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Re: [Axiom-developer] A curious algebra failure
From: |
Gabriel Dos Reis |
Subject: |
Re: [Axiom-developer] A curious algebra failure |
Date: |
Sun, 12 Aug 2007 08:33:44 -0500 (CDT) |
On Sun, 12 Aug 2007, Bill Page wrote:
| On 8/12/07, Gabriel Dos Reis <address@hidden> wrote:
| > On Sat, 11 Aug 2007, Bill Page wrote:
| > | ...
| > | Unnamed categories are just values of type Category.
| >
| > But, that is not what Axiom Book says, section 12.12, page 525:
| >
| > The part of a category to the right of a with is also regarded as
| > a category -- an "anonymous category". [...]
| > [ rewriting packages with named categories skipped ]
| > There is no reason, however, to give this list of exports a name since no
| > other domain of package exports it. In fact, it is rare for a package to
| > export a named category. [...]
| >
| > This, to me, suggest that the semantics described and intended in the
| > Axiom Book is that two unnamed categories always yields different categories
| > irrespective of their bodies.
| >
|
| You must be reading between the lines :-)
certainly, as there is no formal description of the semantics! :-)
Anything we can do is to guess, to read between the lines.
| since I certainly can not
| deduce that two unnamed categories are always distinct from the
| quotation. In fact the opposite. The discussion of exporting a named
| category here is rather gratuitous unless you assume that there is a
| better reason for exporting "anonymous" categories than simple
| convenience. The reason why most packages export anonymous categories
| is precisely because of how named categories are interpreted:
| categories with different names but identical structure are considered
| distinct. This is important because Axiom wants to associate these
| *names* with mathematical properties. In many cases the name must
| carry the proper mathematical interpretation irrespective of whether
| or not the categories have the same structure.
|
| See the examples at:
|
| http://wiki.axiom-developer.org/SandBoxCategories
Thanks.
| But notice that these examples also illustrate what I think is an
| error in the result of evaluating has for category-valued expressions
| in Spad.
How does the compiler behave when the error we are discussing is fixed?
I'm trying Juergen's suggested fix, which has different semantics than
that of Stephen.
-- Gaby
- Re: [Axiom-developer] A curious algebra failure, (continued)
- Re: [Axiom-developer] A curious algebra failure, Stephen Wilson, 2007/08/11
- Re: [Axiom-developer] A curious algebra failure, Gabriel Dos Reis, 2007/08/11
- Re: [Axiom-developer] A curious algebra failure, Stephen Wilson, 2007/08/11
- Re: [Axiom-developer] A curious algebra failure, Stephen Wilson, 2007/08/11
- Re: [Axiom-developer] A curious algebra failure, Gabriel Dos Reis, 2007/08/12
- Re: [Axiom-developer] A curious algebra failure, Bill Page, 2007/08/11
- Re: [Axiom-developer] A curious algebra failure, Bill Page, 2007/08/11
- Re: [Axiom-developer] A curious algebra failure, Gabriel Dos Reis, 2007/08/12
- Re: [Axiom-developer] A curious algebra failure, Gabriel Dos Reis, 2007/08/12
- Re: [Axiom-developer] A curious algebra failure, Bill Page, 2007/08/12
- Re: [Axiom-developer] A curious algebra failure,
Gabriel Dos Reis <=
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), William Sit, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Bill Page, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Bill Page, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/12
- RE: [Axiom-developer] "has" and "with" (was curious algebra failure), Weiss, Juergen, 2007/08/12
- RE: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), William Sit, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Bill Page, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/12