Hi Tom,
It seems we are thinking of different things. I was referring to the characterization of a type of the form P => t as being "ambiguous" if there is a type variable in P that is not determined by the variables in t; this condition is used in Haskell to establish coherence (i.e., to show that a program has a well-defined semantics).
[...]
Technically, one could ignore the ambiguous type signature for bar, because the *principal* type of bar (as opposed to the *declared type*) is not ambiguous. However, in practice, there is little reason to allow the definition of a function with an ambiguous type because such functions cannot be used in practice: the ambiguity that is introduced in the type of bar will propagate to any other function that calls it, either directly or indirectly. For this reason, it makes sense to report the ambiguity at the point where bar is defined, instead of deferring that error to places where it is used, like the definition of bar'. (The latter is what I mean by "delayed" ambiguity checking.)
Thanks for explaining the ambiguity issue, Mark. I wasn't thinking about that. We have thought about ambiguity. See Section 7.3 in our paper http://www.cs.kuleuven.be/~toms/Research/papers/draft_type_functions_2008.pd... Note that neither Definition 3 nor Definition 4 demands that all unification variables are substituted with ground types during type checking. So we do allow for a form of ambiguity: when any type is valid (this has no impact on the semantics). Consider the initial program type family F a foo :: F a -> F a foo = id You propose to reject function Foo because it cannot be used unambiguously. We propose to accept foo, because the program could be extended with type instance F x = Int and, for instance, this would be valid: foo2 :: F Char -> F Bool foo2 = foo If you look at the level of the equality constraints: (F Char -> F Bool) ~ (F alpha -> F alpha) we normalise first wrt the instance F x = Int, and get (Int -> Int) ~ (Int -> Int) which is trivially true. In this process we do not substitute alpha. So alpha is ambiguous, but any solution will do and not have an impact on program execution. GHC already did this before type functions, for this kind of ambiguity, it substitutes alpha for an arbitrary type. That's not unreasonable, is it? Cheers, Tom -- Tom Schrijvers Department of Computer Science K.U. Leuven Celestijnenlaan 200A B-3001 Heverlee Belgium tel: +32 16 327544 e-mail: tom.schrijvers@cs.kuleuven.be url: http://www.cs.kuleuven.be/~toms/