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module List where
import Test.QuickCheck
import Test.QuickCheck.Checkers
data List a =
Nil
| Cons a (List a)
deriving (Eq, Show)
instance Functor List where
fmap f Nil = Nil
fmap f (Cons x xs) = Cons (f x) (fmap f xs)
append :: List a -> List a -> List a
append Nil ys = ys
append (Cons x xs) ys = Cons x $ xs `append` ys
fold :: (a -> b -> b) -> b -> List a -> b
fold _ b Nil = b
fold f b (Cons h t) = f h (fold f b t)
concat' :: List (List a) -> List a
concat' = fold append Nil
flatMap :: (a -> List b) -> List a -> List b
flatMap f as = concat' $ fmap f as
instance Applicative List where
pure f = Cons f Nil
Nil <*> _ = Nil
_ <*> Nil = Nil
f <*> x = flatMap (\f' -> fmap f' x) f
instance Monad List where
return = pure
x >>= f = concat' $ fmap f x
instance Arbitrary a => Arbitrary (List a) where
arbitrary = frequency [(1, pure Nil),
(5, Cons <$> arbitrary <*> arbitrary)]
instance Eq a => EqProp (List a) where
(=-=) = eq
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