[Axiom-math] Re: [fricas-devel] Re: [open-axiom-devel] [fricas-devel] Re: [fricas-devel] Re: [fricas-devel] Re: iterators and cartesian product.

[Bill Page]

On 10/24/07, Gabriel Dos Reis  wrote:
>
> On Tue, 23 Oct 2007, Bill Page wrote:
>
> | But as I said earlier in this thread, this sort of construction is not
> | as general as I would hope for. How would I write for example?
> |
> |   [i for i in Product(OVAR [a,b,c], 1..3)]
> |
> |               [ (a,1), (a,2), (a,3), (b,1), ... ]
>
> My fundemantal issue to understand is making 1..9 a domain.  I'm fine
> with no having the most general construct, but I'm concerned with
> semantics and typeing rules.  In general, I'm suspicious of any
> extension that is driven by just syntax.
>

I understand your suspicion however I do believe (as you may also
believe) that syntax is quite critical - particularly in *mathematics*
where I think it has often been demonstrated that proper notation is
90% (99% ?) of the problem. A good notation should help "suggest" a
solution and the language itself should be economical and dense in the
sense that almost everything that you *can* write that is
syntactically correct should have some presumably sensible and useful
meaning. Attempting to find the most general construct (: As abstract
as possible but not abstract nonsense :) is one way to approach this.

Earlier in this thread I suggested introducing a new domain I called
'IntegerSegment(S)' abbreviated INTS that would be the domain
equivalent to a given 'S:Segment(Integer)'. Then we could write:

  [i for i in Product(OVAR [a,b,c], INTS 1..3)]

This does not require that '1..3' denote a domain although it does
seem less "economical".

Regards,
Bill Page.