Add remaining haskell book exercises

Haskell-book/14/qc/tests/UsingQuickCheckTest.hs

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+module Main where
+
+import Data.List (sort)
+import UsingQuickCheck
+import Test.QuickCheck
+
+prop_half :: (Eq a, Fractional a) => a -> Bool
+prop_half x = (halfIdentity x) == x
+
+associativeGen :: (Integer -> Integer -> Integer -> Bool) -> Gen Bool
+associativeGen f = do
+    x <- (arbitrary :: Gen Integer)
+    y <- (arbitrary :: Gen Integer)
+    z <- (arbitrary :: Gen Integer)
+    elements [f x y z]
+
+commutativeGen :: (Integer -> Integer -> Bool) -> Gen Bool
+commutativeGen f = do
+    x <- (arbitrary :: Gen Integer)
+    y <- (arbitrary :: Gen Integer)
+    elements [f x y]
+
+assocNotNegGen :: (Int -> Int -> Int -> Bool) -> Gen Bool
+assocNotNegGen f = do
+    x <- choose (1 :: Int, 100)
+    y <- choose (1 :: Int, 100)
+    z <- choose (1 :: Int, 100)
+    elements [f x y z]
+
+commutNotNegGen :: (Int -> Int -> Bool) -> Gen Bool
+commutNotNegGen f = do
+    x <- choose (1 :: Int, 100)
+    y <- choose (1 :: Int, 100)
+    elements [f x y]
+    
+
+prop_quotRem :: Property
+prop_quotRem =
+    forAll (prop_quotRem') (\(x ,y) -> (quot x y) * y + (rem x y) == x)
+    where prop_quotRem' = do
+          x <- choose (1 :: Int, 10000)
+          y <- choose (1 :: Int, 10000)
+          return (x, y)
+
+prop_divMod :: Property
+prop_divMod =
+    forAll (prop_divMod') (\(x ,y) -> (div x y) * y + (mod x y) == x)
+    where prop_divMod' = do
+          x <- choose (1 :: Int, 10000)
+          y <- choose (1 :: Int, 10000)
+          return (x, y)
+
+prop_reverse :: Property
+prop_reverse =
+    forAll prop_reverse' (\xs -> (reverse . reverse) xs == id xs)
+    where prop_reverse' = do
+          x <- (arbitrary :: Gen [Integer])
+          return x
+
+prop_dollar :: Property
+prop_dollar =
+    forAll prop_dollar' (\x -> x)
+    where prop_dollar' = do
+          x <- (arbitrary :: Gen Integer)
+          return ((id $ x) == (id x))
+
+prop_point :: Property
+prop_point =
+    forAll prop_point' (\x -> x)
+    where prop_point' = do
+          x <- (arbitrary :: Gen Integer)
+          let pointFunc = negate . id
+          let appliedFunc = \y -> negate (id y)
+          return (pointFunc x == appliedFunc x)
+
+prop_foldr1 :: Property
+prop_foldr1 =
+    forAll prop_foldr1' (\x -> x)
+    where prop_foldr1' = do
+          x <- (arbitrary :: Gen [Integer])
+          y <- (arbitrary :: Gen [Integer])
+          return ((foldr (:) x y) == (x ++ y))
+
+prop_foldr2 :: Property
+prop_foldr2 =
+    forAll prop_foldr2' (\x -> x)
+    where prop_foldr2' = do
+          x <- (arbitrary :: Gen [[Integer]])
+          return ((foldr (++) [] x) == (concat x))
+
+prop_length :: Property
+prop_length =
+    forAll prop_length' (\x -> x)
+    where prop_length' = do
+          n <- (arbitrary :: Gen Int)
+          xs <- (arbitrary :: Gen [Integer])
+          return ((length (take n xs)) == n)
+
+prop_readShow :: Property
+prop_readShow =
+    forAll prop_readShow' (\x -> x)
+    where prop_readShow' = do
+          x <- (arbitrary :: Gen Integer)
+          return ((read (show x)) == x)
+
+main :: IO ()
+main = do
+    quickCheck (prop_half :: Double -> Bool)
+    quickCheck $ (listOrdered :: [Int] -> Bool) . sort
+    
+    quickCheck $ associativeGen plusAssociative
+    quickCheck $ commutativeGen plusCommutative
+    quickCheck $ associativeGen mulAssociative
+    quickCheck $ commutativeGen mulCommutative
+
+    quickCheck prop_quotRem
+    quickCheck prop_divMod
+
+    quickCheck $ assocNotNegGen (\x y z -> x ^ (y ^ z) == (x ^ y) ^ z)
+    quickCheck $ commutNotNegGen (\x y -> x ^ y == y ^ x)
+
+    quickCheck prop_reverse
+    quickCheck prop_dollar
+    quickCheck prop_point
+    quickCheck prop_foldr1
+    quickCheck prop_foldr2
+    quickCheck prop_length
+    quickCheck prop_readShow