{-# LANGUAGE CPP #-}

#ifdef STRICT
import Data.Map.Strict as Data.Map
#else
import Data.Map.Lazy as Data.Map
#endif

import Data.Monoid
import Data.Maybe hiding (mapMaybe)
import qualified Data.Maybe as Maybe (mapMaybe)
import Data.Ord
import Data.Function
import Prelude hiding (lookup, null, map, filter, foldr, foldl)
import qualified Prelude (map)

import Data.List (nub,sort)
import qualified Data.List as List
import qualified Data.Set
import Test.Framework
import Test.Framework.Providers.HUnit
import Test.Framework.Providers.QuickCheck2
import Test.HUnit hiding (Test, Testable)
import Test.QuickCheck
import Text.Show.Functions ()

default (Int)

main :: IO ()
main = defaultMain
         [ testCase "ticket4242" test_ticket4242
         , testCase "index"      test_index
         , testCase "size"       test_size
         , testCase "size2"      test_size2
         , testCase "member"     test_member
         , testCase "notMember"  test_notMember
         , testCase "lookup"     test_lookup
         , testCase "findWithDefault"     test_findWithDefault
         , testCase "lookupLT"   test_lookupLT
         , testCase "lookupGT"   test_lookupGT
         , testCase "lookupLE"   test_lookupLE
         , testCase "lookupGE"   test_lookupGE
         , testCase "empty" test_empty
         , testCase "mempty" test_mempty
         , testCase "singleton" test_singleton
         , testCase "insert" test_insert
         , testCase "insertWith" test_insertWith
         , testCase "insertWithKey" test_insertWithKey
         , testCase "insertLookupWithKey" test_insertLookupWithKey
         , testCase "delete" test_delete
         , testCase "adjust" test_adjust
         , testCase "adjustWithKey" test_adjustWithKey
         , testCase "update" test_update
         , testCase "updateWithKey" test_updateWithKey
         , testCase "updateLookupWithKey" test_updateLookupWithKey
         , testCase "alter" test_alter
         , testCase "union" test_union
         , testCase "mappend" test_mappend
         , testCase "unionWith" test_unionWith
         , testCase "unionWithKey" test_unionWithKey
         , testCase "unions" test_unions
         , testCase "mconcat" test_mconcat
         , testCase "unionsWith" test_unionsWith
         , testCase "difference" test_difference
         , testCase "differenceWith" test_differenceWith
         , testCase "differenceWithKey" test_differenceWithKey
         , testCase "intersection" test_intersection
         , testCase "intersectionWith" test_intersectionWith
         , testCase "intersectionWithKey" test_intersectionWithKey
         , testCase "map" test_map
         , testCase "mapWithKey" test_mapWithKey
         , testCase "mapAccum" test_mapAccum
         , testCase "mapAccumWithKey" test_mapAccumWithKey
         , testCase "mapAccumRWithKey" test_mapAccumRWithKey
         , testCase "mapKeys" test_mapKeys
         , testCase "mapKeysWith" test_mapKeysWith
         , testCase "mapKeysMonotonic" test_mapKeysMonotonic
         , testCase "elems" test_elems
         , testCase "keys" test_keys
         , testCase "assocs" test_assocs
         , testCase "keysSet" test_keysSet
         , testCase "fromSet" test_fromSet
         , testCase "toList" test_toList
         , testCase "fromList" test_fromList
         , testCase "fromListWith" test_fromListWith
         , testCase "fromListWithKey" test_fromListWithKey
         , testCase "toAscList" test_toAscList
         , testCase "toDescList" test_toDescList
         , testCase "showTree" test_showTree
         , testCase "showTree'" test_showTree'
         , testCase "fromAscList" test_fromAscList
         , testCase "fromAscListWith" test_fromAscListWith
         , testCase "fromAscListWithKey" test_fromAscListWithKey
         , testCase "fromDistinctAscList" test_fromDistinctAscList
         , testCase "filter" test_filter
         , testCase "filterWithKey" test_filteWithKey
         , testCase "partition" test_partition
         , testCase "partitionWithKey" test_partitionWithKey
         , testCase "mapMaybe" test_mapMaybe
         , testCase "mapMaybeWithKey" test_mapMaybeWithKey
         , testCase "mapEither" test_mapEither
         , testCase "mapEitherWithKey" test_mapEitherWithKey
         , testCase "split" test_split
         , testCase "splitLookup" test_splitLookup
         , testCase "isSubmapOfBy" test_isSubmapOfBy
         , testCase "isSubmapOf" test_isSubmapOf
         , testCase "isProperSubmapOfBy" test_isProperSubmapOfBy
         , testCase "isProperSubmapOf" test_isProperSubmapOf
         , testCase "lookupIndex" test_lookupIndex
         , testCase "findIndex" test_findIndex
         , testCase "elemAt" test_elemAt
         , testCase "updateAt" test_updateAt
         , testCase "deleteAt" test_deleteAt
         , testCase "findMin" test_findMin
         , testCase "findMax" test_findMax
         , testCase "deleteMin" test_deleteMin
         , testCase "deleteMax" test_deleteMax
         , testCase "deleteFindMin" test_deleteFindMin
         , testCase "deleteFindMax" test_deleteFindMax
         , testCase "updateMin" test_updateMin
         , testCase "updateMax" test_updateMax
         , testCase "updateMinWithKey" test_updateMinWithKey
         , testCase "updateMaxWithKey" test_updateMaxWithKey
         , testCase "minView" test_minView
         , testCase "maxView" test_maxView
         , testCase "minViewWithKey" test_minViewWithKey
         , testCase "maxViewWithKey" test_maxViewWithKey
         , testCase "valid" test_valid
         , testProperty "valid"                prop_valid
         , testProperty "insert to singleton"  prop_singleton
         , testProperty "insert"               prop_insert
         , testProperty "insert then lookup"   prop_insertLookup
         , testProperty "insert then delete"   prop_insertDelete
         , testProperty "insert then delete2"  prop_insertDelete2
         , testProperty "delete non member"    prop_deleteNonMember
         , testProperty "deleteMin"            prop_deleteMin
         , testProperty "deleteMax"            prop_deleteMax
         , testProperty "split"                prop_split
         , testProperty "splitRoot"            prop_splitRoot
         , testProperty "split then link"      prop_link
         , testProperty "split then merge"     prop_merge
         , testProperty "union"                prop_union
         , testProperty "union model"          prop_unionModel
         , testProperty "union singleton"      prop_unionSingleton
         , testProperty "union associative"    prop_unionAssoc
         , testProperty "union+unionWith"      prop_unionWith
         , testProperty "unionWith"            prop_unionWith2
         , testProperty "union sum"            prop_unionSum
         , testProperty "difference"           prop_difference
         , testProperty "difference model"     prop_differenceModel
         , testProperty "intersection"         prop_intersection
         , testProperty "intersection model"   prop_intersectionModel
         , testProperty "intersectionWith"     prop_intersectionWith
         , testProperty "intersectionWithModel" prop_intersectionWithModel
         , testProperty "intersectionWithKey"  prop_intersectionWithKey
         , testProperty "intersectionWithKeyModel" prop_intersectionWithKeyModel
         , testProperty "mergeWithKey model"   prop_mergeWithKeyModel
         , testProperty "fromAscList"          prop_ordered
         , testProperty "fromList then toList" prop_list
         , testProperty "toDescList"           prop_descList
         , testProperty "toAscList+toDescList" prop_ascDescList
         , testProperty "fromList"             prop_fromList
         , testProperty "alter"                prop_alter
         , testProperty "index"                prop_index
         , testProperty "null"                 prop_null
         , testProperty "member"               prop_member
         , testProperty "notmember"            prop_notmember
         , testProperty "lookup"               prop_lookup
         , testProperty "find"                 prop_find
         , testProperty "findWithDefault"      prop_findWithDefault
         , testProperty "lookupLT"             prop_lookupLT
         , testProperty "lookupGT"             prop_lookupGT
         , testProperty "lookupLE"             prop_lookupLE
         , testProperty "lookupGE"             prop_lookupGE
         , testProperty "findIndex"            prop_findIndex
         , testProperty "lookupIndex"          prop_lookupIndex
         , testProperty "findMin"              prop_findMin
         , testProperty "findMax"              prop_findMax
         , testProperty "deleteMin"            prop_deleteMinModel
         , testProperty "deleteMax"            prop_deleteMaxModel
         , testProperty "filter"               prop_filter
         , testProperty "partition"            prop_partition
         , testProperty "map"                  prop_map
         , testProperty "fmap"                 prop_fmap
         , testProperty "mapkeys"              prop_mapkeys
         , testProperty "split"                prop_splitModel
         , testProperty "foldr"                prop_foldr
         , testProperty "foldr'"               prop_foldr'
         , testProperty "foldl"                prop_foldl
         , testProperty "foldl'"               prop_foldl'
         , testProperty "keysSet"              prop_keysSet
         , testProperty "fromSet"              prop_fromSet
         ]

{--------------------------------------------------------------------
  Arbitrary, reasonably balanced trees
--------------------------------------------------------------------}
instance (Enum k,Arbitrary a) => Arbitrary (Map k a) where
  arbitrary = sized (arbtree 0 maxkey)
    where maxkey = 10^5

          arbtree :: (Enum k, Arbitrary a) => Int -> Int -> Int -> Gen (Map k a)
          arbtree lo hi n = do t <- gentree lo hi n
                               if balanced t then return t else arbtree lo hi n
            where gentree lo hi n
                    | n <= 0        = return Tip
                    | lo >= hi      = return Tip
                    | otherwise     = do{ x  <- arbitrary
                                        ; i  <- choose (lo,hi)
                                        ; m  <- choose (1,70)
                                        ; let (ml,mr)  | m==(1::Int)= (1,2)
                                                       | m==2       = (2,1)
                                                       | m==3       = (1,1)
                                                       | otherwise  = (2,2)
                                        ; l  <- gentree lo (i-1) (n `div` ml)
                                        ; r  <- gentree (i+1) hi (n `div` mr)
                                        ; return (bin (toEnum i) x l r)
                                        }

------------------------------------------------------------------------

type UMap = Map Int ()
type IMap = Map Int Int
type SMap = Map Int String

----------------------------------------------------------------
-- Unit tests
----------------------------------------------------------------

test_ticket4242 :: Assertion
test_ticket4242 = (valid $ deleteMin $ deleteMin $ fromList [ (i, ()) | i <- [0,2,5,1,6,4,8,9,7,11,10,3] :: [Int] ]) @?= True

----------------------------------------------------------------
-- Operators

test_index :: Assertion
test_index = fromList [(5,'a'), (3,'b')] ! 5 @?= 'a'

----------------------------------------------------------------
-- Query

test_size :: Assertion
test_size = do
    null (empty)           @?= True
    null (singleton 1 'a') @?= False

test_size2 :: Assertion
test_size2 = do
    size empty                                   @?= 0
    size (singleton 1 'a')                       @?= 1
    size (fromList([(1,'a'), (2,'c'), (3,'b')])) @?= 3

test_member :: Assertion
test_member = do
    member 5 (fromList [(5,'a'), (3,'b')]) @?= True
    member 1 (fromList [(5,'a'), (3,'b')]) @?= False

test_notMember :: Assertion
test_notMember = do
    notMember 5 (fromList [(5,'a'), (3,'b')]) @?= False
    notMember 1 (fromList [(5,'a'), (3,'b')]) @?= True

test_lookup :: Assertion
test_lookup = do
    employeeCurrency "John" @?= Just "Euro"
    employeeCurrency "Pete" @?= Nothing
  where
    employeeDept = fromList([("John","Sales"), ("Bob","IT")])
    deptCountry = fromList([("IT","USA"), ("Sales","France")])
    countryCurrency = fromList([("USA", "Dollar"), ("France", "Euro")])
    employeeCurrency :: String -> Maybe String
    employeeCurrency name = do
        dept <- lookup name employeeDept
        country <- lookup dept deptCountry
        lookup country countryCurrency

test_findWithDefault :: Assertion
test_findWithDefault = do
    findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) @?= 'x'
    findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) @?= 'a'

test_lookupLT :: Assertion
test_lookupLT = do
    lookupLT 3 (fromList [(3,'a'), (5,'b')]) @?= Nothing
    lookupLT 4 (fromList [(3,'a'), (5,'b')]) @?= Just (3, 'a')

test_lookupGT :: Assertion
test_lookupGT = do
    lookupGT 4 (fromList [(3,'a'), (5,'b')]) @?= Just (5, 'b')
    lookupGT 5 (fromList [(3,'a'), (5,'b')]) @?= Nothing

test_lookupLE :: Assertion
test_lookupLE = do
    lookupLE 2 (fromList [(3,'a'), (5,'b')]) @?= Nothing
    lookupLE 4 (fromList [(3,'a'), (5,'b')]) @?= Just (3, 'a')
    lookupLE 5 (fromList [(3,'a'), (5,'b')]) @?= Just (5, 'b')

test_lookupGE :: Assertion
test_lookupGE = do
    lookupGE 3 (fromList [(3,'a'), (5,'b')]) @?= Just (3, 'a')
    lookupGE 4 (fromList [(3,'a'), (5,'b')]) @?= Just (5, 'b')
    lookupGE 6 (fromList [(3,'a'), (5,'b')]) @?= Nothing

----------------------------------------------------------------
-- Construction

test_empty :: Assertion
test_empty = do
    (empty :: UMap)  @?= fromList []
    size empty @?= 0

test_mempty :: Assertion
test_mempty = do
    (mempty :: UMap)  @?= fromList []
    size (mempty :: UMap) @?= 0

test_singleton :: Assertion
test_singleton = do
    singleton 1 'a'        @?= fromList [(1, 'a')]
    size (singleton 1 'a') @?= 1

test_insert :: Assertion
test_insert = do
    insert 5 'x' (fromList [(5,'a'), (3,'b')]) @?= fromList [(3, 'b'), (5, 'x')]
    insert 7 'x' (fromList [(5,'a'), (3,'b')]) @?= fromList [(3, 'b'), (5, 'a'), (7, 'x')]
    insert 5 'x' empty                         @?= singleton 5 'x'

test_insertWith :: Assertion
test_insertWith = do
    insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "xxxa")]
    insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a"), (7, "xxx")]
    insertWith (++) 5 "xxx" empty                         @?= singleton 5 "xxx"

test_insertWithKey :: Assertion
test_insertWithKey = do
    insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "5:xxx|a")]
    insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a"), (7, "xxx")]
    insertWithKey f 5 "xxx" empty                         @?= singleton 5 "xxx"
  where
    f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value

test_insertLookupWithKey :: Assertion
test_insertLookupWithKey = do
    insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) @?= (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
    insertLookupWithKey f 2 "xxx" (fromList [(5,"a"), (3,"b")]) @?= (Nothing,fromList [(2,"xxx"),(3,"b"),(5,"a")])
    insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) @?= (Nothing,  fromList [(3, "b"), (5, "a"), (7, "xxx")])
    insertLookupWithKey f 5 "xxx" empty                         @?= (Nothing,  singleton 5 "xxx")
  where
    f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value

----------------------------------------------------------------
-- Delete/Update

test_delete :: Assertion
test_delete = do
    delete 5 (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "b"
    delete 7 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a")]
    delete 5 empty                         @?= (empty :: IMap)

test_adjust :: Assertion
test_adjust = do
    adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "new a")]
    adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a")]
    adjust ("new " ++) 7 empty                         @?= empty

test_adjustWithKey :: Assertion
test_adjustWithKey = do
    adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "5:new a")]
    adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a")]
    adjustWithKey f 7 empty                         @?= empty
  where
    f key x = (show key) ++ ":new " ++ x

test_update :: Assertion
test_update = do
    update f 5 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "new a")]
    update f 7 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a")]
    update f 3 (fromList [(5,"a"), (3,"b")]) @?= singleton 5 "a"
  where
    f x = if x == "a" then Just "new a" else Nothing

test_updateWithKey :: Assertion
test_updateWithKey = do
    updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "5:new a")]
    updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a")]
    updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) @?= singleton 5 "a"
 where
     f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing

test_updateLookupWithKey :: Assertion
test_updateLookupWithKey = do
    updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) @?= (Just "5:new a", fromList [(3, "b"), (5, "5:new a")])
    updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) @?= (Nothing,  fromList [(3, "b"), (5, "a")])
    updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) @?= (Just "b", singleton 5 "a")
  where
    f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing

test_alter :: Assertion
test_alter = do
    alter f 7 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a")]
    alter f 5 (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "b"
    alter g 7 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "a"), (7, "c")]
    alter g 5 (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "c")]
  where
    f _ = Nothing
    g _ = Just "c"

----------------------------------------------------------------
-- Combine

test_union :: Assertion
test_union = union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) @?= fromList [(3, "b"), (5, "a"), (7, "C")]

test_mappend :: Assertion
test_mappend = mappend (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) @?= fromList [(3, "b"), (5, "a"), (7, "C")]

test_unionWith :: Assertion
test_unionWith = unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) @?= fromList [(3, "b"), (5, "aA"), (7, "C")]

test_unionWithKey :: Assertion
test_unionWithKey = unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) @?= fromList [(3, "b"), (5, "5:a|A"), (7, "C")]
  where
    f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value

test_unions :: Assertion
test_unions = do
    unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
        @?= fromList [(3, "b"), (5, "a"), (7, "C")]
    unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
        @?= fromList [(3, "B3"), (5, "A3"), (7, "C")]

test_mconcat :: Assertion
test_mconcat = do
    mconcat [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
        @?= fromList [(3, "b"), (5, "a"), (7, "C")]
    mconcat [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
        @?= fromList [(3, "B3"), (5, "A3"), (7, "C")]

test_unionsWith :: Assertion
test_unionsWith = unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
     @?= fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]

test_difference :: Assertion
test_difference = difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) @?= singleton 3 "b"

test_differenceWith :: Assertion
test_differenceWith = differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
     @?= singleton 3 "b:B"
 where
   f al ar = if al== "b" then Just (al ++ ":" ++ ar) else Nothing

test_differenceWithKey :: Assertion
test_differenceWithKey = differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
     @?= singleton 3 "3:b|B"
  where
    f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing

test_intersection :: Assertion
test_intersection = intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) @?= singleton 5 "a"


test_intersectionWith :: Assertion
test_intersectionWith = intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) @?= singleton 5 "aA"

test_intersectionWithKey :: Assertion
test_intersectionWithKey = intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) @?= singleton 5 "5:a|A"
  where
    f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar

----------------------------------------------------------------
-- Traversal

test_map :: Assertion
test_map = map (++ "x") (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "bx"), (5, "ax")]

test_mapWithKey :: Assertion
test_mapWithKey = mapWithKey f (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "3:b"), (5, "5:a")]
  where
    f key x = (show key) ++ ":" ++ x

test_mapAccum :: Assertion
test_mapAccum = mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) @?= ("Everything: ba", fromList [(3, "bX"), (5, "aX")])
  where
    f a b = (a ++ b, b ++ "X")

test_mapAccumWithKey :: Assertion
test_mapAccumWithKey = mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) @?= ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])
  where
    f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")

test_mapAccumRWithKey :: Assertion
test_mapAccumRWithKey = mapAccumRWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) @?= ("Everything: 5-a 3-b", fromList [(3, "bX"), (5, "aX")])
  where
    f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")

test_mapKeys :: Assertion
test_mapKeys = do
    mapKeys (+ 1) (fromList [(5,"a"), (3,"b")])                        @?= fromList [(4, "b"), (6, "a")]
    mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) @?= singleton 1 "c"
    mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) @?= singleton 3 "c"

test_mapKeysWith :: Assertion
test_mapKeysWith = do
    mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) @?= singleton 1 "cdab"
    mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) @?= singleton 3 "cdab"

test_mapKeysMonotonic :: Assertion
test_mapKeysMonotonic = do
    mapKeysMonotonic (+ 1) (fromList [(5,"a"), (3,"b")])          @?= fromList [(4, "b"), (6, "a")]
    mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) @?= fromList [(6, "b"), (10, "a")]
    valid (mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")])) @?= True
    valid (mapKeysMonotonic (\ _ -> 1)     (fromList [(5,"a"), (3,"b")])) @?= False

----------------------------------------------------------------
-- Conversion

test_elems :: Assertion
test_elems = do
    elems (fromList [(5,"a"), (3,"b")]) @?= ["b","a"]
    elems (empty :: UMap) @?= []

test_keys :: Assertion
test_keys = do
    keys (fromList [(5,"a"), (3,"b")]) @?= [3,5]
    keys (empty :: UMap) @?= []

test_assocs :: Assertion
test_assocs = do
    assocs (fromList [(5,"a"), (3,"b")]) @?= [(3,"b"), (5,"a")]
    assocs (empty :: UMap) @?= []

test_keysSet :: Assertion
test_keysSet = do
    keysSet (fromList [(5,"a"), (3,"b")]) @?= Data.Set.fromList [3,5]
    keysSet (empty :: UMap) @?= Data.Set.empty

test_fromSet :: Assertion
test_fromSet = do
   fromSet (\k -> replicate k 'a') (Data.Set.fromList [3, 5]) @?= fromList [(5,"aaaaa"), (3,"aaa")]
   fromSet undefined Data.Set.empty @?= (empty :: IMap)

----------------------------------------------------------------
-- Lists

test_toList :: Assertion
test_toList = do
    toList (fromList [(5,"a"), (3,"b")]) @?= [(3,"b"), (5,"a")]
    toList (empty :: SMap) @?= []

test_fromList :: Assertion
test_fromList = do
    fromList [] @?= (empty :: SMap)
    fromList [(5,"a"), (3,"b"), (5, "c")] @?= fromList [(5,"c"), (3,"b")]
    fromList [(5,"c"), (3,"b"), (5, "a")] @?= fromList [(5,"a"), (3,"b")]

test_fromListWith :: Assertion
test_fromListWith = do
    fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] @?= fromList [(3, "ab"), (5, "aba")]
    fromListWith (++) [] @?= (empty :: SMap)

test_fromListWithKey :: Assertion
test_fromListWithKey = do
    fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] @?= fromList [(3, "3ab"), (5, "5a5ba")]
    fromListWithKey f [] @?= (empty :: SMap)
  where
    f k a1 a2 = (show k) ++ a1 ++ a2

----------------------------------------------------------------
-- Ordered lists

test_toAscList :: Assertion
test_toAscList = toAscList (fromList [(5,"a"), (3,"b")]) @?= [(3,"b"), (5,"a")]

test_toDescList :: Assertion
test_toDescList = toDescList (fromList [(5,"a"), (3,"b")]) @?= [(5,"a"), (3,"b")]

test_showTree :: Assertion
test_showTree =
       (let t = fromDistinctAscList [(x,()) | x <- [1..5]]
        in showTree t) @?= "4:=()\n+--2:=()\n|  +--1:=()\n|  +--3:=()\n+--5:=()\n"

test_showTree' :: Assertion
test_showTree' =
       (let t = fromDistinctAscList [(x,()) | x <- [1..5]]
        in s t ) @?= "+--5:=()\n|\n4:=()\n|\n|  +--3:=()\n|  |\n+--2:=()\n   |\n   +--1:=()\n"
   where
    showElem k x  = show k ++ ":=" ++ show x

    s = showTreeWith showElem False True


test_fromAscList :: Assertion
test_fromAscList = do
    fromAscList [(3,"b"), (5,"a")]          @?= fromList [(3, "b"), (5, "a")]
    fromAscList [(3,"b"), (5,"a"), (5,"b")] @?= fromList [(3, "b"), (5, "b")]
    valid (fromAscList [(3,"b"), (5,"a"), (5,"b")]) @?= True
    valid (fromAscList [(5,"a"), (3,"b"), (5,"b")]) @?= False

test_fromAscListWith :: Assertion
test_fromAscListWith = do
    fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] @?= fromList [(3, "b"), (5, "ba")]
    valid (fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")]) @?= True
    valid (fromAscListWith (++) [(5,"a"), (3,"b"), (5,"b")]) @?= False

test_fromAscListWithKey :: Assertion
test_fromAscListWithKey = do
    fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")] @?= fromList [(3, "b"), (5, "5:b5:ba")]
    valid (fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")]) @?= True
    valid (fromAscListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) @?= False
  where
    f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2

test_fromDistinctAscList :: Assertion
test_fromDistinctAscList = do
    fromDistinctAscList [(3,"b"), (5,"a")] @?= fromList [(3, "b"), (5, "a")]
    valid (fromDistinctAscList [(3,"b"), (5,"a")])          @?= True
    valid (fromDistinctAscList [(3,"b"), (5,"a"), (5,"b")]) @?= False

----------------------------------------------------------------
-- Filter

test_filter :: Assertion
test_filter = do
    filter (> "a") (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "b"
    filter (> "x") (fromList [(5,"a"), (3,"b")]) @?= empty
    filter (< "a") (fromList [(5,"a"), (3,"b")]) @?= empty

test_filteWithKey :: Assertion
test_filteWithKey = filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) @?= singleton 5 "a"

test_partition :: Assertion
test_partition = do
    partition (> "a") (fromList [(5,"a"), (3,"b")]) @?= (singleton 3 "b", singleton 5 "a")
    partition (< "x") (fromList [(5,"a"), (3,"b")]) @?= (fromList [(3, "b"), (5, "a")], empty)
    partition (> "x") (fromList [(5,"a"), (3,"b")]) @?= (empty, fromList [(3, "b"), (5, "a")])

test_partitionWithKey :: Assertion
test_partitionWithKey = do
    partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) @?= (singleton 5 "a", singleton 3 "b")
    partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) @?= (fromList [(3, "b"), (5, "a")], empty)
    partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) @?= (empty, fromList [(3, "b"), (5, "a")])

test_mapMaybe :: Assertion
test_mapMaybe = mapMaybe f (fromList [(5,"a"), (3,"b")]) @?= singleton 5 "new a"
  where
    f x = if x == "a" then Just "new a" else Nothing

test_mapMaybeWithKey :: Assertion
test_mapMaybeWithKey = mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "key : 3"
  where
    f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing

test_mapEither :: Assertion
test_mapEither = do
    mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
        @?= (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])
    mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
        @?= ((empty :: SMap), fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
 where
   f a = if a < "c" then Left a else Right a

test_mapEitherWithKey :: Assertion
test_mapEitherWithKey = do
    mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
     @?= (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")])
    mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
     @?= ((empty :: SMap), fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])
  where
    f k a = if k < 5 then Left (k * 2) else Right (a ++ a)

test_split :: Assertion
test_split = do
    split 2 (fromList [(5,"a"), (3,"b")]) @?= (empty, fromList [(3,"b"), (5,"a")])
    split 3 (fromList [(5,"a"), (3,"b")]) @?= (empty, singleton 5 "a")
    split 4 (fromList [(5,"a"), (3,"b")]) @?= (singleton 3 "b", singleton 5 "a")
    split 5 (fromList [(5,"a"), (3,"b")]) @?= (singleton 3 "b", empty)
    split 6 (fromList [(5,"a"), (3,"b")]) @?= (fromList [(3,"b"), (5,"a")], empty)

test_splitLookup :: Assertion
test_splitLookup = do
    splitLookup 2 (fromList [(5,"a"), (3,"b")]) @?= (empty, Nothing, fromList [(3,"b"), (5,"a")])
    splitLookup 3 (fromList [(5,"a"), (3,"b")]) @?= (empty, Just "b", singleton 5 "a")
    splitLookup 4 (fromList [(5,"a"), (3,"b")]) @?= (singleton 3 "b", Nothing, singleton 5 "a")
    splitLookup 5 (fromList [(5,"a"), (3,"b")]) @?= (singleton 3 "b", Just "a", empty)
    splitLookup 6 (fromList [(5,"a"), (3,"b")]) @?= (fromList [(3,"b"), (5,"a")], Nothing, empty)

----------------------------------------------------------------
-- Submap

test_isSubmapOfBy :: Assertion
test_isSubmapOfBy = do
    isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) @?= True
    isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)]) @?= True
    isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)]) @?= True
    isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)]) @?= False
    isSubmapOfBy (<)  (fromList [('a',1)]) (fromList [('a',1),('b',2)]) @?= False
    isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)]) @?= False

test_isSubmapOf :: Assertion
test_isSubmapOf = do
    isSubmapOf (fromList [('a',1)]) (fromList [('a',1),('b',2)]) @?= True
    isSubmapOf (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)]) @?= True
    isSubmapOf (fromList [('a',2)]) (fromList [('a',1),('b',2)]) @?= False
    isSubmapOf (fromList [('a',1),('b',2)]) (fromList [('a',1)]) @?= False

test_isProperSubmapOfBy :: Assertion
test_isProperSubmapOfBy = do
    isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) @?= True
    isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)]) @?= True
    isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) @?= False
    isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)]) @?= False
    isProperSubmapOfBy (<)  (fromList [(1,1)])       (fromList [(1,1),(2,2)]) @?= False

test_isProperSubmapOf :: Assertion
test_isProperSubmapOf = do
    isProperSubmapOf (fromList [(1,1)]) (fromList [(1,1),(2,2)]) @?= True
    isProperSubmapOf (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)]) @?= False
    isProperSubmapOf (fromList [(1,1),(2,2)]) (fromList [(1,1)]) @?= False

----------------------------------------------------------------
-- Indexed

test_lookupIndex :: Assertion
test_lookupIndex = do
    isJust (lookupIndex 2 (fromList [(5,"a"), (3,"b")]))   @?= False
    fromJust (lookupIndex 3 (fromList [(5,"a"), (3,"b")])) @?= 0
    fromJust (lookupIndex 5 (fromList [(5,"a"), (3,"b")])) @?= 1
    isJust (lookupIndex 6 (fromList [(5,"a"), (3,"b")]))   @?= False

test_findIndex :: Assertion
test_findIndex = do
    findIndex 3 (fromList [(5,"a"), (3,"b")]) @?= 0
    findIndex 5 (fromList [(5,"a"), (3,"b")]) @?= 1

test_elemAt :: Assertion
test_elemAt = do
    elemAt 0 (fromList [(5,"a"), (3,"b")]) @?= (3,"b")
    elemAt 1 (fromList [(5,"a"), (3,"b")]) @?= (5, "a")

test_updateAt :: Assertion
test_updateAt = do
    updateAt (\ _ _ -> Just "x") 0    (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "x"), (5, "a")]
    updateAt (\ _ _ -> Just "x") 1    (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "x")]
    updateAt (\_ _  -> Nothing)  0    (fromList [(5,"a"), (3,"b")]) @?= singleton 5 "a"
    updateAt (\_ _  -> Nothing)  1    (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "b"
--    updateAt (\_ _  -> Nothing)  7    (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "b"

test_deleteAt :: Assertion
test_deleteAt = do
    deleteAt 0  (fromList [(5,"a"), (3,"b")]) @?= singleton 5 "a"
    deleteAt 1  (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "b"

----------------------------------------------------------------
-- Min/Max

test_findMin :: Assertion
test_findMin = findMin (fromList [(5,"a"), (3,"b")]) @?= (3,"b")

test_findMax :: Assertion
test_findMax = findMax (fromList [(5,"a"), (3,"b")]) @?= (5,"a")

test_deleteMin :: Assertion
test_deleteMin = do
    deleteMin (fromList [(5,"a"), (3,"b"), (7,"c")]) @?= fromList [(5,"a"), (7,"c")]
    deleteMin (empty :: SMap) @?= empty

test_deleteMax :: Assertion
test_deleteMax = do
    deleteMax (fromList [(5,"a"), (3,"b"), (7,"c")]) @?= fromList [(3,"b"), (5,"a")]
    deleteMax (empty :: SMap) @?= empty

test_deleteFindMin :: Assertion
test_deleteFindMin = deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) @?= ((3,"b"), fromList[(5,"a"), (10,"c")])

test_deleteFindMax :: Assertion
test_deleteFindMax = deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) @?= ((10,"c"), fromList [(3,"b"), (5,"a")])

test_updateMin :: Assertion
test_updateMin = do
    updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "Xb"), (5, "a")]
    updateMin (\ _ -> Nothing)         (fromList [(5,"a"), (3,"b")]) @?= singleton 5 "a"

test_updateMax :: Assertion
test_updateMax = do
    updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) @?= fromList [(3, "b"), (5, "Xa")]
    updateMax (\ _ -> Nothing)         (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "b"

test_updateMinWithKey :: Assertion
test_updateMinWithKey = do
    updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) @?= fromList [(3,"3:b"), (5,"a")]
    updateMinWithKey (\ _ _ -> Nothing)                     (fromList [(5,"a"), (3,"b")]) @?= singleton 5 "a"

test_updateMaxWithKey :: Assertion
test_updateMaxWithKey = do
    updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) @?= fromList [(3,"b"), (5,"5:a")]
    updateMaxWithKey (\ _ _ -> Nothing)                     (fromList [(5,"a"), (3,"b")]) @?= singleton 3 "b"

test_minView :: Assertion
test_minView = do
    minView (fromList [(5,"a"), (3,"b")]) @?= Just ("b", singleton 5 "a")
    minView (empty :: SMap) @?= Nothing

test_maxView :: Assertion
test_maxView = do
    maxView (fromList [(5,"a"), (3,"b")]) @?= Just ("a", singleton 3 "b")
    maxView (empty :: SMap) @?= Nothing

test_minViewWithKey :: Assertion
test_minViewWithKey = do
    minViewWithKey (fromList [(5,"a"), (3,"b")]) @?= Just ((3,"b"), singleton 5 "a")
    minViewWithKey (empty :: SMap) @?= Nothing

test_maxViewWithKey :: Assertion
test_maxViewWithKey = do
    maxViewWithKey (fromList [(5,"a"), (3,"b")]) @?= Just ((5,"a"), singleton 3 "b")
    maxViewWithKey (empty :: SMap) @?= Nothing

----------------------------------------------------------------
-- Debug

test_valid :: Assertion
test_valid = do
    valid (fromAscList [(3,"b"), (5,"a")]) @?= True
    valid (fromAscList [(5,"a"), (3,"b")]) @?= False

----------------------------------------------------------------
-- QuickCheck
----------------------------------------------------------------

prop_valid :: UMap -> Bool
prop_valid t = valid t

prop_singleton :: Int -> Int -> Bool
prop_singleton k x = insert k x empty == singleton k x

prop_insert :: Int -> UMap -> Bool
prop_insert k t = valid $ insert k () t

prop_insertLookup :: Int -> UMap -> Bool
prop_insertLookup k t = lookup k (insert k () t) /= Nothing

prop_insertDelete :: Int -> UMap -> Bool
prop_insertDelete k t = valid $ delete k (insert k () t)

prop_insertDelete2 :: Int -> UMap -> Property
prop_insertDelete2 k t = (lookup k t == Nothing) ==> (delete k (insert k () t) == t)

prop_deleteNonMember :: Int -> UMap -> Property
prop_deleteNonMember k t = (lookup k t == Nothing) ==> (delete k t == t)

prop_deleteMin :: UMap -> Bool
prop_deleteMin t = valid $ deleteMin $ deleteMin t

prop_deleteMax :: UMap -> Bool
prop_deleteMax t = valid $ deleteMax $ deleteMax t

----------------------------------------------------------------

prop_split :: Int -> UMap -> Bool
prop_split k t = let (r,l) = split k t
                 in (valid r, valid l) == (True, True)

prop_splitRoot :: UMap -> Bool
prop_splitRoot s = loop ls && (s == unions ls)
 where
  ls = splitRoot s
  loop [] = True
  loop (s1:rst) = List.null
                  [ (x,y) | x <- toList s1
                          , y <- toList (unions rst)
                          , x > y ]

prop_link :: Int -> UMap -> Bool
prop_link k t = let (l,r) = split k t
                in valid (link k () l r)

prop_merge :: Int -> UMap -> Bool
prop_merge k t = let (l,r) = split k t
                 in valid (merge l r)

----------------------------------------------------------------

prop_union :: UMap -> UMap -> Bool
prop_union t1 t2 = valid (union t1 t2)

prop_unionModel :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_unionModel xs ys
  = sort (keys (union (fromList xs) (fromList ys)))
    == sort (nub (Prelude.map fst xs ++ Prelude.map fst ys))

prop_unionSingleton :: IMap -> Int -> Int -> Bool
prop_unionSingleton t k x = union (singleton k x) t == insert k x t

prop_unionAssoc :: IMap -> IMap -> IMap -> Bool
prop_unionAssoc t1 t2 t3 = union t1 (union t2 t3) == union (union t1 t2) t3

prop_unionWith :: IMap -> IMap -> Bool
prop_unionWith t1 t2 = (union t1 t2 == unionWith (\_ y -> y) t2 t1)

prop_unionWith2 :: IMap -> IMap -> Bool
prop_unionWith2 t1 t2 = valid (unionWithKey (\_ x y -> x+y) t1 t2)

prop_unionSum :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_unionSum xs ys
  = sum (elems (unionWith (+) (fromListWith (+) xs) (fromListWith (+) ys)))
    == (sum (Prelude.map snd xs) + sum (Prelude.map snd ys))

prop_difference :: IMap -> IMap -> Bool
prop_difference t1 t2 = valid (difference t1 t2)

prop_differenceModel :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_differenceModel xs ys
  = sort (keys (difference (fromListWith (+) xs) (fromListWith (+) ys)))
    == sort ((List.\\) (nub (Prelude.map fst xs)) (nub (Prelude.map fst ys)))

prop_intersection :: IMap -> IMap -> Bool
prop_intersection t1 t2 = valid (intersection t1 t2)

prop_intersectionModel :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_intersectionModel xs ys
  = sort (keys (intersection (fromListWith (+) xs) (fromListWith (+) ys)))
    == sort (nub ((List.intersect) (Prelude.map fst xs) (Prelude.map fst ys)))

prop_intersectionWith :: (Int -> Int -> Maybe Int) -> IMap -> IMap -> Bool
prop_intersectionWith f t1 t2 = valid (intersectionWith f t1 t2)

prop_intersectionWithModel :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_intersectionWithModel xs ys
  = toList (intersectionWith f (fromList xs') (fromList ys'))
    == [(kx, f vx vy) | (kx, vx) <- List.sort xs', (ky, vy) <- ys', kx == ky]
    where xs' = List.nubBy ((==) `on` fst) xs
          ys' = List.nubBy ((==) `on` fst) ys
          f l r = l + 2 * r

prop_intersectionWithKey :: (Int -> Int -> Int -> Maybe Int) -> IMap -> IMap -> Bool
prop_intersectionWithKey f t1 t2 = valid (intersectionWithKey f t1 t2)

prop_intersectionWithKeyModel :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_intersectionWithKeyModel xs ys
  = toList (intersectionWithKey f (fromList xs') (fromList ys'))
    == [(kx, f kx vx vy) | (kx, vx) <- List.sort xs', (ky, vy) <- ys', kx == ky]
    where xs' = List.nubBy ((==) `on` fst) xs
          ys' = List.nubBy ((==) `on` fst) ys
          f k l r = k + 2 * l + 3 * r

prop_mergeWithKeyModel :: [(Int,Int)] -> [(Int,Int)] -> Bool
prop_mergeWithKeyModel xs ys
  = and [ testMergeWithKey f keep_x keep_y
        | f <- [ \_k x1  _x2 -> Just x1
               , \_k _x1 x2  -> Just x2
               , \_k _x1 _x2 -> Nothing
               , \k  x1  x2  -> if k `mod` 2 == 0 then Nothing else Just (2 * x1 + 3 * x2)
               ]
        , keep_x <- [ True, False ]
        , keep_y <- [ True, False ]
        ]

    where xs' = List.nubBy ((==) `on` fst) xs
          ys' = List.nubBy ((==) `on` fst) ys

          xm = fromList xs'
          ym = fromList ys'

          testMergeWithKey f keep_x keep_y
            = toList (mergeWithKey f (keep keep_x) (keep keep_y) xm ym) == emulateMergeWithKey f keep_x keep_y
              where keep False _ = empty
                    keep True  m = m

                    emulateMergeWithKey f keep_x keep_y
                      = Maybe.mapMaybe combine (sort $ List.union (List.map fst xs') (List.map fst ys'))
                        where combine k = case (List.lookup k xs', List.lookup k ys') of
                                            (Nothing, Just y) -> if keep_y then Just (k, y) else Nothing
                                            (Just x, Nothing) -> if keep_x then Just (k, x) else Nothing
                                            (Just x, Just y) -> (\v -> (k, v)) `fmap` f k x y

          -- We prevent inlining testMergeWithKey to disable the SpecConstr
          -- optimalization. There are too many call patterns here so several
          -- warnings are issued if testMergeWithKey gets inlined.
          {-# NOINLINE testMergeWithKey #-}

----------------------------------------------------------------

prop_ordered :: Property
prop_ordered
  = forAll (choose (5,100)) $ \n ->
    let xs = [(x,()) | x <- [0..n::Int]]
    in fromAscList xs == fromList xs

prop_list :: [Int] -> Bool
prop_list xs = (sort (nub xs) == [x | (x,()) <- toList (fromList [(x,()) | x <- xs])])

prop_descList :: [Int] -> Bool
prop_descList xs = (reverse (sort (nub xs)) == [x | (x,()) <- toDescList (fromList [(x,()) | x <- xs])])

prop_ascDescList :: [Int] -> Bool
prop_ascDescList xs = toAscList m == reverse (toDescList m)
  where m = fromList $ zip xs $ repeat ()

prop_fromList :: [Int] -> Bool
prop_fromList xs
  = case fromList (zip xs xs) of
      t -> t == fromAscList (zip sort_xs sort_xs) &&
           t == fromDistinctAscList (zip nub_sort_xs nub_sort_xs) &&
           t == List.foldr (uncurry insert) empty (zip xs xs)
  where sort_xs = sort xs
        nub_sort_xs = List.map List.head $ List.group sort_xs

----------------------------------------------------------------

prop_alter :: UMap -> Int -> Bool
prop_alter t k = balanced t' && case lookup k t of
    Just _  -> (size t - 1) == size t' && lookup k t' == Nothing
    Nothing -> (size t + 1) == size t' && lookup k t' /= Nothing
  where
    t' = alter f k t
    f Nothing   = Just ()
    f (Just ()) = Nothing

------------------------------------------------------------------------
-- Compare against the list model (after nub on keys)

prop_index :: [Int] -> Property
prop_index xs = length xs > 0 ==>
  let m  = fromList (zip xs xs)
  in  xs == [ m ! i | i <- xs ]

prop_null :: IMap -> Bool
prop_null m = null m == (size m == 0)

prop_member :: [Int] -> Int -> Bool
prop_member xs n =
  let m  = fromList (zip xs xs)
  in all (\k -> k `member` m == (k `elem` xs)) (n : xs)

prop_notmember :: [Int] -> Int -> Bool
prop_notmember xs n =
  let m  = fromList (zip xs xs)
  in all (\k -> k `notMember` m == (k `notElem` xs)) (n : xs)

prop_lookup :: [(Int, Int)] -> Int -> Bool
prop_lookup xs n =
  let xs' = List.nubBy ((==) `on` fst) xs
      m = fromList xs'
  in all (\k -> lookup k m == List.lookup k xs') (n : List.map fst xs')

prop_find :: [(Int, Int)] -> Bool
prop_find xs =
  let xs' = List.nubBy ((==) `on` fst) xs
      m = fromList xs'
  in all (\(k, v) -> m ! k == v) xs'

prop_findWithDefault :: [(Int, Int)] -> Int -> Int -> Bool
prop_findWithDefault xs n x =
  let xs' = List.nubBy ((==) `on` fst) xs
      m = fromList xs'
  in all (\k -> findWithDefault x k m == maybe x id (List.lookup k xs')) (n : List.map fst xs')

test_lookupSomething :: (Int -> Map Int Int -> Maybe (Int, Int)) -> (Int -> Int -> Bool) -> [(Int, Int)] -> Bool
test_lookupSomething lookup' cmp xs =
  let odd_sorted_xs = filter_odd $ sort $ List.nubBy ((==) `on` fst) xs
      t = fromList odd_sorted_xs
      test k = case List.filter ((`cmp` k) . fst) odd_sorted_xs of
                 []             -> lookup' k t == Nothing
                 cs | 0 `cmp` 1 -> lookup' k t == Just (last cs) -- we want largest such element
                    | otherwise -> lookup' k t == Just (head cs) -- we want smallest such element
  in all test (List.map fst xs)

  where filter_odd [] = []
        filter_odd [_] = []
        filter_odd (_ : o : xs) = o : filter_odd xs

prop_lookupLT :: [(Int, Int)] -> Bool
prop_lookupLT = test_lookupSomething lookupLT (<)

prop_lookupGT :: [(Int, Int)] -> Bool
prop_lookupGT = test_lookupSomething lookupGT (>)

prop_lookupLE :: [(Int, Int)] -> Bool
prop_lookupLE = test_lookupSomething lookupLE (<=)

prop_lookupGE :: [(Int, Int)] -> Bool
prop_lookupGE = test_lookupSomething lookupGE (>=)

prop_findIndex :: [(Int, Int)] -> Property
prop_findIndex ys = length ys > 0 ==>
  let m = fromList ys
  in  findIndex (fst (head ys)) m `seq` True

prop_lookupIndex :: [(Int, Int)] -> Property
prop_lookupIndex ys = length ys > 0 ==>
  let m = fromList ys
  in  isJust (lookupIndex (fst (head ys)) m)

prop_findMin :: [(Int, Int)] -> Property
prop_findMin ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  findMin m == List.minimumBy (comparing fst) xs

prop_findMax :: [(Int, Int)] -> Property
prop_findMax ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  findMax m == List.maximumBy (comparing fst) xs

prop_deleteMinModel :: [(Int, Int)] -> Property
prop_deleteMinModel ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  toAscList (deleteMin m) == tail (sort xs)

prop_deleteMaxModel :: [(Int, Int)] -> Property
prop_deleteMaxModel ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  toAscList (deleteMax m) == init (sort xs)

prop_filter :: (Int -> Bool) -> [(Int, Int)] -> Property
prop_filter p ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  filter p m == fromList (List.filter (p . snd) xs)

prop_partition :: (Int -> Bool) -> [(Int, Int)] -> Property
prop_partition p ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  partition p m == let (a,b) = (List.partition (p . snd) xs) in (fromList a, fromList b)

prop_map :: (Int -> Int) -> [(Int, Int)] -> Property
prop_map f ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  map f m == fromList [ (a, f b) | (a,b) <- xs ]

prop_fmap :: (Int -> Int) -> [(Int, Int)] -> Property
prop_fmap f ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  fmap f m == fromList [ (a, f b) | (a,b) <- xs ]

prop_mapkeys :: (Int -> Int) -> [(Int, Int)] -> Property
prop_mapkeys f ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  mapKeys f m == (fromList $ List.nubBy ((==) `on` fst) $ reverse [ (f a, b) | (a,b) <- sort xs])

prop_splitModel :: Int -> [(Int, Int)] -> Property
prop_splitModel n ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      (l, r) = split n $ fromList xs
  in  toAscList l == sort [(k, v) | (k,v) <- xs, k < n] &&
      toAscList r == sort [(k, v) | (k,v) <- xs, k > n]

prop_foldr :: Int -> [(Int, Int)] -> Property
prop_foldr n ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  foldr (+) n m == List.foldr (+) n (List.map snd xs) &&
      foldr (:) [] m == List.map snd (List.sort xs) &&
      foldrWithKey (\_ a b -> a + b) n m == List.foldr (+) n (List.map snd xs) &&
      foldrWithKey (\k _ b -> k + b) n m == List.foldr (+) n (List.map fst xs) &&
      foldrWithKey (\k x xs -> (k,x):xs) [] m == List.sort xs


prop_foldr' :: Int -> [(Int, Int)] -> Property
prop_foldr' n ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  foldr' (+) n m == List.foldr (+) n (List.map snd xs) &&
      foldr' (:) [] m == List.map snd (List.sort xs) &&
      foldrWithKey' (\_ a b -> a + b) n m == List.foldr (+) n (List.map snd xs) &&
      foldrWithKey' (\k _ b -> k + b) n m == List.foldr (+) n (List.map fst xs) &&
      foldrWithKey' (\k x xs -> (k,x):xs) [] m == List.sort xs

prop_foldl :: Int -> [(Int, Int)] -> Property
prop_foldl n ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  foldl (+) n m == List.foldr (+) n (List.map snd xs) &&
      foldl (flip (:)) [] m == reverse (List.map snd (List.sort xs)) &&
      foldlWithKey (\b _ a -> a + b) n m == List.foldr (+) n (List.map snd xs) &&
      foldlWithKey (\b k _ -> k + b) n m == List.foldr (+) n (List.map fst xs) &&
      foldlWithKey (\xs k x -> (k,x):xs) [] m == reverse (List.sort xs)

prop_foldl' :: Int -> [(Int, Int)] -> Property
prop_foldl' n ys = length ys > 0 ==>
  let xs = List.nubBy ((==) `on` fst) ys
      m  = fromList xs
  in  foldl' (+) n m == List.foldr (+) n (List.map snd xs) &&
      foldl' (flip (:)) [] m == reverse (List.map snd (List.sort xs)) &&
      foldlWithKey' (\b _ a -> a + b) n m == List.foldr (+) n (List.map snd xs) &&
      foldlWithKey' (\b k _ -> k + b) n m == List.foldr (+) n (List.map fst xs) &&
      foldlWithKey' (\xs k x -> (k,x):xs) [] m == reverse (List.sort xs)

prop_keysSet :: [(Int, Int)] -> Bool
prop_keysSet xs =
  keysSet (fromList xs) == Data.Set.fromList (List.map fst xs)

prop_fromSet :: [(Int, Int)] -> Bool
prop_fromSet ys =
  let xs = List.nubBy ((==) `on` fst) ys
  in fromSet (\k -> fromJust $ List.lookup k xs) (Data.Set.fromList $ List.map fst xs) == fromList xs
