On Fri, Jul 4, 2008 at 6:06 PM, Ralf Hemmecke wrote: > ... > I have no proof of it, but in my understanding Type is the type of > all Aldor types including itself. Type lives conceptually above > domains and categories. Maybe 'Type' is comparable to > 'the class of all classes' in set theory (even if NBG > http://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory > does not admit it). >
Since there is no requirement that a Type be a classical set, I would strongly prefer to let Type simply be non-well-founded in the sense of http://en.wikipedia.org/wiki/Non-well-founded_set_theory > ... > For me 'Category' and 'Type' are somewhat special. > Let me define as Saul Youssef did in Section 2 of > http://axiom-portal.newsynthesis.org/refs/articles/Youssef-ProspectsForCategoryTheoryInAldor.pdf > > Domain: Category == with; > I don't have any problems with defining a category of this sort for specific purposes. In fact such categories are called "properties" in all flavors of Axiom. > then I would (roughly) say that > > Type = Category + Domain + {Type} > > i.e. Type comprises all categories, all domains and itself. The constant > 'Category' (which is a keyword) is on the same level as 'Type' but with > less inhabitants than 'Type'. > I don't like this much since it seem to conflict with the actual usage of these terms in both Axiom and Alsor. > Forgive me if anything is wrong, I am not a language expert. Well Ralf, I think you qualify as much as an "expert" as anyone else here... :-) Thanks for contributing to the discussion. 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
