[Haskell-cafe] Re: Numeric type classes (Was: map (-2) [1..5])

[Ross Paterson]

On Mon, Sep 11, 2006 at 04:26:30PM +0200, Henning Thielemann wrote:
> On Sat, 9 Sep 2006, Ross Paterson wrote:
> > I think that a finer grain numeric hierarchy, while retaining Num, etc,
> > is feasible without changing the language: unlike the case of monads,
> > the people who will be defining instances of numeric classes are the
> > very ones who are inconvenienced by the current hierarchy.  The main
> > impact on clients of the classes is that some functions would have
> > more general types.
>
> There are many Num instances around in libraries where people wrap to
> external libraries: functionalMetapost, CSound wrapper in Haskore,
> SuperCollider (GSL too?). What about Num (algebraically Ring) instances of
> polynomials, residue classes and other such advanced mathematical objects?

And what do abs and signum mean for Haskore's orchestra expressions,
polynomials, residue classes, vectors, matrices, functions, etc?
The people who define those wish they were defining Ring, but they
must define Num.