content: import Data.Bits ((.&.))
  import Data.IntSet
  import Data.List (nub,sort)
  import qualified Data.List as List
  import Data.Monoid (mempty)
  import qualified Data.Set as Set
  import Prelude hiding (lookup, null, map, filter, foldr, foldl)
  import Test.Framework
  import Test.Framework.Providers.HUnit
  import Test.Framework.Providers.QuickCheck2
  import Test.HUnit hiding (Test, Testable)
  import Test.QuickCheck hiding ((.&.))
  
  main :: IO ()
  main = defaultMainWithOpts [ testCase "lookupLT" test_lookupLT
                             , testCase "lookupGT" test_lookupGT
                             , testCase "lookupLE" test_lookupLE
                             , testCase "lookupGE" test_lookupGE
                             , testCase "split" test_split
                             , testProperty "prop_Single" prop_Single
                             , testProperty "prop_Member" prop_Member
                             , testProperty "prop_NotMember" prop_NotMember
                             , testProperty "prop_LookupLT" prop_LookupLT
                             , testProperty "prop_LookupGT" prop_LookupGT
                             , testProperty "prop_LookupLE" prop_LookupLE
                             , testProperty "prop_LookupGE" prop_LookupGE
                             , testProperty "prop_InsertDelete" prop_InsertDelete
                             , testProperty "prop_MemberFromList" prop_MemberFromList
                             , testProperty "prop_UnionInsert" prop_UnionInsert
                             , testProperty "prop_UnionAssoc" prop_UnionAssoc
                             , testProperty "prop_UnionComm" prop_UnionComm
                             , testProperty "prop_Diff" prop_Diff
                             , testProperty "prop_Int" prop_Int
                             , testProperty "prop_Ordered" prop_Ordered
                             , testProperty "prop_List" prop_List
                             , testProperty "prop_DescList" prop_DescList
                             , testProperty "prop_AscDescList" prop_AscDescList
                             , testProperty "prop_fromList" prop_fromList
                             , testProperty "prop_MaskPow2" prop_MaskPow2
                             , testProperty "prop_Prefix" prop_Prefix
                             , testProperty "prop_LeftRight" prop_LeftRight
                             , testProperty "prop_isProperSubsetOf" prop_isProperSubsetOf
                             , testProperty "prop_isProperSubsetOf2" prop_isProperSubsetOf2
                             , testProperty "prop_isSubsetOf" prop_isSubsetOf
                             , testProperty "prop_isSubsetOf2" prop_isSubsetOf2
                             , testProperty "prop_size" prop_size
                             , testProperty "prop_findMax" prop_findMax
                             , testProperty "prop_findMin" prop_findMin
                             , testProperty "prop_ord" prop_ord
                             , testProperty "prop_readShow" prop_readShow
                             , testProperty "prop_foldR" prop_foldR
                             , testProperty "prop_foldR'" prop_foldR'
                             , testProperty "prop_foldL" prop_foldL
                             , testProperty "prop_foldL'" prop_foldL'
                             , testProperty "prop_map" prop_map
                             , testProperty "prop_maxView" prop_maxView
                             , testProperty "prop_minView" prop_minView
                             , testProperty "prop_split" prop_split
                             , testProperty "prop_splitMember" prop_splitMember
                             , testProperty "prop_partition" prop_partition
                             , testProperty "prop_filter" prop_filter
                             ] opts
    where
      opts = mempty { ropt_test_options = Just $ mempty { topt_maximum_generated_tests = Just 500
                                                        , topt_maximum_unsuitable_generated_tests = Just 500
                                                        }
                    }
  
  ----------------------------------------------------------------
  -- Unit tests
  ----------------------------------------------------------------
  
  test_lookupLT :: Assertion
  test_lookupLT = do
      lookupLT 3 (fromList [3, 5]) @?= Nothing
      lookupLT 5 (fromList [3, 5]) @?= Just 3
  
  test_lookupGT :: Assertion
  test_lookupGT = do
     lookupGT 4 (fromList [3, 5]) @?= Just 5
     lookupGT 5 (fromList [3, 5]) @?= Nothing
  
  test_lookupLE :: Assertion
  test_lookupLE = do
     lookupLE 2 (fromList [3, 5]) @?= Nothing
     lookupLE 4 (fromList [3, 5]) @?= Just 3
     lookupLE 5 (fromList [3, 5]) @?= Just 5
  
  test_lookupGE :: Assertion
  test_lookupGE = do
     lookupGE 3 (fromList [3, 5]) @?= Just 3
     lookupGE 4 (fromList [3, 5]) @?= Just 5
     lookupGE 6 (fromList [3, 5]) @?= Nothing
  
  test_split :: Assertion
  test_split = do
     split 3 (fromList [1..5]) @?= (fromList [1,2], fromList [4,5])
  
  {--------------------------------------------------------------------
    Arbitrary, reasonably balanced trees
  --------------------------------------------------------------------}
  instance Arbitrary IntSet where
    arbitrary = do{ xs <- arbitrary
                  ; return (fromList xs)
                  }
  
  
  {--------------------------------------------------------------------
    Single, Member, Insert, Delete, Member, FromList
  --------------------------------------------------------------------}
  prop_Single :: Int -> Bool
  prop_Single x
    = (insert x empty == singleton x)
  
  prop_Member :: [Int] -> Int -> Bool
  prop_Member xs n =
    let m  = fromList xs
    in all (\k -> k `member` m == (k `elem` xs)) (n : xs)
  
  prop_NotMember :: [Int] -> Int -> Bool
  prop_NotMember xs n =
    let m  = fromList xs
    in all (\k -> k `notMember` m == (k `notElem` xs)) (n : xs)
  
  test_LookupSomething :: (Int -> IntSet -> Maybe Int) -> (Int -> Int -> Bool) -> [Int] -> Bool
  test_LookupSomething lookup' cmp xs =
    let odd_sorted_xs = filter_odd $ nub $ sort xs
        t = fromList odd_sorted_xs
        test x = case List.filter (`cmp` x) odd_sorted_xs of
                   []             -> lookup' x t == Nothing
                   cs | 0 `cmp` 1 -> lookup' x t == Just (last cs) -- we want largest such element
                      | otherwise -> lookup' x t == Just (head cs) -- we want smallest such element
    in all test xs
  
    where filter_odd [] = []
          filter_odd [_] = []
          filter_odd (_ : o : xs) = o : filter_odd xs
  
  prop_LookupLT :: [Int] -> Bool
  prop_LookupLT = test_LookupSomething lookupLT (<)
  
  prop_LookupGT :: [Int] -> Bool
  prop_LookupGT = test_LookupSomething lookupGT (>)
  
  prop_LookupLE :: [Int] -> Bool
  prop_LookupLE = test_LookupSomething lookupLE (<=)
  
  prop_LookupGE :: [Int] -> Bool
  prop_LookupGE = test_LookupSomething lookupGE (>=)
  
  prop_InsertDelete :: Int -> IntSet -> Property
  prop_InsertDelete k t
    = not (member k t) ==> delete k (insert k t) == t
  
  prop_MemberFromList :: [Int] -> Bool
  prop_MemberFromList xs
    = all (`member` t) abs_xs && all ((`notMember` t) . negate) abs_xs
    where abs_xs = [abs x | x <- xs, x /= 0]
          t = fromList abs_xs
  
  {--------------------------------------------------------------------
    Union
  --------------------------------------------------------------------}
  prop_UnionInsert :: Int -> IntSet -> Bool
  prop_UnionInsert x t
    = union t (singleton x) == insert x t
  
  prop_UnionAssoc :: IntSet -> IntSet -> IntSet -> Bool
  prop_UnionAssoc t1 t2 t3
    = union t1 (union t2 t3) == union (union t1 t2) t3
  
  prop_UnionComm :: IntSet -> IntSet -> Bool
  prop_UnionComm t1 t2
    = (union t1 t2 == union t2 t1)
  
  prop_Diff :: [Int] -> [Int] -> Bool
  prop_Diff xs ys
    =  toAscList (difference (fromList xs) (fromList ys))
      == List.sort ((List.\\) (nub xs)  (nub ys))
  
  prop_Int :: [Int] -> [Int] -> Bool
  prop_Int xs ys
    =  toAscList (intersection (fromList xs) (fromList ys))
      == List.sort (nub ((List.intersect) (xs)  (ys)))
  
  {--------------------------------------------------------------------
    Lists
  --------------------------------------------------------------------}
  prop_Ordered
    = forAll (choose (5,100)) $ \n ->
      let xs = concat [[i-n,i-n]|i<-[0..2*n :: Int]]
      in fromAscList xs == fromList xs
  
  prop_List :: [Int] -> Bool
  prop_List xs
    = (sort (nub xs) == toAscList (fromList xs))
  
  prop_DescList :: [Int] -> Bool
  prop_DescList xs = (reverse (sort (nub xs)) == toDescList (fromList xs))
  
  prop_AscDescList :: [Int] -> Bool
  prop_AscDescList xs = toAscList s == reverse (toDescList s)
    where s = fromList xs
  
  prop_fromList :: [Int] -> Bool
  prop_fromList xs
    = case fromList xs of
        t -> t == fromAscList sort_xs &&
             t == fromDistinctAscList nub_sort_xs &&
             t == List.foldr insert empty xs
    where sort_xs = sort xs
          nub_sort_xs = List.map List.head $ List.group sort_xs
  
  {--------------------------------------------------------------------
    Bin invariants
  --------------------------------------------------------------------}
  powersOf2 :: IntSet
  powersOf2 = fromList [2^i | i <- [0..63]]
  
  -- Check the invariant that the mask is a power of 2.
  prop_MaskPow2 :: IntSet -> Bool
  prop_MaskPow2 (Bin _ msk left right) = member msk powersOf2 && prop_MaskPow2 left && prop_MaskPow2 right
  prop_MaskPow2 _ = True
  
  -- Check that the prefix satisfies its invariant.
  prop_Prefix :: IntSet -> Bool
  prop_Prefix s@(Bin prefix msk left right) = all (\elem -> match elem prefix msk) (toList s) && prop_Prefix left && prop_Prefix right
  prop_Prefix _ = True
  
  -- Check that the left elements don't have the mask bit set, and the right
  -- ones do.
  prop_LeftRight :: IntSet -> Bool
  prop_LeftRight (Bin _ msk left right) = and [x .&. msk == 0 | x <- toList left] && and [x .&. msk == msk | x <- toList right]
  prop_LeftRight _ = True
  
  {--------------------------------------------------------------------
    IntSet operations are like Set operations
  --------------------------------------------------------------------}
  toSet :: IntSet -> Set.Set Int
  toSet = Set.fromList . toList
  
  -- Check that IntSet.isProperSubsetOf is the same as Set.isProperSubsetOf.
  prop_isProperSubsetOf :: IntSet -> IntSet -> Bool
  prop_isProperSubsetOf a b = isProperSubsetOf a b == Set.isProperSubsetOf (toSet a) (toSet b)
  
  -- In the above test, isProperSubsetOf almost always returns False (since a
  -- random set is almost never a subset of another random set).  So this second
  -- test checks the True case.
  prop_isProperSubsetOf2 :: IntSet -> IntSet -> Bool
  prop_isProperSubsetOf2 a b = isProperSubsetOf a c == (a /= c) where
    c = union a b
  
  prop_isSubsetOf :: IntSet -> IntSet -> Bool
  prop_isSubsetOf a b = isSubsetOf a b == Set.isSubsetOf (toSet a) (toSet b)
  
  prop_isSubsetOf2 :: IntSet -> IntSet -> Bool
  prop_isSubsetOf2 a b = isSubsetOf a (union a b)
  
  prop_size :: IntSet -> Bool
  prop_size s = size s == List.length (toList s)
  
  prop_findMax :: IntSet -> Property
  prop_findMax s = not (null s) ==> findMax s == maximum (toList s)
  
  prop_findMin :: IntSet -> Property
  prop_findMin s = not (null s) ==> findMin s == minimum (toList s)
  
  prop_ord :: IntSet -> IntSet -> Bool
  prop_ord s1 s2 = s1 `compare` s2 == toList s1 `compare` toList s2
  
  prop_readShow :: IntSet -> Bool
  prop_readShow s = s == read (show s)
  
  prop_foldR :: IntSet -> Bool
  prop_foldR s = foldr (:) [] s == toList s
  
  prop_foldR' :: IntSet -> Bool
  prop_foldR' s = foldr' (:) [] s == toList s
  
  prop_foldL :: IntSet -> Bool
  prop_foldL s = foldl (flip (:)) [] s == List.foldl (flip (:)) [] (toList s)
  
  prop_foldL' :: IntSet -> Bool
  prop_foldL' s = foldl' (flip (:)) [] s == List.foldl' (flip (:)) [] (toList s)
  
  prop_map :: IntSet -> Bool
  prop_map s = map id s == s
  
  prop_maxView :: IntSet -> Bool
  prop_maxView s = case maxView s of
      Nothing -> null s
      Just (m,s') -> m == maximum (toList s) && s == insert m s' && m `notMember` s'
  
  prop_minView :: IntSet -> Bool
  prop_minView s = case minView s of
      Nothing -> null s
      Just (m,s') -> m == minimum (toList s) && s == insert m s' && m `notMember` s'
  
  prop_split :: IntSet -> Int -> Bool
  prop_split s i = case split i s of
      (s1,s2) -> all (<i) (toList s1) && all (>i) (toList s2) && i `delete` s == union s1 s2
  
  prop_splitMember :: IntSet -> Int -> Bool
  prop_splitMember s i = case splitMember i s of
      (s1,t,s2) -> all (<i) (toList s1) && all (>i) (toList s2) && t == i `member` s && i `delete` s == union s1 s2
  
  prop_partition :: IntSet -> Int -> Bool
  prop_partition s i = case partition odd s of
      (s1,s2) -> all odd (toList s1) && all even (toList s2) && s == s1 `union` s2
  
  prop_filter :: IntSet -> Int -> Bool
  prop_filter s i = partition odd s == (filter odd s, filter even s)
  