Re: [Axiom-math] missing exports in Finite DirectProduct and Product

[Martin Rubey]

"Bill Page" <address@hidden> writes:

> I would be interested in your opinions about this approach to
> providing Cartesian products for the Axiom library.

I think you did something quite interesting.  Unfortunately, I'm very busy
right now, but you might be interested in digging up a proposal of mine I made
a year ago or so, concerning StepThrough.  It was rejected back then (for good
theoretic reasons), but I still have the feeling that the behaviour I
critisized should be changed.  The following also goes into that direction:

> I think it is interesting to see how domains in the category Finite able to
> participate like "sets" in the language. Of course it is also possible to
> represent countably infinite sets in Axiom via the Stream domain. This
> suggests the that the category constructor StepThrough could also usefully be
> provided with an export that expands to such Stream. Perhaps the underlying
> Spad language should support this sort of expansion of Finite and countably
> infinite domains as a standard form of iterator in the [ ... for i in ... ]
> construction?

> Of course Aldor already has implemented some basic abstractions of this kind
> but it is not entirely obvious to me how best to extend Axiom's library and
> still stay within the limitations of the current Spad language.

Really, what is missing are generators.  I do not think that adding them to
SPAD in a naive manner would be too difficult, but I never tried.


Many thanks for your effort,

Martin