From: "trans.  (T. Onoma)" <transami@...>
Date: 2004-10-08T03:07:32+09:00
Subject: Re: Range behavior (Re: [RCR] New [] Semantics)

On Thursday 07 October 2004 01:26 pm, Markus wrote:
| On Thu, 2004-10-07 at 09:55, trans. (T. Onoma) wrote:
| > On Thursday 07 October 2004 11:27 am, Markus wrote:
| > | On Thu, 2004-10-07 at 07:11, trans. (T. Onoma) wrote:
| > | > --only Numeric ranges can be Continuous.
| > |
| > |      Not so.  Time ranges, for example, can be Continuous, as could
| > | Colour or FuzzyTruthValue or...
| >
| > True. Although I think one could argue, that the defining characteristic
| > is a *capability* to functionally map to rational numbers. So in a sense
| > they are numeric too, even if they don't use Numeric as a base class. Is
| > that important?
|
|      Well, there are continuous mathematical constructs that _don't_ map
| to the rationals (e.g. the reals), so I think it's a bad definition.  I
| may someday want to implement something that can represent sqrt(2)
| exactly...

Sorry, I meant reals.

| > So yes, you are right. We need to consider Intervals of variant objects.
| > But how?
|
|       By having an Interval class that uses duck typing on its
| sentinels?  Maybe I'm missing the problem (I'm busy trying to get my
| roll-your-own-operators patch working and haven't been following this
| thread as closely as I'd like to) but why is this considered a problem?

Okay, yes. I just meant which methods apply? I guess #<=> is all we have. So 
if they are comparable they can form a continuous range. And membership is 
constitute on falling between the sentinels.

|      It seems to me that restricting them to a specific base class would
| be the harder (and less useful) of the options.
|
| > | > Consider further how succ determines successive members --a Range is
| > | > an indeterminate ordered set built by iteration. Oddly one defines a
| > | > Range with a first and last argument, but iterations are supposed to
| > | > be defined by a seed (first) and the number of successive iterations.
| > |
| > |      Supposed by whom?  You can just as easily define an iteration with
| > | a termination test (e.g. iterating over the lines of a File).
| >
| > Okay, sure. My point was simply that you get no promises with a
| > termination test.
|
|      Start: first
|      Succ: next = (2+sqr(this))*(2+sqr(step))
|      Test: this < last
|
|      Here's a simple (albeit contrived) case with a termination test
| where you can promise that it terminates, even without knowing how many
| steps it takes.

I knew you were going to say something like that! But I think you know what I 
mean ... just that you don't _always_ know -- and in fact a range might 
terminate with one seed but not another. But I don't think that's too 
important. We can go the "shoot yourself in the foot route". That's fine with 
me. It would be nice to offer a notation, though, for "keep your foot out of 
trouble" too. ;)  (i.e. seed,steps)

I'll have to finish later.... got to run.

T.