module Lib where

import Test.QuickCheck
import Test.QuickCheck.Checkers


data List a = Nil
            | Cons a (List a)
            deriving(Eq, Show)


instance Functor List where
  fmap _ Nil = Nil
  fmap f (Cons a al) = Cons (f a) (fmap f al)

instance (Arbitrary a) => Arbitrary (List a) where
  arbitrary = do
    a <- arbitrary
    b <- arbitrary
    frequency [ (1, return Nil), (1, return (Cons a b))]

instance Eq a => EqProp (List a) where (=-=) = eq

instance  Applicative List where
  pure  x   = Cons x Nil
  _ <*> Nil = Nil
  Nil <*> _ = Nil
  Cons f fs <*> Cons a as = append (Cons (f a)  (fmap f as)) (fs <*> Cons a as)

instance Monad List where
  return = pure
  (>>=) (Cons a al) f = (f a ) (>>= al f)