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Re: [Axiom-developer] StepThrough

From: C Y
Subject: Re: [Axiom-developer] StepThrough
Date: Fri, 4 Nov 2005 09:25:17 -0800 (PST)

--- Martin Rubey <address@hidden> wrote:

> Dear Bill, Cliff,
> Clifford, are you still there? I'm not quite sure about your status
> now, are you interested in pursuing this project?

I am, but probably not immediately - I'm working again on the units
package concepts so that will take some time.  My current thought is:

1)  Finish the draft of the "paper/documentation" part of the units and
dimensions package, so first Dr. Sit (if he has time) and then the
general audience can judge the summary of the issues and features in
question.  I am making progress on this but some of the papers I need
to review are taking time to digest.  

2)  While demolition of 1) is proceeding, I'll dive into the
StepThrough issue, which will also be the time when I will really have
to come to grips with the design and SPAD programming language of
Axiom.  StepThrough is an excellent start because it should be
informative, useful, but still relatively elementary (famous last
words).  I think it's the usual thing - driving isn't so bad once you
know how to drive, and in Axiom's case I need to learn how to drive.

3)  If by some chance any significant part of the units draft survives
review the process of 1), I'll proceed to implement the actual SPAD (or
maybe Aldor depending on the prospects of being able to use it in
Axiom) required to bring it into being.  2) will hopefully supply me
with the Axiom specific tools and knowledge needed to do this

> "Bill Page" <address@hidden> writes:
> > > Float is -- although obviously different from the reals 
> > > -- a *model* for them. So it would *not* have COUNTABLE.
> > 
> > I am not exactly sure what you mean by *model* in this case but I
> do not
> > think Float is any more of a model for reals than is Fraction
> Integer. 
> > It is no more difficult to define 'nextItem' in Float than it is in
> Fraction
> > Integer. Instead of 'numer' and 'denom' we have 'mantissa' and
> 'exponent'.
> OK, I surrender.

So we're agreeing nextItem makes sense in Float?

> > On the other hand there is some very important work on "Exact Real
> Numbers"
> > and "Computable Numbers". See:
> > 
> >
> > 
> > which in my opinion might well be said to be models for the reals.
> Although
> > these numbers are "computable" it seems to me that it might be
> rather hard to
> > construct a useful total ordering and to compute something like
> 'nextItem'.
> Since the set of computable numbers is countable and we can clearly
> only define domains containing computable numbers in Axiom, all 
> domains would have COUNTABLE. Of course for some domains it will be
> more difficult to come up with an enumeration than for others.

> I had the feeling that FLOAT and EXPR INT were domains which should
> not be countable, but it seems that this feeling should not be 
> trusted.

I suppose in once sense any mathematics stored as digital information
is somehow countable, although that counting might in some cases have
little to do with the conceptual uses to which the tools are put.
> In any case, it does make sense to sharpen the meaning of
> StepThrough.



> It is not difficult to extend my code to "finite fraction objects".
> In fact, I coded it that way first, until I discovered that the 
> parameter domain is not allowed to be finite.
> Thus, it might be better to implement nextItem in the domain
> Localize.

Heh - I'm reminded again of Tim's mantra - "there's no such thing as a
simple problem" :-).


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