Typing problems with polymorphic recursion and typeclasses

[oleg@pobox.com]

[Commenting of the problem in the message "GHC doesn't like its own
type?", Iavor Diatchki wrote]
> i remeber some time ago levent erkok run intro a simillar problem.  take 
> a look at this post:
> http://www.mail-archive.com/haskell@haskell.org/msg06754.html

The problems seem different. However, Levent Erkok's problem as well
as the problem in the follow-up message to categorical maxima point
out that there is something else goes on besides the explicit
typing. Let us use Levent Erkok's problem as it is simpler:

> class X a where
>   u :: a b -> a b
 
> f :: X a => b -> a b
> f = f
 
> g :: X a => a b -> b
> g = g

> -- h :: X a => b -> a c
> h b = f (g (h b))

This file loads and checks both in GHC and Hugs. The problem is that if
we uncomment the explicit type declaration of h (which is identical to
the inferred type reported by the compiler), typechecker complains.

Let us keep the function h without the explicit type declaration. Let
us apply what I thought as an equivalent transformation:

> h = \b -> f (g (h b))

Hugs now reports
	ERROR "/tmp/b.hs":12 - Unresolved top-level overloading
	*** Binding             : h
	*** Outstanding context : X b
and GHCi reports
    /tmp/b.hs:12:
    Ambiguous type variable(s) `a' in the constraint `X a'
    arising from use of `f' at /tmp/b.hs:12
    In a lambda abstraction: f (g (h b))

It is interesting that the error message is exactly the same as when
we used the explicit type declaration for the old "h b=..." definition.

Something seems to be going on...