[Haskell-cafe] type classes

[Cotton Seed]

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?

Thank you for your attention,

Cotton
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