Re: [Axiom-developer] A curious algebra failure

[Gabriel Dos Reis]

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