Can't infer type (type family as "element" type)

Suppose I have a class C,

class C a where
  type E a
  c :: E a -> a -> a

a datatype T,

data T a = T a

and an instance of C for T

instance C (T a) where
  type E (T a) = a
  c x (T _) = T x

I would like to write a function such as f

f t@(T x) = c x t

without a type signature. Unfortunately, I can't because GHC tells me

    Couldn't match expected type `t' against inferred type `T (E t)'
    In the second argument of `c', namely `t'
    In the expression: c x t
    In the definition of `f': f (t@(T x)) = c x t

There are at least three possible ways to write the above code such that it works.

(1) Give a type signature for f

f :: T a -> T a

(2) Define the class C using an equality constraint

class C t where
  type E t
  c :: (E t ~ e) => e -> t -> t

(3) Define the class C using functional dependencies

class C t e | t -> e where
  c :: e -> t -> t

But the real question is why don't I get a type for f?

This has been tested in GHC 6.10.1 and 6.12.1.

Trac metadata

Trac field	Value
Version	6.12.1
Type	Bug
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	Compiler (Type checker)
Test case
Differential revisions
BlockedBy
Related
Blocking
CC	leather@cs.uu.nl
Operating system
Architecture