \xs -> vertexSet % vertices xs == Set.fromList xs test "vertexSet . clique == Set.fromList" $ \xs -> vertexSet % clique xs == Set.fromList xs testVertexIntSet :: Testsuite -> IO () testVertexIntSet (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "vertexIntSet ============" test "vertexIntSet empty == IntSet.empty" $ vertexIntSet % empty == IntSet.empty test "vertexIntSet . vertex == IntSet.singleton" $ \x -> vertexIntSet % vertex x == IntSet.singleton x test "vertexIntSet . vertices == IntSet.fromList" $ \xs -> vertexIntSet % vertices xs == IntSet.fromList xs test "vertexIntSet . clique == IntSet.fromList" $ \xs -> vertexIntSet % clique xs == IntSet.fromList xs testEdgeSet :: Testsuite -> IO () testEdgeSet (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "edgeSet ============" test "edgeSet empty == Set.empty" $ edgeSet % empty == Set.empty test "edgeSet (vertex x) == Set.empty" $ \x -> edgeSet % vertex x == Set.empty test "edgeSet (edge x y) == Set.singleton (x,y)" $ \x y -> edgeSet % edge x y == Set.singleton (x,y) test "edgeSet . edges == Set.fromList" $ \xs -> edgeSet % edges xs == Set.fromList xs testPreSet :: Testsuite -> IO () testPreSet (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "preSet ============" test "preSet x empty == Set.empty" $ \x -> preSet x % empty == Set.empty test "preSet x (vertex x) == Set.empty" $ \x -> preSet x % vertex x == Set.empty test "preSet 1 (edge 1 2) == Set.empty" $ preSet 1 % edge 1 2 == Set.empty test "preSet y (edge x y) == Set.fromList [x]" $ \x y -> preSet y % edge x y == Set.fromList [x] testPostSet :: Testsuite -> IO () testPostSet (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "postSet ============" test "postSet x empty == Set.empty" $ \x -> postSet x % empty == Set.empty test "postSet x (vertex x) == Set.empty" $ \x -> postSet x % vertex x == Set.empty test "postSet x (edge x y) == Set.fromList [y]" $ \x y -> postSet x % edge x y == Set.fromList [y] test "postSet 2 (edge 1 2) == Set.empty" $ postSet 2 % edge 1 2 == Set.empty testPostIntSet :: Testsuite -> IO () testPostIntSet (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "postIntSet ============" test "postIntSet x empty == IntSet.empty" $ \x -> postIntSet x % empty == IntSet.empty test "postIntSet x (vertex x) == IntSet.empty" $ \x -> postIntSet x % vertex x == IntSet.empty test "postIntSet x (edge x y) == IntSet.fromList [y]" $ \x y -> postIntSet x % edge x y == IntSet.fromList [y] test "postIntSet 2 (edge 1 2) == IntSet.empty" $ postIntSet 2 % edge 1 2 == IntSet.empty testPath :: Testsuite -> IO () testPath (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "path ============" test "path [] == empty" $ path [] == id % empty test "path [x] == vertex x" $ \x -> path [x] == id % vertex x test "path [x,y] == edge x y" $ \x y -> path [x,y] == id % edge x y testCircuit :: Testsuite -> IO () testCircuit (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "circuit ============" test "circuit [] == empty" $ circuit [] == id % empty test "circuit [x] == edge x x" $ \x -> circuit [x] == id % edge x x test "circuit [x,y] == edges [(x,y), (y,x)]" $ \x y -> circuit [x,y] == id % edges [(x,y), (y,x)] testClique :: Testsuite -> IO () testClique (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "clique ============" test "clique [] == empty" $ clique [] == id % empty test "clique [x] == vertex x" $ \x -> clique [x] == id % vertex x test "clique [x,y] == edge x y" $ \x y -> clique [x,y] == id % edge x y test "clique [x,y,z] == edges [(x,y), (x,z), (y,z)]" $ \x y z -> clique [x,y,z] == id % edges [(x,y), (x,z), (y,z)] test "clique (xs ++ ys) == connect (clique xs) (clique ys)" $ \xs ys -> clique (xs ++ ys) == connect (clique xs) % clique ys testBiclique :: Testsuite -> IO () testBiclique (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "biclique ============" test "biclique [] [] == empty" $ biclique [] [] == id % empty test "biclique [x] [] == vertex x" $ \x -> biclique [x] [] == id % vertex x test "biclique [] [y] == vertex y" $ \y -> biclique [] [y] == id % vertex y test "biclique [x1,x2] [y1,y2] == edges [(x1,y1), (x1,y2), (x2,y1), (x2,y2)]" $ \x1 x2 y1 y2 -> biclique [x1,x2] [y1,y2] == id % edges [(x1,y1), (x1,y2), (x2,y1), (x2,y2)] test "biclique xs ys == connect (vertices xs) (vertices ys)" $ \xs ys -> biclique xs ys == connect (vertices xs) % vertices ys testStar :: Testsuite -> IO () testStar (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "star ============" test "star x [] == vertex x" $ \x -> star x [] == id % vertex x test "star x [y] == edge x y" $ \x y -> star x [y] == id % edge x y test "star x [y,z] == edges [(x,y), (x,z)]" $ \x y z -> star x [y,z] == id % edges [(x,y), (x,z)] test "star x ys == connect (vertex x) (vertices ys)" $ \x ys -> star x ys == connect (vertex x) % (vertices ys) testStarTranspose :: Testsuite -> IO () testStarTranspose (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "starTranspose ============" test "starTranspose x [] == vertex x" $ \x -> starTranspose x [] == id % vertex x test "starTranspose x [y] == edge y x" $ \x y -> starTranspose x [y] == id % edge y x test "starTranspose x [y,z] == edges [(y,x), (z,x)]" $ \x y z -> starTranspose x [y,z] == id % edges [(y,x), (z,x)] test "starTranspose x ys == connect (vertices ys) (vertex x)" $ \x ys -> starTranspose x ys == connect (vertices ys) % (vertex x) test "starTranspose x ys == transpose (star x ys)" $ \x ys -> starTranspose x ys == transpose % (star x ys) testTree :: Testsuite -> IO () testTree (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "tree ============" test "tree (Node x []) == vertex x" $ \x -> tree (Node x []) == id % vertex x test "tree (Node x [Node y [Node z []]]) == path [x,y,z]" $ \x y z -> tree (Node x [Node y [Node z []]]) == id % path [x,y,z] test "tree (Node x [Node y [], Node z []]) == star x [y,z]" $ \x y z -> tree (Node x [Node y [], Node z []]) == id % star x [y,z] test "tree (Node 1 [Node 2 [], Node 3 [Node 4 [], Node 5 []]]) == edges [(1,2), (1,3), (3,4), (3,5)]" $ tree (Node 1 [Node 2 [], Node 3 [Node 4 [], Node 5 []]]) == id % edges [(1,2), (1,3), (3,4), (3,5)] testForest :: Testsuite -> IO () testForest (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "forest ============" test "forest [] == empty" $ forest [] == id % empty test "forest [x] == tree x" $ \x -> forest [x] == id % tree x test "forest [Node 1 [Node 2 [], Node 3 []], Node 4 [Node 5 []]] == edges [(1,2), (1,3), (4,5)]" $ forest [Node 1 [Node 2 [], Node 3 []], Node 4 [Node 5 []]] == id % edges [(1,2), (1,3), (4,5)] test "forest == overlays . map tree" $ \x -> forest x == id % (overlays . map tree) x testRemoveVertex :: Testsuite -> IO () testRemoveVertex (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "removeVertex ============" test "removeVertex x (vertex x) == empty" $ \x -> removeVertex x % vertex x == empty test "removeVertex 1 (vertex 2) == vertex 2" $ removeVertex 1 % (vertex 2) == vertex 2 test "removeVertex x (edge x x) == empty" $ \x -> removeVertex x % (edge x x) == empty test "removeVertex 1 (edge 1 2) == vertex 2" $ removeVertex 1 % (edge 1 2) == vertex 2 test "removeVertex x . removeVertex x == removeVertex x" $ \x y -> (removeVertex x . removeVertex x) y == removeVertex x % y testRemoveEdge :: Testsuite -> IO () testRemoveEdge (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "removeEdge ============" test "removeEdge x y (edge x y) == vertices [x, y]" $ \x y -> removeEdge x y % edge x y == vertices [x, y] test "removeEdge x y . removeEdge x y == removeEdge x y" $ \x y z -> (removeEdge x y . removeEdge x y) z == removeEdge x y % z test "removeEdge x y . removeVertex x == removeVertex x" $ \x y z -> (removeEdge x y . removeVertex x) z == removeVertex x % z test "removeEdge 1 1 (1 * 1 * 2 * 2) == 1 * 2 * 2" $ removeEdge 1 1 % (1 * 1 * 2 * 2) == 1 * 2 * 2 test "removeEdge 1 2 (1 * 1 * 2 * 2) == 1 * 1 + 2 * 2" $ removeEdge 1 2 % (1 * 1 * 2 * 2) == 1 * 1 + 2 * 2 -- TODO: Ouch. Generic tests are becoming awkward. We need a better way. when (prefix == "Fold." || prefix == "Graph.") $ do test "size (removeEdge x y z) <= 3 * size z" $ \x y z -> size % (removeEdge x y z) <= 3 * size z testReplaceVertex :: Testsuite -> IO () testReplaceVertex (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "replaceVertex ============" test "replaceVertex x x == id" $ \x y -> replaceVertex x x % y == y test "replaceVertex x y (vertex x) == vertex y" $ \x y -> replaceVertex x y % vertex x == vertex y test "replaceVertex x y == mergeVertices (== x) y" $ \x y z -> replaceVertex x y % z == mergeVertices (== x) y z testMergeVertices :: Testsuite -> IO () testMergeVertices (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "mergeVertices ============" test "mergeVertices (const False) x == id" $ \x y -> mergeVertices (const False) x % y == y test "mergeVertices (== x) y == replaceVertex x y" $ \x y z -> mergeVertices (== x) y % z == replaceVertex x y z test "mergeVertices even 1 (0 * 2) == 1 * 1" $ mergeVertices even 1 % (0 * 2) == 1 * 1 test "mergeVertices odd 1 (3 + 4 * 5) == 4 * 1" $ mergeVertices odd 1 % (3 + 4 * 5) == 4 * 1 testTranspose :: Testsuite -> IO () testTranspose (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "transpose ============" test "transpose empty == empty" $ transpose % empty == empty test "transpose (vertex x) == vertex x" $ \x -> transpose % vertex x == vertex x test "transpose (edge x y) == edge y x" $ \x y -> transpose % edge x y == edge y x test "transpose . transpose == id" $ mapSize (min 10) $ \x -> (transpose . transpose) % x == x test "edgeList . transpose == sort . map swap . edgeList" $ \x -> edgeList % transpose x == (sort . map swap . edgeList) x testGmap :: Testsuite -> IO () testGmap (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "gmap ============" test "gmap f empty == empty" $ \(apply -> f) -> gmap f % empty == empty test "gmap f (vertex x) == vertex (f x)" $ \(apply -> f) x -> gmap f % vertex x == vertex (f x) test "gmap f (edge x y) == edge (f x) (f y)" $ \(apply -> f) x y -> gmap f % edge x y == edge (f x) (f y) test "gmap id == id" $ \x -> gmap id % x == x test "gmap f . gmap g == gmap (f . g)" $ \(apply -> f) (apply -> g) x -> (gmap f . gmap g) x == gmap (f . g) % x testInduce :: Testsuite -> IO () testInduce (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "induce ============" test "induce (const True ) x == x" $ \x -> induce (const True ) % x == x test "induce (const False) x == empty" $ \x -> induce (const False) % x == empty test "induce (/= x) == removeVertex x" $ \x y -> induce (/= x) % y == removeVertex x y test "induce p . induce q == induce (\\x -> p x && q x)" $ \(apply -> p) (apply -> q) y -> (induce p . induce q) % y == induce (\x -> p x && q x) y test "isSubgraphOf (induce p x) x == True" $ \(apply -> p) x -> isSubgraphOf (induce p x) % x == True testSplitVertex :: Testsuite -> IO () testSplitVertex (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "splitVertex ============" test "splitVertex x [] == removeVertex x" $ \x y -> splitVertex x [] % y == removeVertex x y test "splitVertex x [x] == id" $ \x y -> splitVertex x [x] % y == y test "splitVertex x [y] == replaceVertex x y" $ \x y z -> splitVertex x [y] % z == replaceVertex x y z test "splitVertex 1 [0, 1] $ 1 * (2 + 3) == (0 + 1) * (2 + 3)" $ splitVertex 1 [0, 1] % (1 * (2 + 3)) == (0 + 1) * (2 + 3) testBind :: Testsuite -> IO () testBind (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "bind ============" test "bind empty f == empty" $ \(apply -> f) -> bind empty f == id % empty test "bind (vertex x) f == f x" $ \(apply -> f) x -> bind (vertex x) f == id % f x test "bind (edge x y) f == connect (f x) (f y)" $ \(apply -> f) x y -> bind (edge x y) f == connect (f x) % f y test "bind (vertices xs) f == overlays (map f xs)" $ mapSize (min 10) $ \xs (apply -> f) -> bind (vertices xs) f == id % overlays (map f xs) test "bind x (const empty) == empty" $ \x -> bind x (const empty) == id % empty test "bind x vertex == x" $ \x -> bind x vertex == id % x test "bind (bind x f) g == bind x (\\y -> bind (f y) g)" $ mapSize (min 10) $ \x (apply -> f) (apply -> g) -> bind (bind x f) g == bind (id % x) (\y -> bind (f y) g) testSimplify :: Testsuite -> IO () testSimplify (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "simplify ============" test "simplify == id" $ \x -> simplify % x == x test "size (simplify x) <= size x" $ \x -> size % simplify x <= size x testDfsForest :: Testsuite -> IO () testDfsForest (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "dfsForest ============" test "forest (dfsForest $ edge 1 1) == vertex 1" $ forest (dfsForest % edge 1 1) == id % vertex 1 test "forest (dfsForest $ edge 1 2) == edge 1 2" $ forest (dfsForest % edge 1 2) == id % edge 1 2 test "forest (dfsForest $ edge 2 1) == vertices [1, 2]" $ forest (dfsForest % edge 2 1) == id % vertices [1, 2] test "isSubgraphOf (forest $ dfsForest x) x == True" $ \x -> isSubgraphOf (forest $ dfsForest x) % x == True test "dfsForest . forest . dfsForest == dfsForest" $ \x -> dfsForest % forest (dfsForest x) == dfsForest % x test "dfsForest (vertices vs) == map (\\v -> Node v []) (nub $ sort vs)" $ \vs -> dfsForest % vertices vs == map (\v -> Node v []) (nub $ sort vs) test "dfsForest $ 3 * (1 + 4) * (1 + 5) == " $ dfsForest % (3 * (1 + 4) * (1 + 5)) == [ Node { rootLabel = 1 , subForest = [ Node { rootLabel = 5 , subForest = [] }]} , Node { rootLabel = 3 , subForest = [ Node { rootLabel = 4 , subForest = [] }]}] testDfsForestFrom :: Testsuite -> IO () testDfsForestFrom (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "dfsForestFrom ============" test "forest (dfsForestFrom [1] $ edge 1 1) == vertex 1" $ forest (dfsForestFrom [1] % edge 1 1) == id % vertex 1 test "forest (dfsForestFrom [1] $ edge 1 2) == edge 1 2" $ forest (dfsForestFrom [1] % edge 1 2) == id % edge 1 2 test "forest (dfsForestFrom [2] $ edge 1 2) == vertex 2" $ forest (dfsForestFrom [2] % edge 1 2) == id % vertex 2 test "forest (dfsForestFrom [3] $ edge 1 2) == empty" $ forest (dfsForestFrom [3] % edge 1 2) == id % empty test "forest (dfsForestFrom [2, 1] $ edge 1 2) == vertices [1, 2]" $ forest (dfsForestFrom [2, 1] % edge 1 2) == id % vertices [1, 2] test "isSubgraphOf (forest $ dfsForestFrom vs x) x == True" $ \vs x -> isSubgraphOf (forest $ dfsForestFrom vs x) % x == True test "dfsForestFrom (vertexList x) x == dfsForest x" $ \x -> dfsForestFrom (vertexList x) % x == dfsForest % x test "dfsForestFrom vs (vertices vs) == map (\\v -> Node v []) (nub vs)" $ \vs -> dfsForestFrom vs % vertices vs == map (\v -> Node v []) (nub vs) test "dfsForestFrom [] x == []" $ \x -> dfsForestFrom [] % x == [] test "dfsForestFrom [1, 4] $ 3 * (1 + 4) * (1 + 5) == " $ dfsForestFrom [1, 4] % (3 * (1 + 4) * (1 + 5)) == [ Node { rootLabel = 1 , subForest = [ Node { rootLabel = 5 , subForest = [] }]} , Node { rootLabel = 4 , subForest = [] }] testDfs :: Testsuite -> IO () testDfs (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "dfs ============" test "dfs [1] $ edge 1 1 == [1]" $ dfs [1] % edge 1 1 == [1] test "dfs [1] $ edge 1 2 == [1, 2]" $ dfs [1] % edge 1 2 == [1, 2] test "dfs [2] $ edge 1 2 == [2]" $ dfs [2] % edge 1 2 == [2] test "dfs [3] $ edge 1 2 == []" $ dfs [3] % edge 1 2 == [] test "dfs [1, 2] $ edge 1 2 == [1, 2]" $ dfs [1, 2] % edge 1 2 == [1, 2] test "dfs [2, 1] $ edge 1 2 == [2, 1]" $ dfs [2, 1] % edge 1 2 == [2, 1] test "dfs [] $ x == []" $ \x -> dfs [] % x == [] test "dfs [1, 4] $ 3 * (1 + 4) * (1 + 5) == [1, 5, 4]" $ dfs [1, 4] % (3 * (1 + 4) * (1 + 5)) == [1, 5, 4] test "isSubgraphOf (vertices $ dfs vs x) x == True" $ \vs x -> isSubgraphOf (vertices $ dfs vs x) % x == True testTopSort :: Testsuite -> IO () testTopSort (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "topSort ============" test "topSort (1 * 2 + 3 * 1) == Just [3,1,2]" $ topSort % (1 * 2 + 3 * 1) == Just [3,1,2] test "topSort (1 * 2 + 2 * 1) == Nothing" $ topSort % (1 * 2 + 2 * 1) == Nothing test "fmap (flip isTopSort x) (topSort x) /= Just False" $ \x -> fmap (flip isTopSort x) (topSort % x) /= Just False testIsTopSort :: Testsuite -> IO () testIsTopSort (Testsuite prefix (%)) = do putStrLn $ "\n============ " ++ prefix ++ "isTopSort ============" test "isTopSort [3, 1, 2] (1 * 2 + 3 * 1) == True" $ isTopSort [3, 1, 2] % (1 * 2 + 3 * 1) == True test "isTopSort [1, 2, 3] (1 * 2 + 3 * 1) == False" $ isTopSort [1, 2, 3] % (1 * 2 + 3 * 1) == False test "isTopSort [] (1 * 2 + 3 * 1) == False" $ isTopSort [] % (1 * 2 + 3 * 1) == False test "isTopSort [] empty == True" $ isTopSort [] % empty == True test "isTopSort [x] (vertex x) == True" $ \x -> isTopSort [x] % vertex x == True test "isTopSort [x] (edge x x) == False" $ \x -> isTopSort [x] % edge x x == False