--- Martin Rubey <[EMAIL PROTECTED]> 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 intelligently. > "Bill Page" <[EMAIL PROTECTED]> 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: > > > > http://wiki.axiom-developer.org/RealNumbers > > > > 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. Indeed. > 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. Agreed. [snip] > 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" :-). Cheers, CY __________________________________ Yahoo! Mail - PC Magazine Editors' Choice 2005 http://mail.yahoo.com _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
