On Fri, Jul 4, 2008 at 7:24 PM, Gabriel Dos Reis wrote:
> Bill Page writes:
> ...
> | Ring is still a category.
>
> So, in your scheme something can be both a domain and a category.
> Is that right?
>
I realize that it might seem a bit like "waffling" and avoiding the
question, but I would prefer to say that a category is just a category
- a kind of design predicate or interface specification, as you said.
But that in a context that normally requires a domain, that it can
serve as a shorthand for the associated domain:
Union(x for x in Domain where x has Ring)
> ...
> Evaluation of category forms already yields objects of the domain
> Category -- at least in OpenAxiom.
>
In that case shall I submit:
(1) -> T:Category := IntegerNumberSystem
Category is a category, not a domain, and declarations require
domains.
as a bug report?
> | In the case that T in 'f(x:T): U == ... ' is a category I
> | have proposed that in this context T be interpreted as the domain
> |
> | Union(x for x in Domain where x has T)
>
> I do not fully understand why this
> (1) is computationally effective solution,
> (2) solves all the issues,
> (3) is better aternative.
>
> Would you mind exploring each of those points?
>...
I will indeed continue to think about this subject.
Regards,
Bill Page.
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