On Wednesday 02 July 2008, Cotton Seed wrote:
Hi everyone,
I'm working on a computational algebra program and I've run into a problem. In my program, I have types for instances of algebraic objects, e.g. ZModN for modular integers, and types for the objects themselves, e.g. ZModNTy for the ring of modular integers.
Now, I want to subclass ZModNTy from something like
class RingTy a b where order :: a -> Integer units :: a -> [b]
where `a' represents algebraic object, and `b' the type of instances of that object. I want an instance
instance RingTy ZModNTy ZModN where ...
but then code that only uses order fails with errors like
No instance for (RingTy ZModNTy b) arising from a use of `order' at Test2.hs:16:8-15
since there is no constraint on the second type variable.
I think what I really want is
class RingTy a where order :: a b -> Integer units :: a b -> [b]
but this doesn't work either since ZModNTy is not parametric in its type like, say, `Polynomial a' is.
Is this a common problem? Is there a standard way to handle it?
Correct me if I'm wrong, but wouldn't the a uniquely determine the b? In that case, you'd probably want a functional dependency: class RingTy a b | a -> b where order :: a -> Integer units :: a -> [b] This solves the problem with order, because with multi-parameter type classes, all the variables should be determined for a use of a method. Since b is not involved with order, it could be anything, so it's rather ambiguous. The functional dependency solves this by uniquely determined b from a, so order is no longer ambiguous. Alternately, with the new type families, this can become: class RingTy a where type RingElem a :: * order :: a -> Integer units :: a -> [RingElem a] Or something along those lines. Hope that helps. -- Dan