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

[Bill Page]

---------- Forwarded message ----------
From: Ralf Hemmecke <address@hidden>
Date: Oct 30, 2007 4:58 PM
Subject: Re: [open-axiom-devel] [fricas-devel] Re: [fricas-devel]
Re:     iterators and cartesian product.
To: Bill Page <address@hidden>


Hi Bill,

this goes offlist since I don't want to spam them...

On 10/22/2007 08:06 PM, Bill Page wrote:
> On 10/22/07, Gabriel Dos Reis <address@hidden> 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.

As you know I like the categorical approach, but I don't understand,
what a definition like your "product" has anything to do with how the
"for" loop is traversed?

You certainly know that a function

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

is easily implemented (in Aldor, I don't know for spad).
But I really don't see the connection to the "for".

Ralf