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

[Gabriel Dos Reis]

Martin Rubey <address@hidden> writes:

| Here you go:
| 
| http://lists.nongnu.org/archive/html/axiom-developer/2005-09/msg00130.html
| 
| or page 124 of 
| 
| http://worldofnic.org/research/phd.ps

Thanks, I'll read that carefully.

| Gabriel Dos Reis <address@hidden> writes:
| 
| > | In fact it seems that this problem cannot be properly solved
| > | with Aldor. There was some discussion on this list, too.
| > | 
| > | The reason is 
| > | 
| > | Rng(): Category == Join(AbelianGroup,SemiGroup)
| > | 
| > | would give a problem...
| > 
| > What problems?
| 
| Well, if you inherit an operation, you cannot alter the name of the
| operation. Rng inherits really two different monoids, one for addition and one
| for multiplication. Thus there would be a name conflict...

Yes, that is what we discussed in the other messages.
Fundamentally, the problem is because inappropriate inheritance was
chosen, or rather, inheritance is inappropriate.

Suppose that the operation (and associated constants) are parameters
to Monoid, Group and so forth; why would now have a construct like

    Ring(mul, add, zero, one)  == Join(Group(add, zero),
                                       SemiGroup(mul, one)) ....

would cause a conflict?

-- Gaby