On Tue, Sep 16, 2008 at 8:35 AM, Ralf Hemmecke wrote: > >> The singleton category 'Cat(D)' is *defined* as the category >> containing just domain D. That is a definition - not something that >> can be shown by an example. > > OK, but then you should more rigorously explain how "Cat" fits in a > non-contratictory way into the Aldor/SPAD language. (Sounds like > you are thinking of yet another language... which was not clear to me > up to now). >
As I said before: I am thinking of a small extension of Spad that would make it possible to extend domains in a manner similar (or at least equivalent) to what is possible in Aldor now. Of course I would like this extension to depend on a set of definitions that are not self-contradictory. >> Ralf, did what I write about anonymous categories make sense to >> you? I.e. that anonymous categories are not reflexive? > > Ehm, you mean whether the category > > with > > equals the category > > with > > or rather is not equal. Yes, that is exactly the issue. > I think we have discussed that before, but now we have 3 mailing > archives to look for such a thread. :-( But maybe it is on aldor-l. > Perhaps you are thinking of this thread? http://www.aldor.org/pipermail/aldor-l/2007-October/000745.html > The point is, I would not bet. In > > D1: with == add ... > D2: with == add ... > > the "with" appears in "type context" (see AUG). > Now, whether that has something to do with "reflexiveness", > I don't know. No, I don't think so. > But, I would see "with" rather as a function than a constant. Ok, or rather I think AUG refers to "with ..." as a category-valued expression. In any case, it is something that needs to be evaluated and the result is a category value. Each time it is evaluated it returns a *different* value with the same set of exports. http://www.aldor.org/docs/HTML/chap7.html#9 > So, being in type context, you cannot know whether the two > "with"s are equal or not. > ??? I don't understand that. What does it have to so with type context? This issue is discussed in some depth here: http://axiom-portal.newsynthesis.org/refs/articles/define.pdf?page=14 > In this case also "has" does not help you to decide whether these > "with"s are equal or not, since > > (D1 has with) and (D2 has with) > > will certainly return true. > > Does that help? > I am not sure. It still seems to me that this is a matter of defintion. If the definitions one chooses are contradictory, obviously that is not good. I am claiming that saying that anonymous categories are not reflexive does not lead to any such contradictions. And that the category-valued expression Cat(D) where D is a domain is anonymous just like 'with ...'. Regards, Bill Page. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
