Add remaining haskell book exercises

1 files changed, 58 insertions, 0 deletions

diff --git a/Haskell-book/14/qc/src/UsingQuickCheck.hs b/Haskell-book/14/qc/src/UsingQuickCheck.hs
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+++ b/Haskell-book/14/qc/src/UsingQuickCheck.hs
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+module UsingQuickCheck where
+
+import Test.QuickCheck
+
+--
+-- 1
+--
+half :: (Eq a, Fractional a) => a -> a
+half x = x / 2
+
+halfIdentity :: (Eq a, Fractional a) => a -> a
+halfIdentity = (*2) . half
+
+--
+-- 2
+--
+-- for any list you apply sort to
+-- this property should hold
+listOrdered :: (Ord a) => [a] -> Bool
+listOrdered xs =
+    snd $ foldr go (Nothing, True) xs
+    where go _ status@(_, False) = status
+          go y (Nothing, t) = (Just y, t)
+          go y (Just x, _) = (Just y, x >= y)
+
+--
+-- 3
+--
+plusAssociative :: (Ord a, Integral a) => a -> a -> a -> Bool
+plusAssociative x y z = x + (y + z) == (x + y) + z
+
+plusCommutative :: (Ord a, Integral a) => a -> a -> Bool
+plusCommutative x y = x + y == y + x
+
+--
+-- 4
+--
+mulAssociative :: (Ord a, Integral a) => a -> a -> a -> Bool
+mulAssociative x y z = x * (y * z) == (x * y) * z
+
+mulCommutative :: (Ord a, Integral a) => a -> a -> Bool
+mulCommutative x y = x * y == y * x
+
+data Fool = Fulse
+          | Frue
+          deriving (Eq, Show)
+
+data Fool' = Fulse' -- 2/3
+           | Frue'  -- 1/3
+           deriving (Eq, Show)
+
+instance Arbitrary Fool where
+    arbitrary = oneof [ return Fulse
+                      , return Frue ]
+
+instance Arbitrary Fool' where
+    arbitrary = frequency [ (3, return Fulse')
+                          , (1, return Frue')]
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