{-# LANGUAGE MultiParamTypeClasses  #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances      #-}

data N
data R

newtype List t a = List { unList :: [a] }

class Reverse a t u | t -> u, u -> t where
    rev :: List t a -> List u a

instance Reverse a N R where rev = reverse'
instance Reverse a R N where rev = reverse'

reverse' :: List t a -> List u a
reverse' = List . reverse . unList

id'      :: List t a -> List t a
id'      = List . id . unList

xs :: List N Int
xs = List [1..10]

{-
So now we see the type toggle. 


*Main> :t xs
xs :: List N Int

*Main> :t rev xs
rev xs :: List R Int

*Main> :t rev (rev xs)
rev (rev xs) :: List N Int
-}