gistfile1.hs

type Square = Square' Nil
data Square' t a = Zero (t (t a)) | Succ (Square' (Cons t) a)  
data Nil a = Nil                                               deriving Show
data Cons t a = Cons a (t a)                                   deriving Show

mapNil :: (a -> b) -> Nil a -> Nil b
mapNil _ _ = Nil

mapCons  ::  ((a -> b) -> (t a -> t b))
         ->  (a -> b)
         ->  (Cons t a -> Cons t b)
mapCons fT fA (Cons x xs) = Cons (fA x) (fT fA xs)

mapSquare'  ::  (forall b. (a -> b) -> (t a -> t b))
            ->  (a -> b)
            ->  (Square' t a -> Square' t b)
mapSquare' fT fA  (Zero xs)  = fT (fT fA) xs
mapSquare' fT fA  (Succ xs)  = mapSquare' (mapCons fT) fA xs

-- Yields:
Ass5.lhs:134:31:
    Occurs check: cannot construct the infinite type: t = Cons t
    In the first argument of `mapSquare'', namely `(mapCons fT)'
    In the expression: mapSquare' (mapCons fT) fA xs
    In the definition of `mapSquare'':
        mapSquare' fT fA (Succ xs) = mapSquare' (mapCons fT) fA xs