On Fri, Jul 4, 2008 at 1:57 PM, I wrote: > On Fri, Jul 4, 2008 at 1:07 PM, Gabriel Dos Reis wrote: > ... >> 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 want to withdraw this comment which I now think is wrong. 'Union(x for x in Domain where x has Ring)' would be a domain with values from any of the domains in Ring but this is not what is meant by using a category in a declaration of a variable or a parameter in Axiom. I would like to replace this with something that I hope is not equally wrong: A category is a subdomain (subset) of Domain so its values are some of the domains from Domain - not the values of these domains in turn. So it makes sense to me to say simply that the category Ring (a subdomain of Domain) is itself a domain that inherits the structure and implementation of Domain, e.g. equality. But as a value of the domain Category, Ring remains distinct so it is also a category - however twisted that might sound to some people. :-) Categories are values of the domain Category, so the domain Category is the domain of subdomains of Domain. Category is like a power set object in category theory. See my definitions at: http://axiom-wiki.newsynthesis.org/[EMAIL PROTECTED] 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
