FixListF.hs

{-# LANGUAGE TypeSynonymInstances #-}
{-# LANGUAGE FlexibleInstances #-}

newtype Fix f = Fix
  { unFix :: f (Fix f)
  }

cata :: Functor f => (f a -> a) -> Fix f -> a
cata f (Fix x) = f $ fmap (cata f) x

data ListF a b = Cons a b | Nil
  deriving (Show)

instance Functor (ListF a) where
  fmap _ Nil = Nil
  fmap f (Cons x y) = Cons x $ f y

type List a = Fix (ListF a)

instance Show a => Show (List a) where
  show (Fix Nil) = "Nil"
  show (Fix (Cons x y)) = show x <> ", " <> show y

xs :: List Int
xs = Fix (Cons 10 $ Fix (Cons 20 $ Fix Nil))

main :: IO ()
main = print xs
-- 10, 20, Nil