> | > | I think the way out of this mess was correctly identified by Stephen > | > | Watt in the description of Aldor when he wrote: (ibid.): > | > | > | > | "Each domain is itself a value belonging to the domain Type. Domains > | > | may additionally belong to some number of subtypes (of Type), known > | > | as categories." >> ... >> Nothing in the semantics specification (the quote above without the >> first sentence) requires Type to be a domain.
> I agree. Yep. 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). I know it proves nothing, but have you looked at a comment in https://svn.origo.ethz.ch/algebraist/trunk/aldor/lib/aldor/src/lang/sal_lang.as where it says? -- Nice idea, but rejected by the compiler -- Type:Category == add; (Just a funny side remark.) 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; 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'. Forgive me if anything is wrong, I am not a language expert. Ralf ------------------------------------------------------------------------- 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