[Haskell] GHC Error question

[Lennart Augustsson]

If the type checker really deduces the type 'forall a b . C a b => a - 
 > a' then an inference algorithm that works seems easy.  Do type  
inference for f, then check that the signature the user has given is  
alpha-convertible with the deduced type (well, in general it's more  
complicated than that, of course).
If the type checker doesn't really deduce 'forall a b . C a b => a ->  
a' then it shouldn't print what it does.
So I'm curious, what is the exact deduced type?

	-- Lennart

On Dec 11, 2006, at 07:16 , Simon Peyton-Jones wrote:

> | Tell me how this make sense:
> |     1. I enter the definition for f.
> |     2. I ask ghc for the type of f and get an answer.
> |     3. I take the answer and tell ghc this is the type of f, and ghc
> | tells me I'm wrong.
> | Somewhere in this sequence something is going wrong.
>
> I agree!  Indeed I wrote:
>
> | It doesn't get much simpler than that!  With the type sig, GHC  
> can't see that the (C a b) provided can
> | satisfy the (C a b1) which arises from the call to op.   However,  
> without the constraint, GHC simply
> | abstracts over the constrains arising in the RHS, namely (C a  
> b1), and hence infers the type
> |         f :: C a b1 => a -> a
> | It is extremely undesirable that the inferred type does not work  
> as a type signature, but I don't see
> | how to fix it
>
> If you have an idea for an inference algorithm that would typecheck  
> this program, I'd be glad to hear it.  Just to summarise, the  
> difficulty is this:
>         I have a dictionary of type (C a b1)
>         I need a dictionary of type (C a b2)
>         There is no functional dependency between C's parameters
>
> Simon
>
> PS: the complete program is this:
>         class C a b where
>                 op :: a -> a
>
>         f :: C a b => a -> a
>         f x = op x
>