"Bill Page" <[EMAIL PROTECTED]> writes:

[...]

| >  | >  I don't see a point in build a tower of hacks over hacks.
| >  |
| >  | I do agree with you there! Let's fix the original hacks. :-)
| >
| >  Please, don't hesitate to submit patches fundamentally grounded in
| >  category theory and of practical use.
| >
| 
| Ok. That is work in progress.

Great!  

| I see the Record, Union and Mapping
| types in Axiom as directly related to categorical constructions and I
| think it is possible to extend SPAD to more directly support these
| ideas. Being able to at least syntactically define equality for
| functions is critically important to this goal.

I'm a constructivist -- I'm awaiting the construction.

| 
| >
| >  | >  The fact that Mapping belongs to SetCategory is largely
| >  | >  historical accident.  I would rather ditch that relationship out.
| >  | >
| >  |
| >  | I think SetCategory is mis-named. It does not provide anything
| >  | substantially more than BasicType. Would you propose that
| >  | Mapping not even belong to BasicType?
| >
| >  The question is not whether foo belongs to bar.  The question is
| >  what does bar mean?  What is the semantics of BasicType?
| >
| 
| The source code says:
| 
| "BasicType is the basic category for describing a collection of
| elements with = (equality)."

I can read the source code.  That wasn't my problem.
All the above says has to do with _syntax_.  I was asking a question
about *semantics*.

| Like Mapping, both Record and Union currently also belong to
| SetCategory. Do you also object to this?

One thing at a time.  Once you nail down the semantics of BasicType,
we can see whatelse should be there.

-- Gaby

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