content: {-# LANGUAGE OverloadedLists, ViewPatterns #-}
  -----------------------------------------------------------------------------
  -- |
  -- Module     : Algebra.Graph.Test.Bipartite.AdjacencyMap
  -- Copyright  : (c) Andrey Mokhov 2016-2025
  -- License    : MIT (see the file LICENSE)
  -- Maintainer : andrey.mokhov@gmail.com
  -- Stability  : experimental
  --
  -- Testsuite for "Algebra.Graph.Bipartite.AdjacencyMap".
  -----------------------------------------------------------------------------
  module Algebra.Graph.Test.Bipartite.AdjacencyMap (
      -- * Testsuite
      testBipartiteAdjacencyMap,
      testBipartiteAdjacencyMapAlgorithm
      ) where
  
  import Algebra.Graph.Bipartite.AdjacencyMap
  import Algebra.Graph.Bipartite.AdjacencyMap.Algorithm
  import Algebra.Graph.Test
  import Data.Either
  import Data.Either.Extra
  import Data.List (nub)
  import Data.Map.Strict (Map)
  import Data.Set (Set)
  
  import qualified Algebra.Graph.AdjacencyMap           as AM
  import qualified Algebra.Graph.Bipartite.AdjacencyMap as B
  import qualified Data.Bifunctor                       as Bifunctor
  import qualified Data.Map.Strict                      as Map
  import qualified Data.Set                             as Set
  import qualified Data.Tuple
  
  type AI   = AM.AdjacencyMap Int
  type AII  = AM.AdjacencyMap (Either Int Int)
  type BAII = AdjacencyMap Int Int
  type MII  = Matching Int Int
  type MIC  = Matching Int Char
  type LII  = List Int Int
  
  testBipartiteAdjacencyMap :: IO ()
  testBipartiteAdjacencyMap = do
      -- Help with type inference by shadowing overly polymorphic functions
      let consistent :: BAII -> Bool
          consistent = B.consistent
          show :: BAII -> String
          show = Prelude.show
          leftAdjacencyMap :: BAII -> Map Int (Set Int)
          leftAdjacencyMap = B.leftAdjacencyMap
          rightAdjacencyMap :: BAII -> Map Int (Set Int)
          rightAdjacencyMap = B.rightAdjacencyMap
          leftAdjacencyList :: BAII -> [(Int, [Int])]
          leftAdjacencyList = B.leftAdjacencyList
          rightAdjacencyList :: BAII -> [(Int, [Int])]
          rightAdjacencyList = B.rightAdjacencyList
          empty :: BAII
          empty = B.empty
          vertex :: Either Int Int -> BAII
          vertex = B.vertex
          leftVertex :: Int -> BAII
          leftVertex = B.leftVertex
          rightVertex :: Int -> BAII
          rightVertex = B.rightVertex
          edge :: Int -> Int -> BAII
          edge = B.edge
          isEmpty :: BAII -> Bool
          isEmpty = B.isEmpty
          hasLeftVertex :: Int -> BAII -> Bool
          hasLeftVertex = B.hasLeftVertex
          hasRightVertex :: Int -> BAII -> Bool
          hasRightVertex = B.hasRightVertex
          hasVertex :: Either Int Int -> BAII -> Bool
          hasVertex = B.hasVertex
          hasEdge :: Int -> Int -> BAII -> Bool
          hasEdge = B.hasEdge
          vertexCount :: BAII -> Int
          vertexCount = B.vertexCount
          edgeCount :: BAII -> Int
          edgeCount = B.edgeCount
          vertices :: [Int] -> [Int] -> BAII
          vertices = B.vertices
          edges :: [(Int, Int)] -> BAII
          edges = B.edges
          overlays :: [BAII] -> BAII
          overlays = B.overlays
          connects :: [BAII] -> BAII
          connects = B.connects
          swap :: BAII -> BAII
          swap = B.swap
          toBipartite :: AII -> BAII
          toBipartite = B.toBipartite
          toBipartiteWith :: Ord a => (a -> Either Int Int) -> AM.AdjacencyMap a -> BAII
          toBipartiteWith = B.toBipartiteWith
          fromBipartite :: BAII -> AII
          fromBipartite = B.fromBipartite
          biclique :: [Int] -> [Int] -> BAII
          biclique = B.biclique
          star :: Int -> [Int] -> BAII
          star = B.star
          stars :: [(Int, [Int])] -> BAII
          stars = B.stars
          removeLeftVertex :: Int -> BAII -> BAII
          removeLeftVertex = B.removeLeftVertex
          removeRightVertex :: Int -> BAII -> BAII
          removeRightVertex = B.removeRightVertex
          removeEdge :: Int -> Int -> BAII -> BAII
          removeEdge = B.removeEdge
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Num ============"
      test "0                     == rightVertex 0" $
            0                     == rightVertex 0
      test "swap 1                == leftVertex 1" $
            swap 1                == leftVertex 1
      test "swap 1 + 2            == vertices [1] [2]" $
            swap 1 + 2            == vertices [1] [2]
      test "swap 1 * 2            == edge 1 2" $
            swap 1 * 2            == edge 1 2
      test "swap 1 + 2 * swap 3   == overlay (leftVertex 1) (edge 3 2)" $
            swap 1 + 2 * swap 3   == overlay (leftVertex 1) (edge 3 2)
      test "swap 1 * (2 + swap 3) == connect (leftVertex 1) (vertices [3] [2])" $
            swap 1 * (2 + swap 3) == connect (leftVertex 1) (vertices [3] [2])
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Show ============"
      test "show empty                 == \"empty\"" $
            show empty                 == "empty"
      test "show 1                     == \"rightVertex 1\"" $
            show 1                     == "rightVertex 1"
      test "show (swap 2)              == \"leftVertex 2\"" $
            show (swap 2)              == "leftVertex 2"
      test "show 1 + 2                 == \"vertices [] [1,2]\"" $
            show (1 + 2)               == "vertices [] [1,2]"
      test "show (swap (1 + 2))        == \"vertices [1,2] []\"" $
            show (swap (1 + 2))        == "vertices [1,2] []"
      test "show (swap 1 * 2)          == \"edge 1 2\"" $
            show (swap 1 * 2)          == "edge 1 2"
      test "show (swap 1 * 2 * swap 3) == \"edges [(1,2),(3,2)]\"" $
            show (swap 1 * 2 * swap 3) == "edges [(1,2),(3,2)]"
      test "show (swap 1 * 2 + swap 3) == \"overlay (leftVertex 3) (edge 1 2)\"" $
            show (swap 1 * 2 + swap 3) == "overlay (leftVertex 3) (edge 1 2)"
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Eq ============"
      test "(x == y) == (leftAdjacencyMap x == leftAdjacencyMap y && rightAdjacencyMap x == rightAdjacencyMap y)" $ \(x :: BAII) (y :: BAII) ->
            (x == y) == (leftAdjacencyMap x == leftAdjacencyMap y && rightAdjacencyMap x == rightAdjacencyMap y)
  
      putStrLn ""
      test "        x + y == y + x" $ \(x :: BAII) y ->
                    x + y == y + x
      test "  x + (y + z) == (x + y) + z" $ \(x :: BAII) y z ->
              x + (y + z) == (x + y) + z
      test "    x * empty == x" $ \(x :: BAII) ->
                x * empty == x
      test "    empty * x == x" $ \(x :: BAII) ->
                empty * x == x
      test "        x * y == y * x" $ \(x :: BAII) y ->
                    x * y == y * x
      test "  x * (y * z) == (x * y) * z" $ size10 $ \(x :: BAII) y z ->
              x * (y * z) == (x * y) * z
      test "  x * (y + z) == x * y + x * z" $ size10 $ \(x :: BAII) y z ->
              x * (y + z) == x * (y + z)
      test "  (x + y) * z == x * z + y * z" $ size10 $ \(x :: BAII) y z ->
              (x + y) * z == x * z + y * z
      test "    x * y * z == x * y + x * z + y * z" $ size10 $ \(x :: BAII) y z ->
                x * y * z == x * y + x * z + y * z
      test "    x + empty == x" $ \(x :: BAII) ->
                x + empty == x
      test "    empty + x == x" $ \(x :: BAII) ->
                empty + x == x
      test "        x + x == x" $ \(x :: BAII) ->
                    x + x == x
      test "x * y + x + y == x * y" $ \(x :: BAII) (y :: BAII) ->
            x * y + x + y == x * y
      test "    x * x * x == x * x" $ size10 $ \(x :: BAII) ->
                x * x * x == x * x
  
      putStrLn ""
      test " leftVertex x * leftVertex y  ==  leftVertex x + leftVertex y " $ \x y ->
             leftVertex x * leftVertex y  ==  leftVertex x + leftVertex y
      test "rightVertex x * rightVertex y == rightVertex x + rightVertex y" $ \x y ->
            rightVertex x * rightVertex y == rightVertex x + rightVertex y
  
      putStrLn "\n============ Bipartite.AdjacencyMap.leftAdjacencyMap ============"
      test "leftAdjacencyMap empty           == Map.empty" $
            leftAdjacencyMap empty           == Map.empty
      test "leftAdjacencyMap (leftVertex x)  == Map.singleton x Set.empty" $ \x ->
            leftAdjacencyMap (leftVertex x)  == Map.singleton x Set.empty
      test "leftAdjacencyMap (rightVertex x) == Map.empty" $ \x ->
            leftAdjacencyMap (rightVertex x) == Map.empty
      test "leftAdjacencyMap (edge x y)      == Map.singleton x (Set.singleton y)" $ \x y ->
            leftAdjacencyMap (edge x y)      == Map.singleton x (Set.singleton y)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.rightAdjacencyMap ============"
      test "rightAdjacencyMap empty           == Map.empty" $
            rightAdjacencyMap empty           == Map.empty
      test "rightAdjacencyMap (leftVertex x)  == Map.empty" $ \x ->
            rightAdjacencyMap (leftVertex x)  == Map.empty
      test "rightAdjacencyMap (rightVertex x) == Map.singleton x Set.empty" $ \x ->
            rightAdjacencyMap (rightVertex x) == Map.singleton x Set.empty
      test "rightAdjacencyMap (edge x y)      == Map.singleton y (Set.singleton x)" $ \x y ->
            rightAdjacencyMap (edge x y)      == Map.singleton y (Set.singleton x)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.empty ============"
      test "isEmpty empty           == True" $
            isEmpty empty           == True
      test "leftAdjacencyMap empty  == Map.empty" $
            leftAdjacencyMap empty  == Map.empty
      test "rightAdjacencyMap empty == Map.empty" $
            rightAdjacencyMap empty == Map.empty
      test "hasVertex x empty       == False" $ \x ->
            hasVertex x empty       == False
  
      putStrLn "\n============ Bipartite.AdjacencyMap.leftVertex ============"
      test "leftAdjacencyMap (leftVertex x)  == Map.singleton x Set.empty" $ \x ->
            leftAdjacencyMap (leftVertex x)  == Map.singleton x Set.empty
      test "rightAdjacencyMap (leftVertex x) == Map.empty" $ \x ->
            rightAdjacencyMap (leftVertex x) == Map.empty
      test "hasLeftVertex x (leftVertex y)   == (x == y)" $ \x y ->
            hasLeftVertex x (leftVertex y)   == (x == y)
      test "hasRightVertex x (leftVertex y)  == False" $ \x y ->
            hasRightVertex x (leftVertex y)  == False
      test "hasEdge x y (leftVertex z)       == False" $ \x y z ->
            hasEdge x y (leftVertex z)       == False
  
      putStrLn "\n============ Bipartite.AdjacencyMap.rightVertex ============"
      test "leftAdjacencyMap (rightVertex x)  == Map.empty" $ \x ->
            leftAdjacencyMap (rightVertex x)  == Map.empty
      test "rightAdjacencyMap (rightVertex x) == Map.singleton x Set.empty" $  \x ->
            rightAdjacencyMap (rightVertex x) == Map.singleton x Set.empty
      test "hasLeftVertex x (rightVertex y)   == False" $ \x y ->
            hasLeftVertex x (rightVertex y)   == False
      test "hasRightVertex x (rightVertex y)  == (x == y)" $ \x y ->
            hasRightVertex x (rightVertex y)  == (x == y)
      test "hasEdge x y (rightVertex z)       == False" $ \x y z ->
            hasEdge x y (rightVertex z)       == False
  
      putStrLn "\n============ Bipartite.AdjacencyMap.vertex ============"
      test "vertex . Left  == leftVertex" $ \x ->
           (vertex . Left) x == leftVertex x
      test "vertex . Right == rightVertex" $ \x ->
           (vertex . Right) x == rightVertex x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.edge ============"
      test "edge x y                     == connect (leftVertex x) (rightVertex y)" $ \x y ->
            edge x y                     == connect (leftVertex x) (rightVertex y)
      test "leftAdjacencyMap (edge x y)  == Map.singleton x (Set.singleton y)" $ \x y ->
            leftAdjacencyMap (edge x y)  == Map.singleton x (Set.singleton y)
      test "rightAdjacencyMap (edge x y) == Map.singleton y (Set.singleton x)" $ \x y ->
            rightAdjacencyMap (edge x y) == Map.singleton y (Set.singleton x)
      test "hasEdge x y (edge x y)       == True" $ \x y ->
            hasEdge x y (edge x y)       == True
      test "hasEdge 1 2 (edge 2 1)       == False" $
            hasEdge 1 2 (edge 2 1)       == False
  
      putStrLn "\n============ Bipartite.AdjacencyMap.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
  
      putStrLn "\n============ Bipartite.AdjacencyMap.connect ============"
      test "connect (leftVertex x)     (leftVertex y)     == vertices [x,y] []" $ \x y ->
            connect (leftVertex x)     (leftVertex y)     == vertices [x,y] []
      test "connect (leftVertex x)     (rightVertex y)    == edge x y" $ \x y ->
            connect (leftVertex x)     (rightVertex y)    == edge x y
      test "connect (rightVertex x)    (leftVertex y)     == edge y x" $ \x y ->
            connect (rightVertex x)    (leftVertex y)     == edge y x
      test "connect (rightVertex x)    (rightVertex y)    == vertices [] [x,y]" $ \x y ->
            connect (rightVertex x)    (rightVertex y)    == vertices [] [x,y]
      test "connect (vertices xs1 ys1) (vertices xs2 ys2) == overlay (biclique xs1 ys2) (biclique xs2 ys1)" $ \xs1 ys1 xs2 ys2 ->
            connect (vertices xs1 ys1) (vertices xs2 ys2) == overlay (biclique xs1 ys2) (biclique xs2 ys1)
      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)                     >= leftVertexCount x * rightVertexCount y" $ \x y ->
            edgeCount   (connect x y)                     >= leftVertexCount x * rightVertexCount y
      test "edgeCount   (connect x y)                     <= leftVertexCount x * rightVertexCount y + rightVertexCount x * leftVertexCount y + edgeCount x + edgeCount y" $ \x y ->
            edgeCount   (connect x y)                     <= leftVertexCount x * rightVertexCount y + rightVertexCount x * leftVertexCount y + edgeCount x + edgeCount y
  
      putStrLn "\n============ Bipartite.AdjacencyMap.vertices ============"
      test "vertices [] []                    == empty" $
            vertices [] []                    == empty
      test "vertices [x] []                   == leftVertex x" $ \x ->
            vertices [x] []                   == leftVertex x
      test "vertices [] [x]                   == rightVertex x" $ \x ->
            vertices [] [x]                   == rightVertex x
      test "vertices xs ys                    == overlays (map leftVertex xs ++ map rightVertex ys)" $ \xs ys ->
            vertices xs ys                    == overlays (map leftVertex xs ++ map rightVertex ys)
      test "hasLeftVertex  x (vertices xs ys) == elem x xs" $ \x xs ys ->
            hasLeftVertex  x (vertices xs ys) == elem x xs
      test "hasRightVertex y (vertices xs ys) == elem y ys" $ \y xs ys ->
            hasRightVertex y (vertices xs ys) == elem y ys
  
      putStrLn "\n============ Bipartite.AdjacencyMap.edges ============"
      test "edges []            == empty" $
            edges []            == empty
      test "edges [(x,y)]       == edge x y" $ \x y ->
            edges [(x,y)]       == edge x y
      test "edges               == overlays . map (uncurry edge)" $ \xs ->
            edges xs            == (overlays . map (uncurry edge)) xs
      test "hasEdge x y . edges == elem (x,y)" $ \x y es ->
           (hasEdge x y . edges) es == elem (x,y) es
      test "edgeCount   . edges == length . nub" $ \es ->
           (edgeCount   . edges) es == (length . nubOrd) es
  
      putStrLn "\n============ Bipartite.AdjacencyMap.overlays ============"
      test "overlays []        == empty" $
            overlays []        == empty
      test "overlays [x]       == x" $ \x ->
            overlays [x]       == x
      test "overlays [x,y]     == overlay x y" $ \x y ->
            overlays [x,y]     == overlay x y
      test "overlays           == foldr overlay empty" $ size10 $ \xs ->
            overlays xs        == foldr overlay empty xs
      test "isEmpty . overlays == all isEmpty" $ size10 $ \xs ->
           (isEmpty . overlays) xs == all isEmpty xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.connects ============"
      test "connects []        == empty" $
            connects []        == empty
      test "connects [x]       == x" $ \x ->
            connects [x]       == x
      test "connects [x,y]     == connect x y" $ \x y ->
            connects [x,y]     == connect x y
      test "connects           == foldr connect empty" $ size10 $ \xs ->
            connects xs        == foldr connect empty xs
      test "isEmpty . connects == all isEmpty" $ size10 $ \ xs ->
           (isEmpty . connects) xs == all isEmpty xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.swap ============"
      test "swap empty            == empty" $
            swap empty            == empty
      test "swap . leftVertex     == rightVertex" $ \x ->
           (swap . leftVertex) x  == rightVertex x
      test "swap (vertices xs ys) == vertices ys xs" $ \xs ys ->
            swap (vertices xs ys) == vertices ys xs
      test "swap (edge x y)       == edge y x" $ \x y ->
            swap (edge x y)       == edge y x
      test "swap . edges          == edges . map Data.Tuple.swap" $ \es ->
           (swap . edges) es      == (edges . map Data.Tuple.swap) es
      test "swap . swap           == id" $ \x ->
           (swap . swap) x        == x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.toBipartite ============"
      test "toBipartite empty                      == empty" $
            toBipartite AM.empty                   == empty
      test "toBipartite (vertex (Left x))          == leftVertex x" $ \x ->
            toBipartite (AM.vertex (Left x))       == leftVertex x
      test "toBipartite (vertex (Right x))         == rightVertex x" $ \x ->
            toBipartite (AM.vertex (Right x))      == rightVertex x
      test "toBipartite (edge (Left x) (Left y))   == vertices [x,y] []" $ \x y ->
            toBipartite (AM.edge (Left x) (Left y)) == vertices [x,y] []
      test "toBipartite (edge (Left x) (Right y))  == edge x y" $ \x y ->
            toBipartite (AM.edge (Left x) (Right y)) == edge x y
      test "toBipartite (edge (Right x) (Left y))  == edge y x" $ \x y ->
            toBipartite (AM.edge (Right x) (Left y)) == edge y x
      test "toBipartite (edge (Right x) (Right y)) == vertices [] [x,y]" $ \x y ->
            toBipartite (AM.edge (Right x) (Right y)) == vertices [] [x,y]
      test "toBipartite . clique                   == uncurry biclique . partitionEithers" $ \xs ->
           (toBipartite . AM.clique) xs            == (uncurry biclique . partitionEithers) xs
      test "toBipartite . fromBipartite            == id" $ \x ->
           (toBipartite . fromBipartite) x         == x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.toBipartiteWith ============"
      test "toBipartiteWith f empty == empty" $ \(apply -> f) ->
            toBipartiteWith f (AM.empty :: AII) == empty
      test "toBipartiteWith Left x  == vertices (vertexList x) []" $ \x ->
            toBipartiteWith Left x  == vertices (AM.vertexList x) []
      test "toBipartiteWith Right x == vertices [] (vertexList x)" $ \x ->
            toBipartiteWith Right x == vertices [] (AM.vertexList x)
      test "toBipartiteWith f       == toBipartite . gmap f" $ \(apply -> f) x ->
            toBipartiteWith f x     == (toBipartite . AM.gmap f) (x :: AII)
      test "toBipartiteWith id      == toBipartite" $ \x ->
            toBipartiteWith id x    == toBipartite x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.fromBipartite ============"
      test "fromBipartite empty          == empty" $
            fromBipartite empty          == AM.empty
      test "fromBipartite (leftVertex x) == vertex (Left x)" $ \x ->
            fromBipartite (leftVertex x) == AM.vertex (Left x)
      test "fromBipartite (edge x y)     == edges [(Left x, Right y), (Right y, Left x)]" $ \x y ->
            fromBipartite (edge x y)     == AM.edges [(Left x, Right y), (Right y, Left x)]
  
      putStrLn "\n============ Bipartite.AdjacencyMap.fromBipartiteWith ============"
      test "fromBipartiteWith Left Right             == fromBipartite" $ \x ->
            fromBipartiteWith Left Right x           == fromBipartite x
      test "fromBipartiteWith id id (vertices xs ys) == vertices (xs ++ ys)" $ \xs ys ->
            fromBipartiteWith id id (vertices xs ys) == AM.vertices (xs ++ ys)
      test "fromBipartiteWith id id . edges          == symmetricClosure . edges" $ \xs ->
           (fromBipartiteWith id id . edges) xs      == (AM.symmetricClosure . AM.edges) xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.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                       == (==) empty" $ \x ->
            isEmpty x                     == (==) empty x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.hasLeftVertex ============"
      test "hasLeftVertex x empty           == False" $ \x ->
            hasLeftVertex x empty           == False
      test "hasLeftVertex x (leftVertex y)  == (x == y)" $ \x y ->
            hasLeftVertex x (leftVertex y)  == (x == y)
      test "hasLeftVertex x (rightVertex y) == False" $ \x y ->
            hasLeftVertex x (rightVertex y) == False
  
      putStrLn "\n============ Bipartite.AdjacencyMap.hasRightVertex ============"
      test "hasRightVertex x empty           == False" $ \x ->
            hasRightVertex x empty           == False
      test "hasRightVertex x (leftVertex y)  == False" $ \x y ->
            hasRightVertex x (leftVertex y)  == False
      test "hasRightVertex x (rightVertex y) == (x == y)" $ \x y ->
            hasRightVertex x (rightVertex y) == (x == y)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.hasVertex ============"
      test "hasVertex . Left  == hasLeftVertex" $ \x y ->
           (hasVertex . Left) x y == hasLeftVertex x y
      test "hasVertex . Right == hasRightVertex" $ \x y ->
           (hasVertex . Right) x y == hasRightVertex x y
  
      putStrLn "\n============ Bipartite.AdjacencyMap.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            == elem (x,y) . edgeList" $ \x y z -> do
          let es = edgeList z
          (x, y) <- elements ((x, y) : es)
          return $ hasEdge x y z == elem (x, y) es
  
      putStrLn "\n============ Bipartite.AdjacencyMap.leftVertexCount ============"
      test "leftVertexCount empty           == 0" $
            leftVertexCount empty           == 0
      test "leftVertexCount (leftVertex x)  == 1" $ \x ->
            leftVertexCount (leftVertex x)  == 1
      test "leftVertexCount (rightVertex x) == 0" $ \x ->
            leftVertexCount (rightVertex x) == 0
      test "leftVertexCount (edge x y)      == 1" $ \x y ->
            leftVertexCount (edge x y)      == 1
      test "leftVertexCount . edges         == length . nub . map fst" $ \xs ->
           (leftVertexCount . edges) xs     == (length . nub . map fst) xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.rightVertexCount ============"
      test "rightVertexCount empty           == 0" $
            rightVertexCount empty           == 0
      test "rightVertexCount (leftVertex x)  == 0" $ \x ->
            rightVertexCount (leftVertex x)  == 0
      test "rightVertexCount (rightVertex x) == 1" $ \x ->
            rightVertexCount (rightVertex x) == 1
      test "rightVertexCount (edge x y)      == 1" $ \x y ->
            rightVertexCount (edge x y)      == 1
      test "rightVertexCount . edges         == length . nub . map snd" $ \xs ->
           (rightVertexCount . edges) xs     == (length . nub . map snd) xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.vertexCount ============"
      test "vertexCount empty      == 0" $
            vertexCount empty      == 0
      test "vertexCount (vertex x) == 1" $ \x ->
            vertexCount (vertex x) == 1
      test "vertexCount (edge x y) == 2" $ \x y ->
            vertexCount (edge x y) == 2
      test "vertexCount x          == leftVertexCount x + rightVertexCount x" $ \x ->
            vertexCount x          == leftVertexCount x + rightVertexCount x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.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 . edges    == length . nub" $ \xs ->
           (edgeCount . edges) xs == (length . nubOrd) xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.leftVertexList ============"
      test "leftVertexList empty              == []" $
            leftVertexList empty              == []
      test "leftVertexList (leftVertex x)     == [x]" $ \x ->
            leftVertexList (leftVertex x)     == [x]
      test "leftVertexList (rightVertex x)    == []" $ \x ->
            leftVertexList (rightVertex x)    == []
      test "leftVertexList . flip vertices [] == nub . sort" $ \xs ->
           (leftVertexList . flip vertices []) xs == (nubOrd . sort) xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.rightVertexList ============"
      test "rightVertexList empty           == []" $
            rightVertexList empty           == []
      test "rightVertexList (leftVertex x)  == []" $ \x ->
            rightVertexList (leftVertex x)  == []
      test "rightVertexList (rightVertex x) == [x]" $ \x ->
            rightVertexList (rightVertex x) == [x]
      test "rightVertexList . vertices []   == nub . sort" $ \xs ->
           (rightVertexList . vertices []) xs == (nubOrd . sort) xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.vertexList ============"
      test "vertexList empty                             == []" $
            vertexList empty                             == []
      test "vertexList (vertex x)                        == [x]" $ \x ->
            vertexList (vertex x)                        == [x]
      test "vertexList (edge x y)                        == [Left x, Right y]" $ \x y ->
            vertexList (edge x y)                        == [Left x, Right y]
      test "vertexList (vertices (lefts xs) (rights xs)) == nub (sort xs)" $ \xs ->
            vertexList (vertices (lefts xs) (rights xs)) == nubOrd (sort xs)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.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 . edges    == nub . sort" $ \xs ->
           (edgeList . edges) xs == (nubOrd . sort) xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.leftVertexSet ============"
      test "leftVertexSet empty              == Set.empty" $
            leftVertexSet empty              == Set.empty
      test "leftVertexSet . leftVertex       == Set.singleton" $ \x ->
           (leftVertexSet . leftVertex) x    == Set.singleton x
      test "leftVertexSet . rightVertex      == const Set.empty" $ \x ->
           (leftVertexSet . rightVertex) x   == const Set.empty x
      test "leftVertexSet . flip vertices [] == Set.fromList" $ \xs ->
           (leftVertexSet . flip vertices []) xs == Set.fromList xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.rightVertexSet ============"
      test "rightVertexSet empty         == Set.empty" $
            rightVertexSet empty         == Set.empty
      test "rightVertexSet . leftVertex  == const Set.empty" $ \x ->
           (rightVertexSet . leftVertex) x == const Set.empty x
      test "rightVertexSet . rightVertex == Set.singleton" $ \x ->
           (rightVertexSet . rightVertex) x == Set.singleton x
      test "rightVertexSet . vertices [] == Set.fromList" $ \xs ->
           (rightVertexSet . vertices []) xs == Set.fromList xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.vertexSet ============"
      test "vertexSet empty                             == Set.empty" $
            vertexSet empty                             == Set.empty
      test "vertexSet . vertex                          == Set.singleton" $ \x ->
           (vertexSet . vertex) x                       == Set.singleton x
      test "vertexSet (edge x y)                        == Set.fromList [Left x, Right y]" $ \x y ->
            vertexSet (edge x y)                        == Set.fromList [Left x, Right y]
      test "vertexSet (vertices (lefts xs) (rights xs)) == Set.fromList xs" $ \xs ->
            vertexSet (vertices (lefts xs) (rights xs)) == Set.fromList xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.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
  
      putStrLn "\n============ Bipartite.AdjacencyMap.leftAdjacencyList ============"
      test "leftAdjacencyList empty            == []" $
            leftAdjacencyList empty            == []
      test "leftAdjacencyList (vertices [] xs) == []" $ \xs ->
            leftAdjacencyList (vertices [] xs) == []
      test "leftAdjacencyList (vertices xs []) == []" $ \xs ->
            leftAdjacencyList (vertices xs []) == [(x, []) | x <- nubOrd (sort xs)]
      test "leftAdjacencyList (edge x y)       == [(x, [y])]" $ \x y ->
            leftAdjacencyList (edge x y)       == [(x, [y])]
      test "leftAdjacencyList (star x ys)      == [(x, nub (sort ys))]" $ \x ys ->
            leftAdjacencyList (star x ys)      == [(x, nubOrd (sort ys))]
  
      putStrLn "\n============ Bipartite.AdjacencyMap.rightAdjacencyList ============"
      test "rightAdjacencyList empty            == []" $
            rightAdjacencyList empty            == []
      test "rightAdjacencyList (vertices [] xs) == [(x, []) | x <- nub (sort xs)]" $ \xs ->
            rightAdjacencyList (vertices [] xs) == [(x, []) | x <- nubOrd (sort xs)]
      test "rightAdjacencyList (vertices xs []) == []" $ \xs ->
            rightAdjacencyList (vertices xs []) == []
      test "rightAdjacencyList (edge x y)       == [(y, [x])]" $ \x y ->
            rightAdjacencyList (edge x y)       == [(y, [x])]
      test "rightAdjacencyList (star x ys)      == [(y, [x])  | y <- nub (sort ys)]" $ \x ys ->
            rightAdjacencyList (star x ys)      == [(y, [x])  | y <- nubOrd (sort ys)]
  
      putStrLn "\n============ Bipartite.AdjacencyMap.evenList ============"
      test "evenList []                 == Nil" $
            evenList []                 == Nil @Int @Int
      test "evenList [(1,2), (3,4)]     == [1, 2, 3, 4] :: List Int Int" $
            evenList [(1,2), (3,4)]     == ([1, 2, 3, 4] :: List Int Int)
      test "evenList [(1,'a'), (2,'b')] == Cons 1 (Cons 'a' (Cons 2 (Cons 'b' Nil)))" $
            evenList [(1,'a'), (2 :: Int,'b')] == Cons 1 (Cons 'a' (Cons 2 (Cons 'b' Nil)))
  
      putStrLn "\n============ Bipartite.AdjacencyMap.oddList ============"
      test "oddList 1 []                 == Cons 1 Nil" $
            oddList 1 []                 == Cons 1 (Nil @Int @Int)
      test "oddList 1 [(2,3), (4,5)]     == [1, 2, 3, 4, 5] :: List Int Int" $
            oddList 1 [(2,3), (4,5)]     ==([1, 2, 3, 4, 5] :: List Int Int)
      test "oddList 1 [('a',2), ('b',3)] == Cons 1 (Cons 'a' (Cons 2 (Cons 'b' (Cons 3 Nil))))" $
            oddList 1 [('a',2), ('b',3)] == Cons 1 (Cons 'a' (Cons 2 (Cons 'b' (Cons @Int 3 Nil))))
  
      putStrLn "\n============ Bipartite.AdjacencyMap.path ============"
      test "path Nil                   == empty" $
            path Nil                   == empty
      test "path (Cons x Nil)          == leftVertex x" $ \x ->
            path (Cons x Nil)          == leftVertex x
      test "path (Cons x (Cons y Nil)) == edge x y" $ \x y ->
            path (Cons x (Cons y Nil)) == edge x y
      test "path [1, 2, 3, 4, 5]       == edges [(1,2), (3,2), (3,4), (5,4)]" $
            path [1, 2, 3, 4, 5]       == edges [(1,2), (3,2), (3,4), (5,4)]
  
      putStrLn "\n============ Bipartite.AdjacencyMap.circuit ============"
      test "circuit []                    == empty" $
            circuit []                    == empty
      test "circuit [(x,y)]               == edge x y" $ \x y ->
            circuit [(x,y)]               == edge x y
      test "circuit [(1,2), (3,4), (5,6)] == edges [(1,2), (3,2), (3,4), (5,4), (5,6), (1,6)]" $
            circuit [(1,2), (3,4), (5,6)] == edges [(1,2), (3,2), (3,4), (5,4), (5,6), (1,6)]
      test "circuit . reverse             == swap . circuit . map Data.Tuple.swap" $ \xs ->
           (circuit . reverse) xs         == (swap . circuit . map Data.Tuple.swap) xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.biclique ============"
      test "biclique [] [] == empty" $
            biclique [] [] == empty
      test "biclique xs [] == vertices xs []" $ \xs ->
            biclique xs [] == vertices xs []
      test "biclique [] ys == vertices [] ys" $ \ys ->
            biclique [] ys == vertices [] ys
      test "biclique xs ys == connect (vertices xs []) (vertices [] ys)" $ \xs ys ->
            biclique xs ys == connect (vertices xs []) (vertices [] ys)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.star ============"
      test "star x []    == leftVertex x" $ \x ->
            star x []    == leftVertex x
      test "star x [y]   == edge x y" $ \x y ->
            star x [y]   == edge x y
      test "star x [y,z] == edges [(x,y), (x,z)]" $ \x y z ->
            star x [y,z] == edges [(x,y), (x,z)]
      test "star x ys    == connect (leftVertex x) (vertices [] ys)" $ \x ys ->
            star x ys    == connect (leftVertex x) (vertices [] ys)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.stars ============"
      test "stars []                      == empty" $
            stars []                      == empty
      test "stars [(x, [])]               == leftVertex x" $ \x ->
            stars [(x, [])]               == leftVertex x
      test "stars [(x, [y])]              == edge x y" $ \x y ->
            stars [(x, [y])]              == edge x y
      test "stars [(x, ys)]               == star x ys" $ \x ys ->
            stars [(x, ys)]               == star x ys
      test "star x [y,z]                  == edges [(x,y), (x,z)]" $ \x y z ->
            star x [y,z]                  == edges [(x,y), (x,z)]
      test "stars                         == overlays . map (uncurry star)" $ \xs ->
            stars xs                      == (overlays . map (uncurry star)) xs
      test "overlay (stars xs) (stars ys) == stars (xs ++ ys)" $ \xs ys ->
            overlay (stars xs) (stars ys) == stars (xs ++ ys)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.mesh ============"
      test "mesh xs []           == empty" $ \xs ->
            mesh xs []           == B.empty @(Int,Int)
      test "mesh [] ys           == empty" $ \ys ->
            mesh [] ys           == B.empty @(Int,Int)
      test "mesh [x] [y]         == leftVertex (x,y)" $ \x y ->
            mesh [x] [y]         == B.leftVertex @(Int,Int) (x,y)
      test "mesh [1,1] ['a','b'] == biclique [(1,'a'), (1,'b')] [(1,'a'), (1,'b')]" $
            mesh [1,1] ['a','b'] == B.biclique @(Int,Char) [(1,'a'), (1,'b')] [(1,'a'), (1,'b')]
      test "mesh [1,2] ['a','b'] == biclique [(1,'a'), (2,'b')] [(1,'b'), (2,'a')]" $
            mesh [1,2] ['a','b'] == B.biclique @(Int,Char) [(1,'a'), (2,'b')] [(1,'b'), (2,'a')]
  
      putStrLn "\n============ Bipartite.AdjacencyMap.removeLeftVertex ============"
      test "removeLeftVertex x (leftVertex x)       == empty" $ \x ->
            removeLeftVertex x (leftVertex x)       == empty
      test "removeLeftVertex 1 (leftVertex 2)       == leftVertex 2" $
            removeLeftVertex 1 (leftVertex 2)       ==(leftVertex 2 :: BAII)
      test "removeLeftVertex x (rightVertex y)      == rightVertex y" $ \x y ->
            removeLeftVertex x (rightVertex y)      == rightVertex y
      test "removeLeftVertex x (edge x y)           == rightVertex y" $ \x y ->
            removeLeftVertex x (edge x y)           == rightVertex y
      test "removeLeftVertex x . removeLeftVertex x == removeLeftVertex x" $ \x (g :: BAII)->
           (removeLeftVertex x . removeLeftVertex x) g == removeLeftVertex x g
  
      putStrLn "\n============ Bipartite.AdjacencyMap.removeRightVertex ============"
      test "removeRightVertex x (rightVertex x)       == empty" $ \x ->
            removeRightVertex x (rightVertex x)       == empty
      test "removeRightVertex 1 (rightVertex 2)       == rightVertex 2" $
            removeRightVertex 1 (rightVertex 2)       ==(rightVertex 2 :: BAII)
      test "removeRightVertex x (leftVertex y)        == leftVertex y" $ \x y ->
            removeRightVertex x (leftVertex y)        == leftVertex y
      test "removeRightVertex y (edge x y)            == leftVertex x" $ \x y ->
            removeRightVertex y (edge x y)            == leftVertex x
      test "removeRightVertex x . removeRightVertex x == removeRightVertex x" $ \x (y :: BAII)->
           (removeRightVertex x . removeRightVertex x) y == removeRightVertex x y
  
      putStrLn "\n============ Bipartite.AdjacencyMap.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 . removeLeftVertex x  == removeLeftVertex x" $ \x y z ->
           (removeEdge x y . removeLeftVertex x) z == removeLeftVertex x z
      test "removeEdge x y . removeRightVertex y == removeRightVertex y" $ \x y z ->
           (removeEdge x y . removeRightVertex y) z == removeRightVertex y z
  
      putStrLn "\n============ Bipartite.AdjacencyMap.bimap ============"
      test "bimap f g empty           == empty" $ \(apply -> f) (apply -> g) ->
            bimap f g empty           == empty
      test "bimap f g . vertex        == vertex . Data.Bifunctor.bimap f g" $ \(apply -> f) (apply -> g) x ->
           (bimap f g . vertex) x     ==(vertex .      Bifunctor.bimap f g) x
      test "bimap f g (edge x y)      == edge (f x) (g y)" $ \(apply -> f) (apply -> g) x y ->
            bimap f g (edge x y)      == edge (f x) (g y)
      test "bimap id id               == id" $ \(x :: BAII) ->
            bimap id id x             == id x
      test "bimap f1 g1 . bimap f2 g2 == bimap (f1 . f2) (g1 . g2)" $ \(apply -> f1 :: Int -> Int) (apply -> g1 :: Int -> Int) (apply -> f2 :: Int -> Int) (apply -> g2 :: Int -> Int) x ->
           (bimap f1 g1 . bimap f2 g2) x == bimap (f1 . f2) (g1 . g2) x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.box ============"
      test "box (path [0,1]) (path ['a','b']) == <correct result>" $
            box (path [0,1]) (path ['a','b']) == B.edges @(Int,Char) [ ((0,'a'), (0,'b'))
                                                                     , ((0,'a'), (1,'a'))
                                                                     , ((1,'b'), (0,'b'))
                                                                     , ((1,'b'), (1,'a')) ]
      let unit x = (x, ())
          biunit = B.bimap unit unit
          comm (x, y) = (y, x)
          bicomm = B.bimap comm comm
          assoc ((x, y), z) = (x, (y, z))
          biassoc = B.bimap assoc assoc
  
      putStrLn ""
      test "box x y                ~~ box y x" $ size10 $ \(x :: BAII) (y :: BAII) ->
            box x y                == bicomm (box y x)
      test "box x (box y z)        ~~ box (box x y) z" $ size10 $ \(x :: BAII) (y :: BAII) (z :: BAII) ->
            box x (box y z)        == biassoc (box (box x y) z)
      test "box x (box y z)        ~~ box (box x y) z" $ mapSize (min 3) $ \(x :: BAII) (y :: BAII) (z :: BAII) ->
            box x (box y z)        == biassoc (box (box x y) z)
      test "box x (leftVertex ())  ~~ x" $ size10 $ \(x :: BAII) ->
            box x (B.leftVertex ()) == biunit x
      test "box x (rightVertex ()) ~~ swap x" $ size10 $ \(x :: BAII) ->
            box x (B.rightVertex ()) == biunit (B.swap x)
      test "box x empty            ~~ empty" $ size10 $ \(x :: BAII) ->
            box x B.empty          == biunit empty
      test "vertexCount (box x y)  <= vertexCount x * vertexCount y" $ size10 $ \(x :: BAII) (y :: BAII) ->
          B.vertexCount (box x y)  <= vertexCount x * vertexCount y
      test "edgeCount (box x y)    <= vertexCount x * edgeCount y + edgeCount x * vertexCount y" $ size10 $ \(x :: BAII) (y :: BAII) ->
          B.edgeCount (box x y)    <= vertexCount x * edgeCount y + edgeCount x * vertexCount y
  
      putStrLn ""
      test "box == boxWith (,) (,) (,) (,)" $ size10 $ \(x :: BAII) (y :: BAII) ->
            box x y == boxWith (,) (,) (,) (,) x y
  
      putStrLn "\n============ Bipartite.AdjacencyMap.consistent ============"
      test "consistent empty            == True" $
            consistent empty            == True
      test "consistent (vertex x)       == True" $ \x ->
            consistent (vertex x)       == True
      test "consistent (edge x y)       == True" $ \x y ->
            consistent (edge x y)       == True
      test "consistent (edges x)        == True" $ \x ->
            consistent (edges x)        == True
      test "consistent (toBipartite x)  == True" $ \x ->
            consistent (toBipartite x)  == True
      test "consistent (swap x)         == True" $ \x ->
            consistent (swap x)         == True
      test "consistent (circuit xs)     == True" $ \xs ->
            consistent (circuit xs)     == True
      test "consistent (biclique xs ys) == True" $ \xs ys ->
            consistent (biclique xs ys) == True
  
  testBipartiteAdjacencyMapAlgorithm :: IO ()
  testBipartiteAdjacencyMapAlgorithm = do
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.detectParts ============"
      test "detectParts empty                                       == Right empty" $
            detectParts (AM.empty :: AI)                            == Right empty
      test "detectParts (vertex 1)                                  == Right (leftVertex 1)" $
            detectParts (AM.vertex 1 :: AI)                         == Right (leftVertex 1)
      test "detectParts (edge 1 1)                                  == Left [1]" $
            detectParts (AM.edge 1 1 :: AI)                         == Left [1]
      test "detectParts (edge 1 2)                                  == Right (edge 1 2)" $
            detectParts (AM.edge 1 2 :: AI)                         == Right (edge 1 2)
      test "detectParts (edge 0 (-1))                               == Right (edge (-1) 0)" $
            detectParts (AM.edge 0 (-1) :: AI)                      == Right (edge (-1) 0)
      test "detectParts (1 * (2 + 3))                               == Right (edges [(1, 2), (1, 3)])" $
            detectParts (1 * (2 + 3) :: AI)                         == Right (edges [(1, 2), (1, 3)])
      test "detectParts ((1 + 3) * (2 + 4) + 6 * 5)                 == Right (swap (1 + 3) * (2 + 4) + swap 5 * 6" $
            detectParts ((1 + 3) * (2 + 4) + 6 * 5 :: AI)           == Right (swap (1 + 3) * (2 * 4) + swap 5 * 6)
      test "detectParts ((1 + 2) * (3 + 4) * (5 + 6))               == Left [1, 3, 2, 4, 5]" $
            detectParts ((1 + 2) * (3 + 4) * (5 + 6) :: AI)         == Left [1, 3, 2, 4, 5]
      test "detectParts ((1 + 2) * (3 + 4) + (3 + 4) * 5)           == Right (swap (1 + 2) * (3 + 4) + swap 5 * (3 + 4))" $
            detectParts ((1 + 2) * (3 + 4) + (3 + 4) * 5 :: AI)     == Right (swap (1 + 2) * (3 + 4) + swap 5 * (3 + 4))
      test "detectParts (1 * 2 * 3)                                 == Left [2, 3, 1]" $
            detectParts (1 * 2 * 3 :: AI)                           == Left [1, 2, 3]
      test "detectParts ((1 * 3 * 4) + 2 * (1 + 2))                 == Left [2]" $
            detectParts ((1 * 3 * 4) + 2 * (1 + 2) :: AI)           == Left [2]
      test "detectParts (clique [1..10])                            == Left [1, 2, 3]" $
            detectParts (AM.clique [1..10] :: AI)                   == Left [1, 2, 3]
      test "detectParts (circuit [1..11])                           == Left [1..11]" $
            detectParts (AM.circuit [1..11] :: AI)                  == Left [1..11]
      test "detectParts (circuit [1..10])                           == Right (circuit [(2 * x - 1, 2 * x) | x <- [1..5]])" $
            detectParts (AM.circuit [1..10] :: AI)                  == Right (circuit [(2 * x - 1, 2 * x) | x <- [1..5]])
      test "detectParts (biclique [] xs)                            == Right (vertices xs [])" $ \(xs :: [Int]) ->
            detectParts (AM.biclique [] xs :: AI)                   == Right (vertices xs [])
      test "detectParts (biclique (map Left (x:xs)) (map Right ys)) == Right (biclique (map Left (x:xs)) (map Right ys))" $ \(x :: Int) (xs :: [Int]) (ys :: [Int]) ->
            detectParts (AM.biclique (map Left (x:xs)) (map Right ys)) == Right (biclique (map Left (x:xs)) (map Right ys))
      test "isRight (detectParts (star x ys))                       == not (elem x ys)" $ \(x :: Int) (ys :: [Int]) ->
            isRight (detectParts (AM.star x ys))                    == (not $ elem x ys)
      test "isRight (detectParts (fromBipartite (toBipartite x)))   == True" $ \(x :: AII) ->
            isRight (detectParts (fromBipartite (toBipartite x)))   == True
  
      -- TODO: Clean up these tests
      putStrLn ""
      test "((all ((flip Set.member) $ edgeSet $ symmetricClosure x) . edgeSet) <$> detectParts x) /= Right False" $ \(x :: AI) ->
            ((all ((flip Set.member) $ AM.edgeSet $ AM.symmetricClosure x) . edgeSet) <$> detectParts x) /= Right False
      test "(Set.map $ fromEither) <$> (vertexSet <$> (detectParts (fromBipartite (toBipartite x)))) == Right (vertexSet x)" $ \(x :: AII) ->
           ((Set.map $ fromEither) <$> (vertexSet <$> (detectParts (fromBipartite (toBipartite x))))) == Right (AM.vertexSet x)
      test "fromEither (Bifunctor.bimap ((flip Set.isSubsetOf) (vertexSet x) . Set.fromList) (const True) (detectParts x)) == True" $ \(x :: AI) ->
            fromEither (Bifunctor.bimap ((flip Set.isSubsetOf) (AM.vertexSet x) . Set.fromList) (const True) (detectParts x))
      test "fromEither (Bifunctor.bimap ((flip Set.isSubsetOf) (edgeSet (symmetricClosure x)) . AM.edgeSet . circuit) (const True) (detectParts x)) == True" $ \(x :: AI) ->
            fromEither (Bifunctor.bimap ((flip Set.isSubsetOf) (AM.edgeSet (AM.symmetricClosure x)) . AM.edgeSet . AM.circuit) (const True) (detectParts x))
      test "fromEither (Bifunctor.bimap (((==) 1) . ((flip mod) 2) . length) (const True) (detectParts x)) == True" $ \(x :: AI) ->
            fromEither (Bifunctor.bimap (((==) 1) . ((flip mod) 2) . length) (const True) (detectParts x))
  
      putStrLn "\n============ Show (Bipartite.AdjacencyMap.Algorithm.Matching a b) ============"
      test "show (matching [])                == \"matching []\"" $
            show (matching [] :: MII)         ==  "matching []"
      test "show (matching [(2,'a'),(1,'b')]) == \"matching [(1,'b'),(2,'a')]\"" $
            show (matching [(2,'a'),(1,'b')] :: MIC) == "matching [(1,'b'),(2,'a')]"
  
      putStrLn "\n============ Eq (Bipartite.AdjacencyMap.Algorithm.Matching a b) ============"
      test "(x == y) == ((pairOfLeft x == pairOfLeft y) && (pairOfRight x == pairOfRight y))" $ \(x :: MII) (y :: MII) ->
          (x == y) == ((pairOfLeft x == pairOfLeft y) && (pairOfRight x == pairOfRight y))
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.pairOfLeft ============"
      test "pairOfLeft (matching [])                 == Map.empty" $
            pairOfLeft (matching [] :: MII)          == Map.empty
      test "pairOfLeft (matching [(2,'a'), (1,'b')]) == Map.fromList [(2,'a'), (1,'b')]" $
            pairOfLeft (matching [(2,'a'), (1,'b')] :: MIC) == Map.fromList [(2,'a'), (1,'b')]
      test "Map.size . pairOfLeft                    == Map.size . pairOfRight" $ \(x :: MII) ->
           (Map.size . pairOfLeft) x                 ==(Map.size . pairOfRight) x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.pairOfRight ============"
      test "pairOfRight (matching [])                 == Map.empty" $
            pairOfRight (matching [] :: MII)          == Map.empty
      test "pairOfRight (matching [(2,'a'), (1,'b')]) == Map.fromList [('a',2), ('b',1)]" $
            pairOfRight (matching [(2,'a'), (1,'b')] :: MIC) == Map.fromList [('a',2), ('b',1)]
      test "Map.size . pairOfRight                    == Map.size . pairOfLeft" $ \(x :: MII) ->
           (Map.size . pairOfRight) x                 ==(Map.size . pairOfLeft) x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.matching ============"
      test "matching [(1,'a'), (1,'b')]                   == matching [(1,'b')]" $
            matching [(1,'a'), (1,'b')]                   == (matching [(1,'b')] :: MIC)
      test "matching [(1,'a'), (1,'b'), (2,'b'), (2,'a')] == matching [(2,'a')]" $
            matching [(1,'a'), (1,'b'), (2,'b'), (2,'a')] == (matching [(2,'a')] :: MIC)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.isMatchingOf ============"
      test "isMatchingOf (matching []) x               == True" $ \(x :: BAII) ->
            isMatchingOf (matching []) x               == True
      test "isMatchingOf (matching xs) empty           == null xs" $ \(xs :: [(Int, Int)]) ->
            isMatchingOf (matching xs) empty           == null xs
      test "isMatchingOf (matching [(x,y)]) (edge x y) == True" $ \(x :: Int) (y :: Int) ->
            isMatchingOf (matching [(x,y)]) (edge x y) == True
      test "isMatchingOf (matching [(1,2)]) (edge 2 1) == False" $
            isMatchingOf (matching [(1,2)]) (edge 2 1 :: BAII) == False
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.matchingSize ============"
      test "matchingSize (matching [])                 == 0" $
            matchingSize (matching [] :: MII)          == 0
      test "matchingSize (matching [(2,'a'), (1,'b')]) == 2" $
            matchingSize (matching [(2,'a'), (1,'b')] :: MIC) == 2
      test "matchingSize (matching [(1,'a'), (1,'b')]) == 1" $
            matchingSize (matching [(1,'a'), (1,'b')] :: MIC) == 1
      test "matchingSize (matching xs)                 <= length xs" $ \(xs :: [(Int, Int)]) ->
            matchingSize (matching xs)                 <= length xs
      test "matchingSize x                             == Map.size . pairOfLeft" $ \(x :: MII) ->
            matchingSize x                             ==(Map.size . pairOfLeft) x
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.maxMatching ============"
      test "maxMatching empty                                          == matching []" $
            maxMatching (empty :: BAII)                                == matching []
      test "maxMatching (vertices xs ys)                               == matching []" $ \(xs :: [Int]) (ys :: [Int]) ->
            maxMatching (vertices xs ys)                               == matching []
      test "maxMatching (path [1,2,3,4])                               == matching [(1,2), (3,4)]" $
            maxMatching (path ([1,2,3,4] :: LII))                      == matching [(1,2), (3,4)]
      test "matchingSize (maxMatching (circuit [(1,2), (3,4), (5,6)])) == 3" $
            matchingSize (maxMatching (circuit [(1,2), (3,4), (5,6)] :: BAII)) == 3
      test "matchingSize (maxMatching (star x (y:ys)))                 == 1" $ \(x :: Int) (y :: Int) (ys :: [Int]) ->
            matchingSize (maxMatching (star x (y:ys)))                 == 1
      test "matchingSize (maxMatching (biclique xs ys))                == min (length (nub xs)) (length (nub ys))" $ \(xs :: [Int]) (ys :: [Int]) ->
            matchingSize (maxMatching (biclique xs ys))                == min (length (nub xs)) (length (nub ys))
      test "isMatchingOf (maxMatching x) x                             == True" $ \(x :: BAII) ->
            isMatchingOf (maxMatching x) x                             == True
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.isVertexCoverOf ============"
      test "isVertexCoverOf (xs             , ys             ) empty          == Set.null xs && Set.null ys" $ \(xs :: Set Int) (ys :: Set Int) ->
            isVertexCoverOf (xs             , ys             ) empty          ==(Set.null xs && Set.null ys)
      test "isVertexCoverOf (xs             , ys             ) (leftVertex x) == Set.isSubsetOf xs (Set.singleton x) && Set.null ys" $ \(x :: Int) (xs :: Set Int) (ys :: Set Int) ->
            isVertexCoverOf (xs             , ys             ) (leftVertex x) ==(Set.isSubsetOf xs (Set.singleton x) && Set.null ys)
      test "isVertexCoverOf (Set.empty      , Set.empty      ) (edge x y)     == False" $ \(x :: Int) (y :: Int) ->
            isVertexCoverOf (Set.empty      , Set.empty      ) (edge x y)     == False
      test "isVertexCoverOf (Set.singleton x, ys             ) (edge x y)     == Set.isSubsetOf ys (Set.singleton y)" $ \(x :: Int) (y :: Int) (ys :: Set Int) ->
            isVertexCoverOf (Set.singleton x, ys             ) (edge x y)     == Set.isSubsetOf ys (Set.singleton y)
      test "isVertexCoverOf (xs             , Set.singleton y) (edge x y)     == Set.isSubsetOf xs (Set.singleton x)" $ \(x :: Int) (y :: Int) (xs :: Set Int) ->
            isVertexCoverOf (xs             , Set.singleton y) (edge x y)     == Set.isSubsetOf xs (Set.singleton x)
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.minVertexCover ============"
      test "minVertexCover empty                              == (Set.empty, Set.empty)" $
            minVertexCover (empty :: BAII)                    == (Set.empty, Set.empty)
      test "minVertexCover (vertices xs ys)                   == (Set.empty, Set.empty)" $ \(xs :: [Int]) (ys :: [Int]) ->
            minVertexCover (vertices xs ys)                   == (Set.empty, Set.empty)
      test "minVertexCover (path [1,2,3])                     == (Set.empty, Set.singleton 2)" $
            minVertexCover (path [1,2,3] :: BAII)             == (Set.empty, Set.singleton 2)
      test "minVertexCover (star x (1:2:ys))                  == (Set.singleton x, Set.empty)" $ \(x :: Int) (ys :: [Int]) ->
            minVertexCover (star x (1:2:ys) :: BAII)          == (Set.singleton x, Set.empty)
      test "vertexCoverSize (minVertexCover (biclique xs ys)) == min (length (nub xs)) (length (nub ys))" $ size10 $ \(xs :: [Int]) (ys :: [Int]) ->
            vertexCoverSize (minVertexCover (biclique xs ys)) == min (length (nub xs)) (length (nub ys))
      test "vertexCoverSize . minVertexCover                  == matchingSize . maxMatching" $ \(x :: BAII) ->
           (vertexCoverSize . minVertexCover) x               ==(matchingSize . maxMatching) x
      test "isVertexCoverOf (minVertexCover x) x              == True" $ \(x :: BAII) ->
            isVertexCoverOf (minVertexCover x) x              == True
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.isIndependentSetOf ============"
      test "isIndependentSetOf (xs             , ys             ) empty          == Set.null xs && Set.null ys" $ \(xs :: Set Int) (ys :: Set Int) ->
            isIndependentSetOf (xs             , ys             ) empty          ==(Set.null xs && Set.null ys)
      test "isIndependentSetOf (xs             , ys             ) (leftVertex x) == Set.isSubsetOf xs (Set.singleton x) && Set.null ys" $ \(x :: Int) (xs :: Set Int) (ys :: Set Int) ->
            isIndependentSetOf (xs             , ys             ) (leftVertex x) ==(Set.isSubsetOf xs (Set.singleton x) && Set.null ys)
      test "isIndependentSetOf (Set.empty      , Set.empty      ) (edge x y)     == True" $ \(x :: Int) (y :: Int) ->
            isIndependentSetOf (Set.empty      , Set.empty      ) (edge x y)     == True
      test "isIndependentSetOf (Set.singleton x, ys             ) (edge x y)     == Set.null ys" $ \(x :: Int) (y :: Int) (ys :: Set Int) ->
            isIndependentSetOf (Set.singleton x, ys             ) (edge x y)     == Set.null ys
      test "isIndependentSetOf (xs             , Set.singleton y) (edge x y)     == Set.null xs" $ \(x :: Int) (y :: Int) (xs :: Set Int) ->
            isIndependentSetOf (xs             , Set.singleton y) (edge x y)     == Set.null xs
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.maxIndependentSet ============"
      test "maxIndependentSet empty                                 == (Set.empty, Set.empty)" $
            maxIndependentSet (empty :: BAII)                       == (Set.empty, Set.empty)
      test "maxIndependentSet (vertices xs ys)                      == (Set.fromList xs, Set.fromList ys)" $ \(xs :: [Int]) (ys :: [Int]) ->
            maxIndependentSet (vertices xs ys)                      == (Set.fromList xs, Set.fromList ys)
      test "maxIndependentSet (path [1,2,3])                        == (Set.fromList [1,3], Set.empty)" $
            maxIndependentSet (path [1,2,3] :: BAII)                == (Set.fromList [1,3], Set.empty)
      test "maxIndependentSet (star x (1:2:ys))                     == (Set.empty, Set.fromList (1:2:ys))" $ \(x :: Int) (ys :: [Int]) ->
            maxIndependentSet (star x (1:2:ys))                     == (Set.empty, Set.fromList (1:2:ys))
      test "independentSetSize (maxIndependentSet (biclique xs ys)) == max (length (nub xs)) (length (nub ys))" $ \(xs :: [Int]) (ys :: [Int]) ->
            independentSetSize (maxIndependentSet (biclique xs ys)) == max (length (nub xs)) (length (nub ys))
      test "independentSetSize (maxIndependentSet x)                == vertexCount x - vertexCoverSize (minVertexCover x)" $ \(x :: BAII) ->
            independentSetSize (maxIndependentSet x)                == vertexCount x - vertexCoverSize (minVertexCover x)
      test "isIndependentSetOf (maxIndependentSet x) x              == True" $ \(x :: BAII) ->
            isIndependentSetOf (maxIndependentSet x) x              == True
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.augmentingPath ============"
      test "augmentingPath (matching [])      empty            == Left (Set.empty, Set.empty)" $
            augmentingPath (matching [])     (empty :: BAII)   == Left (Set.empty, Set.empty)
      test "augmentingPath (matching [])      (edge 1 2)       == Right [1,2]" $
            augmentingPath (matching [])      (edge 1 2)       == Right ([1,2] :: LII)
      test "augmentingPath (matching [(1,2)]) (path [1,2,3])   == Left (Set.empty, Set.singleton 2)" $
            augmentingPath (matching [(1,2)]) (path [1,2,3] :: BAII) == Left (Set.empty, Set.singleton 2)
      test "augmentingPath (matching [(3,2)]) (path [1,2,3,4]) == Right [1,2,3,4]" $
            augmentingPath (matching [(3,2)]) (path [1,2,3,4]) == Right ([1,2,3,4] :: LII)
      test "isLeft (augmentingPath (maxMatching x) x)          == True" $ \(x :: BAII) ->
            isLeft (augmentingPath (maxMatching x) x)          == True
  
      putStrLn "\n============ Bipartite.AdjacencyMap.Algorithm.consistentMatching ============"
      test "consistentMatching (matching xs)   == True" $ \(xs :: [(Int,Int)]) ->
            consistentMatching (matching xs)   == True
      test "consistentMatching (maxMatching x) == True" $ \(x :: BAII) ->
            consistentMatching (maxMatching x) == True
  