快速检查Wrap类型类的函子定律

如何解决快速检查Wrap类型类的函子定律

我编写了一个代码来测试“常数”和“包装”这两种数据类型的仿函数定律。我完成了用于快速检查Constant数据类型的代码,但被Wrap数据类型卡住了。 (“ wrapGen”功能)我尝试过,但无法实现“ wrapGen”功能。我可以得到一些提示吗?

非常感谢。

import Test.QuickCheck
import Test.QuickCheck.Function  -- for Fun
 
-- Functor laws
functorIdentity :: (Functor f,Eq (f a)) => f a -> Bool
functorIdentity f = fmap id f == f

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)

-- ┌--------------------------------------------┐
-- | Constant datatype (Example)                |
-- └--------------------------------------------┘

newtype Constant a b = Constant { getConstant :: a } deriving (Eq,Show)

instance Functor (Constant m) where
  fmap _ (Constant v) = Constant v

instance (Arbitrary a,Arbitrary b) => Arbitrary (Constant a b) where
  arbitrary = constGen

constGen :: (Arbitrary a,Arbitrary b) => Gen (Constant a b)
constGen = do
  a <- arbitrary
  return (Constant a)  

type IntToInt = Fun Int Int
type ConstFC = (Constant Int Int) -> IntToInt -> IntToInt -> Bool

test_Const :: IO ()
test_Const = do
  quickCheck $ \x -> functorIdentity(x :: Constant Int Int)
  quickCheck (functorCompose' :: ConstFC)

-- ┌--------------------------------------------┐
-- | Wrap datatype (Question)                   |
-- └--------------------------------------------┘

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

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

instance (Functor f,Arbitrary a) => Arbitrary (Wrap f a) where
  arbitrary = wrapGen

wrapGen :: (Functor f,Arbitrary a) => Gen (Wrap f a)
wrapGen = undefined  -- TODO: How can I implement this? 

type WrapFC = (Constant Int Int) -> IntToInt -> IntToInt -> Bool

qcWrap :: IO ()
qcWrap = do 
  quickCheck $ \x -> functorIdentity (x :: Wrap Maybe Int)
  quickCheck (functorCompose :: WrapFC)

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