[Haskell-cafe] Finally tagless - stuck with implementation of "lam"

[Günther Schmidt]

Hi all,

I'm playing around with finally tagless.

Here is the class for my Syntax:


class HOAS repr where
     lam :: (repr a -> repr b) -> repr (a -> b)
     app :: repr (a -> b) -> repr a -> repr b
     fix :: (repr a -> repr a) -> repr a
     let_ :: repr a -> (repr a -> repr b) -> repr b

     int :: Int -> repr Int
     add :: repr Int -> repr Int -> repr Int
     sub :: repr Int -> repr Int -> repr Int
     mul :: repr Int -> repr Int -> repr Int


and here is one instance of that class for semantics.



newtype I a = I { unI :: IO a }

instance HOAS I where
     app e1 e2 = I (do
                     e1' <- unI e1
                     e2' <- unI e2
                     return $ e1' e2')
     int i = I (putStrLn ("setting an integer: " ++ show i) >> return i)
     add e1 e2 = I (do
                     e1' <- unI e1
                     e2' <- unI e2
                     putStrLn (printf "adding %d with %d" e1' e2')
                     return $ e1' + e2')
     sub e1 e2 = I (do
                     e1' <- unI e1
                     e2' <- unI e2
                     putStrLn (printf "subtracting %d from %d" e1' e2')
                     return $ e1' - e2')
     mul e1 e2 = I (do
                     e1' <- unI e1
                     e2' <- unI e2
                     putStrLn (printf "multiplying %d with %d" e1' e2')
                     return $ e1' * e2')


I'm stuck with the "lam" method, for 2 days now I've been trying to get it  
right, but failed.

Is there a possibility that it isn't even possible?

Günther