RE: [Axiom-developer] Time for another crazy idea...

[Bill Page]

On February 22, 2006 10:35 AM C Y wrote:
> > ...
> > > I think we should try to either use names that are (at least
> > > moderately) common in mathematical and other research as they
> > > are commonly used, or in the worst case clearly define what
> > > we are and are not using the word for in the context of Axiom.
> > > It will make it FAR easier for researchers to read and use
> > > Axiom if they don't have to re-adjust their understand of
> > > common terms (IMHO anyway).
> > 
> > Gabriel Dos Reis wrote:
> > Indeed.  That speaks for NOT using 'category' and 'object'
> > when, in fact, we are talking of things that are different
> > from 'category' and 'object' as used in the math litterature.
> 
> That would be my preference.  I know there are often problems with
> multiple uses of terms, but in this case I think we might want to
> give the matter some consideration, at least when we start to do
> the large scale Algebra translation.
> 

I think that unfortunately this idea is impractical. Give all the
existing literature about Axiom and Aldor and the fact that other
systems (such as MuPad) have already borrowed and adopted these
terms, I think it would be very difficult and even more confusing
to write about Axiom using a whole new set of terms - even if
they happen to correspond to correct current usage. Instead I
think we need to be "up front" about this problem and to provide
the reader earlier-on with a clear defintion of terms and a
comparison to the terms used in other systems.

Since Java is very widely known and rather similar to Axiom/Aldor
in at least it's object-oriented aspects, we might start with a
table something like this (first draft):

  Java        Axiom           Mathematics
 ------------------------------------------------------------
  Interface   Category        Many-sorted algebra (signature)
  Class       Domain          Category
  Instance    Member          object

But I am sure that even getting everyone agree on this kind
of translation of terms is likely to be difficult. Plus Axiom
uses several other terms such as 'object' (meaning roughly
Domain in context of Categories, or Members in the context
of Domains) and 'type' (meaning Domain in the context of
Member and Category in the context of Domain), etc. It is
hard to describe this accurately in a few words but I think
we need it to be as short as possible since we can everyone
who meets Axiom to at least read this.

Regards,
Bill Page.