Jan-Willem Maessen:
Is it really a good idea to permit a type signature to include equality constraints among unifiable types? Does the above type signature mean something different from a ->a? Does the type signature: foo :: (a~Bar b) => a -> Bar b mean something different from: foo :: Bar b -> Bar b ? I know that System FC is designed to let us write stuff like: foo :: (Bar a ~ Baz b) => Bar a -> Baz b Which is of course what we need for relating type functions. But I'm wondering if there's a subtlety of using an equality constraint vs just substitution that I've missed---and if not why there are so many ways of writing the same type, many of them arguably unreadable!
Simon answered most of your question, but let me make a remark regarding "why there are so many ways of writing the same type, many of them arguably unreadable!" Equalities of the form "a ~ someType" are essentially a form of let-bindings for types - you can give a type a name and then use the name in place of the type. Just like with value-level let bindings, you can abuse the notation and write unreadable terms. However, this is no reason to remove let-bindings from the value level, so why should it be different at the type level? Manuel