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

On 10/22/07, Gabriel Dos Reis <[email protected]> wrote:
> On Mon, 22 Oct 2007, Bill Page wrote:
>
> | As I said, I want
> |
> |   Product(1..9,1..4)
> |
> | to be a domain - the cross-product of two other domains.
>
> I do not think
>
>     I want 1..9 to be a domain so that I can write
>     Product(1..9, 1..4) to be a cross product of two domains
>
> is an explanation of why `1..9' should be a domain.

As I said earlier, I think the semantics of Product should be given
categorically by the existence of the unique operation

Product(X:Type, Y:Type): with ...

 product: (A:Type, A->X,A->Y) -> (A->%)

as a categorical limit.

Regards,
Bill Page.