Re: [Axiom-developer] Curiosities with Axiom mathematical structures

[Martin Rubey]

Dear Ralf, *,

Ralf Hemmecke <address@hidden> writes:

> On 03/09/2006 03:46 PM, Martin Rubey wrote:
> > I wouldn't want to ask "Integer has Monoid", since this doesn't make any 
> > sense
> > to me. I'd like to ask "Integer has Monoid(Integer, *)" or "Integer has
> > Monoid(*)"
> 
> Well, if one interprets Monoid as the category of monoids then
> 
>    Integer has Monoid
> 
> just say that the integers (now the question is whether you mean the integers
> with the additive or the multiplicative structure) are an object in the
> category of monoids.

There is a simple practical reason why I dislike the idea of asking just
"Integer has Monoid".

Imagine I'm programming a package, and I need that a parameter domain M is a
monoid, so that I can use the monoidal structure, for example for
multiplying. Well, then simply asking M has Monoid doesn't buy me anything,
since I won't be sure that M really is a Monoid with respect to "+".

Of course, usually that is not such a big problem, interesting software can be
written without. However, I find the limitation rather annoying.

Apart from that, thank you very much for your explanation of
MyMonoid(MyInteger, op) giving true for any op having the right signature.

Still I hope that this idea works out somehow. I believe that bringing logic
into play won't make the problem any easier, I think we should try to solve it
with as little modification of aldor as possible for the moment. And most
importantly, we should try to figure out the correct scheme. Maybe we can talk
about it at the workshop.

Martin