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

[Henning Thielemann]

On Sat, 9 Sep 2006, Ross Paterson wrote:

> On Sat, Sep 09, 2006 at 12:57:56AM -0400, Cale Gibbard wrote:
> > Num itself needs to be split, but we can't do it sanely without
> > something like class aliases.
> 
> 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?