Hi, 

In message "[ruby-talk:00429] Re: New feature for Ruby?"
    on 99/07/03, Clemens Hintze <c.hintze / gmx.net> writes:
>But I perhaps lack ability to write articles so that a magazin would
>publish it! But nevertheless, I will try it someday :-)

I long for your articles!

By the way, I also would like to translate Matz and his collaborator's
book about Ruby which will be published in near future in Japan. But I
need a collaborator who correct my Engrish if I'm permitted to
translate.

>But Ruby already have magical increment of Strings, means String#succ!
>And if I do a `"".succ' I will get an `"\377"'. As I didn't consider
>that behavior as the one one would expect, I have patched String#succ,
>so that it would raise an exception.

That maybe important.  I think succ is allowed to be non one-to-one
mapping, such that, str1.succ == str2.succ for str1 != str2.  But
either str.pred.succ == str or str.succ.pred == str should be held for
arbitrary String str, I think.

>ATTENTION PLEASE: If Interval would define Interval#===, it would have
>a slight other task than Range#===!
>
>Interval#=== should checks, whether a certain value would be contained
>by that interval or not. That means
>
>   interval(0,100,2) === 2               # true
>   interval(0,100,2) === 1               # false
>
>The second example would be false, as the interval is [0, 2, 4, ...,
>100] and there is no element 1.

For such objects, I feel a suitable name is `Sequence' rather than
Interval. The name Sequence itself means descrete series, i.e.,
enumerable and one dimensional. But Interval reminds me and
mathematicians so general region as it may be use to a continuum or a
higher dimensional structure. Other opinions?

>>However I feel that makes Interval to become closer to Range. 
>
>You're right! But it is not my desire to make Interval as different as
>possible to Range. If we would obey that rule all the time, it would
>not be necessary to have Fixnum and Integer. Fixnum would enough,
>right?

Hummm, Fixnum is distinct from Integer in its functions, especially,
the spacial cost. I've not recognized yet such major difference
between Range and Interval. I feel some of problems or restrictions on
Range seems to able to be solve by extending Range. I'd like to listen
other persons' (including Matz's again) opinions. 

>>Yes! I understand that. In this point of view, I want also
>>membership specified region class for non-enumerable objects. But it
>>will be defined in the project anyway. In the numerical scene such
>>ranges appear very often.
>
>Perhaps I have not grasp your point at whole. Would you be so kind to
>explain your last paragraph again?

Well, we numerical experimenters very often use regions on Float, Time
or some mathematical/physical quantiteis in order to define
domain/range of functions or data. And sometimes, we want to apply set
theoretical union, intersection or subtraction of them for
readability. Of cource, combinating of inequation-tests can be use to
do equvalent tasks but long conditions are too intensinal and blur
extensional meanings. For example

  dom = interval(1.01, 2.43) - interval(1.981, 1.9842)
  ...
  raise "domain error" unless x.belongs?(dom)

is easy to read. 

-- gotoken