Something more controversial. Why ATS at all? Why not encode them via FDs?
Funny you should say that, just when I've been thinking about the same thing. That doesn't mean that ATS aren't a nice way to describe some special cases of FDs, but my feeling is that if ATS can't be encoded in FDs, then there is something wrong with _current_ FD versions that should be fixed. I'd love to hear the experts' opinions about this claim!-) The main argument for ATS is that the extra parameter for the functionally dependend type disappears, but as you say, that should be codeable in FDs. I say should be, because that does not seem to be the case at the moment. My approach for trying the encoding was slightly different from your's, but also ran into trouble with implementations. First, I think you need a per-class association, so your T a b would be specific to C. Second, I'd use a superclass context to model the necessity of providing an associated type, and instance contexts to model the provision of such a type. No big difference, but it seems closer to the intension of ATS: associated types translate into type association constraints. (a lot like calling an auxiliary function with empty accumulator, to hide the extra parameter from the external interface)
Example
-- ATS class C a where type T a m :: a->T a instance C Int where type T Int = Int m _ = 1
-- alternative FD encoding attempt class CT a b | a -> b instance CT Int Int class CT a b => C a where m :: a-> b instance CT Int b => C Int where m _ = 1::b
-- FD encoding class T a b | a->b instance T Int Int
class C a where m :: T a b => a->b
instance C Int where m _ = 1
-- general recipe: -- encode type functions T a via type relations T a b -- replace T a via fresh b under the constraint C a b
referring to the associated type seems slightly awkward in these encodings, so the special syntax for ATS would still be useful, but I agree that an encoding into FDs should be possible.
The FD program won't type check under ghc but this doesn't mean that it's not a legal FD program.
glad to hear you say that. but is there a consistent version of FDs that allows these things - and if not, is that for lack of trying or because it is known not to work? Cheers, Claus
It's wrong to derive certain conclusions about a language feature by observing the behavior of a particular implementation!
Martin