Functor

Functor.hs

import Test.QuickCheck
import Test.QuickCheck.Function

prop_revapp :: [Int] -> [Int] -> Bool
prop_revapp xs ys = reverse (ys++xs) == reverse xs ++ reverse ys

data Two a b = Two a b deriving (Eq, Show)
data Or a b = First a | Second b deriving (Eq, Show)

instance Functor (Two a) where
  fmap f (Two a b) = Two a (f b)

functorTwoIdentity :: (Functor f, Eq (f a)) => f a -> Bool
functorTwoIdentity f = fmap id f == f

functorTwoCompose :: (Eq (f c), Functor f) => f a -> Fun a b -> Fun b c -> Bool
functorTwoCompose x (Fun _ f) (Fun _ g) = fmap (g . f) x == (fmap g . fmap f $ x)

type IntToInt = Fun Int Int
type IntFC = [Int] -> IntToInt -> IntToInt -> Bool

instance Functor (Or a) where
  fmap f (First a) = First a
  fmap f (Second b) = Second (f b)

data Wrap f a = Wrap (f a) deriving (Eq, Show)

instance Functor (Wrap f) where
  fmap f (Wrap fa) = Wrap (f fa)

instance Functor (Wrap f) where
  fmap f (Wrap fa) = Wrap (fmap f fa)

instance Functor f => Functor (Wrap f) where 
  fmap f (Wrap fa) = Wrap (fmap f fa)

main :: IO ()
main = do
  quickCheck $ \x -> functorTwoIdentity (x :: [Int])
  quickCheck (functorTwoIdentity :: [Int] -> Bool)
  quickCheck (functorTwoCompose :: IntFC)