# [Haskell-cafe] passing a polymorphic function as a parameter vs using it directly in a function definition

Bas van Dijk v.dijk.bas at gmail.com
Thu Jul 15 06:20:19 EDT 2010

```GHC tries to infer the following type for evalAST2:

evalAST2 :: forall a. (Expr a -> IO()) -> AST -> IO ()

However when the type of 'a' has been found in the first alternatives:

evalAST2 k (IntA i) = k \$ Lit i

it is fixed to Int. Then the 'a' doesn't match the type (String) found
in the other alternative:

evalAST2 k (TxtA i) = k \$ Lit i

The reason why evalAST type checks is that the type of 'k' is

k :: forall a. (Show a) => Expr a -> IO ()

So it works not just for one 'a' but for all of them.

The way to correctly generalize evalAST is by telling GHC that 'k'
indeed works for all 'a':

{-# LANGUAGE RankNTypes #-}

evalAST2 :: (forall a. Expr a -> IO()) -> AST -> IO ()

Regards,

Bas

On Thu, Jul 15, 2010 at 11:50 AM, Pasqualino "Titto" Assini
<tittoassini at gmail.com> wrote:
> Hi,
>
> can anyone please explain why in the following code evalAST compiles
> while evalAST2 doesn't?:
>
> Is that because the polymorphic function k is specialised in two
> different ways in evalAST while in evalAST2 it is constrained to be
> the same function?
>
> {-# LANGUAGE GADTs #-}
>
> test = evalAST (TxtA "abc")
>
> -- This is OK
> evalAST :: AST -> IO ()
> evalAST (IntA i) = k \$ Lit i
> evalAST (TxtA i) = k \$ Lit i
>
> k :: (Show a) => Expr a -> IO ()
> k e  = print \$ eval e
>
> -- This is the same thing, only the k function is passed as a parameter.
> -- But it won't compile.
> -- I would expect its type to be:
> -- evalAST2 :: (Expr a -> IO()) -> AST -> IO ()
> -- But is actually:
> -- evalAST2 :: (Expr Int -> IO ()) -> AST -> IO ()
> evalAST2 k (IntA i) = k \$ Lit i
> -- evalAST2 k (TxtA i) = k \$ Lit i
>
>
> -- The untyped expression
> data AST = IntA Int | TxtA String
>
> -- A typed expression.
> data Expr a where Lit  :: a -> Expr a
>
> eval :: Expr a -> a
> eval (Lit i) = i
>
>
>
> Thanks
>
>          titto
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe
>
```

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