Hi all, Below is a program that implements Show for functions whose type is composed of only (->) and type variables (or, more precisely, of (->) and (State Int Term), but any type composed of (->) and type variables can obviously be specialized to that). (-fglasgow-exts is needed only for the convenience of being able to declare "instance MkTerm (State Int Term)" -- if we'd wrap the State Int Term in a newtype, as far as I can see this would be H98.) - Benja {-# OPTIONS_GHC -fglasgow-exts #-} import Control.Monad import Control.Monad.State import Data.Char data Term = Var Int | App Term Term | Lam Int Term showVar i = [chr (ord 'a' + i)] showTerm :: Term -> String showTerm (Var i) = showVar i showTerm (Lam i x) = "\\" ++ showVar i ++ " -> " ++ showTerm x showTerm (App f x) = showTerm f ++ " " ++ showArg x where showArg (Var i) = showVar i; showArg x = "(" ++ showTerm x ++ ")" class MkTerm a where argument :: State Int Term -> a mkTerm :: a -> State Int Term instance MkTerm (State Int Term) where argument = id mkTerm = id instance (MkTerm a, MkTerm b) => MkTerm (a -> b) where argument f x = argument $ liftM2 App f (mkTerm x) mkTerm f = do i <- get; modify (+1) body <- mkTerm (f (argument (return (Var i)))) return $ Lam i body instance (MkTerm a, MkTerm b) => Show (a -> b) where show f = showTerm $ evalState (mkTerm f) 0 type X = State Int Term main = do print (id :: X -> X) print (id :: (X -> X) -> (X -> X)) print ((.) :: (X -> X) -> (X -> X) -> (X -> X)) print ((\x y -> y x) :: X -> (X -> X) -> X) print ((\f x -> f x x) :: (X -> X -> X) -> X -> X) print ((\f -> f id id) :: ((X -> X) -> (X -> X) -> X) -> X)