more bad lists

badlist.hs

{-# LANGUAGE RankNTypes #-}

newtype Listy a = Listy { runListy :: forall b . (a -> b -> b) -> b -> b }

nil :: Listy a
nil = Listy $ \_ init -> init

cons :: a -> Listy a -> Listy a
cons x xs = Listy $ \fn init -> fn x (runListy xs fn init)

foldr :: (a -> b -> b) -> b -> Listy a -> b
foldr fn init xs = runListy xs fn init

-- https://stackoverflow.com/questions/6172004/writing-foldl-using-foldr
foldl :: (b -> a -> b) -> b -> Listy a -> b
foldl fn init xs = runListy xs (\x g a -> g (fn a x)) id $ init

instance Functor Listy where
   fmap f xs = runListy xs (\h t -> cons (f h) t) nil

toList :: Listy a -> [a]
toList xs = runListy xs (:) []