Jean-Philippe Bernardy: > On 3/18/06, Manuel M T Chakravarty <[EMAIL PROTECTED]> wrote: > > Here addition and multiplication on Peano numerals using MPTCs and FDs: > > > > data Z > > data S a > > > > class Add a b c | a b -> c > > instance Add Z b b > > instance Add a b c => Add (S a) b (S c) > > > > class Mul a b c | a b -> c > > instance Mul Z b Z > > instance (Mul a b c, Add c b d) => Mul (S a) b d > > > > It's a mess, isn't it. Besides, this is really untyped programming. > > You can add instances with arguments of types other than Z and S without > > the compiler complaining. So, we are not simply using type classes for > > logic programming, we use them for untyped logic programming. Not very > > Haskell-ish if you ask me. > > > > I'd rather write the following: > > > > kind Nat = Z | S Nat > > > > type Add Z (b :: Nat) = b > > Add (S a) (b :: Nat) = S (Add a b) > > > > type Mul Z (b :: Nat) = Z > > Mul (S a) (b :: Nat) = Add (Mul a b) b > > > > Well, actually, I'd like infix type constructors and some other > > syntactic improvements, but you get the idea. It's functional and > > typesafe. Much nicer. > > Indeed, this looks all very good and I truly believe this is the > direction we should move in. > > Still, a question: do you propose to go as far as to replace the > "traditional" single parameter type-classes with /partial/ type > constructors?
No. Type classes are fine as they are. However, if you want to associate types with classes, where the definition of these types varies on an instance by instance basis, I argue that associated types (ie, type definitions in classes) are more appropriate than MPTCs with FDs[*]: http://hackage.haskell.org/trac/haskell-prime/wiki/AssociatedTypes Associated types are *open* definitions of type functions (ie, you can always extend them by adding more instances). In some situations *closed* definitions of type functions are preferable (as in the Peano arithmetic example above, which can for example be nicely combined with GADTs to define bounded lists). AFAIK nobody has a worked out a proposal for how to add closed type functions to Haskell, but Tim Sheard has argued for their usefulness in his language Omega: http://www.cs.pdx.edu/~sheard/papers/LangOfTheFuture.ps Manuel [*] I am unsure whether we want MPTCs if we have associated types. It seems that the typical uses of MPTCs become single parameter classes when associated types are used instead of FDs. _______________________________________________ Haskell-prime mailing list Haskell-prime@haskell.org http://haskell.org/mailman/listinfo/haskell-prime
