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

[Martin Rubey]

Ralf Hemmecke <address@hidden> writes:

> Hi Martin,
> 
> a quick response to the following...
> 
> > 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 "+".
> 
> Imagine you could ask "if M has Monoid(+)..." or "if M has
> Monoid(*)...". According to which returns true, you would then go on and call
> (m1 +$M m2) or (m1 *$M m2). Well, but M might have a monoid structure with
> respect to the operation ".". Do you really also want to ask "if M has
> Monoid(.)..."? That soon becomes impractical.

No, this is not an issue about practicality.

Look at it this way: Suppose "M has Monoid" returns "true". How do you know
then with respect to which operation M is a monoid? What can you do with the
information that M is a monoid with respect to some operation?

Martin