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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Subject: Re: Generic Package
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Date: Mon, 30 Apr 2007 20:54:31 +0200
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Date: 2007-04-30T20:54:09+02:00
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On Mon, 30 Apr 2007 19:24:52 +0200, Georg Bauhaus wrote:

> On Mon, 2007-04-30 at 18:29 +0200, Dmitry A. Kazakov wrote:
> 
>>> "The foreach procedure operates as if the following body
>>> were written
>>> 
>>>     procedure foreach(S: Set) is
>>>        C: Cursor;
>>>     begin
>>>        C := first(S);
>> 
>> You forgot that first is not defined on Set,
> 
> I was tempted to add
> 
>          C := first(S); -- where first picks any as defined for the
>                         -- `first`  operation on sets; gimmeacursor(S);
> 
>>  which is not well-ordered and 
>> thus does not have visible implementations of
> 
> As I said, Iterate operates as if it were implemented the way shown.
> I had intended to base the argument on your prior remark that we
> can specify the preconditions on next etc. I claim that we can
> give a meaningful definition of First, too, which is not given by
> the usual meaning of First; we could call it Frumble if you like.

But you could not provide *any* implementation of Frumble in the terms of
the operations defined on Set. To build a sequence of elements of S, you
need the well-ordering principle:

   let s1 be the least in S    (well-ordering of S)
   S1 = S / {s1}
   let s2 be the least in S1   (well-ordering of S1)
   S2 = S1 / {s2}
   ...
   until sN such that SN-1 = {sN}

Now { s1, s2, ..., sN } is an ordering of S.

Here it is not "/" which makes problems, but "least," which is as good/bad
as "any" or "Frumble." So giving it any name changes nothing.

>> The set 
>> is declared unordered.
> 
> Yes. An iterator will work without an externally visible order.

= per magic

> No, I only have to combine the semantics of foreach as specified
> previously, ":=", "+", etc. Then I can show that I get what I
> asked for.

But the semantics you have presented relies on a well-ordering of the set,
which is claimed to be unordered.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de