On Fri, Jul 4, 2008 at 1:07 PM, Gabriel Dos Reis wrote: > "Bill Page" <[EMAIL PROTECTED]> writes: > > | On Fri, Jul 4, 2008 at 7:40 AM, Gabriel Dos Reis wrote: > | > ... > | > I would not like to add to the confusion, but when thinking of this > | > problem one should also keep an eye on the status of Mapping. > | > What is it? Is it a domain constructor or a category constructor? > | > > | > | Mapping (e.g. A->B) is clearly a domain constructor since we can > | write: > | > | x:A->B := ... > | > | A->B is the type of x. > > From my perspective, that is putting the cart before the cattle.
Cart before the horse? :-) > It is not because you can write > > x:A->B := ... > > that makes Mapping a domain constructor. If you could write > > y: Ring := Integer > > would that make Ring a domain, as opposed to a category? > Yes, I proposed esentially this in a previous message. Well, not that Ring *is* a domain but rather that through a principle of "comprehension" (the term as used in set theory) Ring might stand in this context as representing the domain Union(x for x in Domain where x has Ring) Such a domain embodies the concept of a category as a subdomain of Domain. > I suspect the answer must come first principles, not from a posteriori > side effects. > I agree. > | But 'with x:A->B' is a category object so we should be able to say: > | > | x:Category := with x:A->B > > yes, and the fact that you can't in OpenAxiom is a relic accidently > carried over from the base AXIOM system. > Ok, good. > But, again, that is orthogonal to what constitute a domain or a > category. Agreed. Regards, Bill Page. ------------------------------------------------------------------------- Sponsored by: SourceForge.net Community Choice Awards: VOTE NOW! Studies have shown that voting for your favorite open source project, along with a healthy diet, reduces your potential for chronic lameness and boredom. Vote Now at http://www.sourceforge.net/community/cca08 _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
