{-# LANGUAGE ViewPatterns #-}

import Func
import Test.QuickCheck
import Test.QuickCheck.Function

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

functorCompose :: (Eq (f c), Functor f) =>
       (a -> b)
    -> (b -> c)
    -> f a
    -> Bool
functorCompose f g x =
    (fmap g (fmap f x)) == (fmap (g . f) x)

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

main :: IO ()
main = do
    quickCheck (functorIdentity :: Identity Int -> Bool)
    quickCheck ((functorCompose (+1) (*2)) :: Identity Int -> Bool)
    quickCheck (functorCompose' :: Identity Int -> Fun Int Int -> Fun Int Int -> Bool)

    quickCheck (functorIdentity :: Pair Int -> Bool)
    quickCheck ((functorCompose (+1) (*2)) :: Pair Int -> Bool)
    quickCheck (functorCompose' :: Pair Int -> Fun Int Int -> Fun Int Int -> Bool)

    quickCheck (functorIdentity :: Two Int Int -> Bool)
    quickCheck ((functorCompose (+1) (*2)) :: Two Int Int -> Bool)
    quickCheck (functorCompose' :: Two Int Int -> Fun Int Int -> Fun Int Int -> Bool)

    quickCheck (functorIdentity :: Three Int Int Int -> Bool)
    quickCheck ((functorCompose (+1) (*2)) :: Three Int Int Int -> Bool)
    quickCheck (functorCompose' :: Three Int Int Int -> Fun Int Int -> Fun Int Int -> Bool)

    quickCheck (functorIdentity :: Three' Int Int -> Bool)
    quickCheck ((functorCompose (+1) (*2)) :: Three' Int Int -> Bool)
    quickCheck (functorCompose' :: Three' Int Int -> Fun Int Int -> Fun Int Int -> Bool)

    quickCheck (functorIdentity :: Four Int Int Int Int -> Bool)
    quickCheck ((functorCompose (+1) (*2)) :: Four Int Int Int Int -> Bool)
    quickCheck (functorCompose' :: Four Int Int Int Int -> Fun Int Int -> Fun Int Int -> Bool)

    quickCheck (functorIdentity :: Four' Int Int -> Bool)
    quickCheck ((functorCompose (+1) (*2)) :: Four' Int Int -> Bool)
    quickCheck (functorCompose' :: Four' Int Int -> Fun Int Int -> Fun Int Int -> Bool)