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From: "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>
Subject: Re: Surprise in array concatenation
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Date: Fri, 2 Sep 2005 21:48:04 +0200
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Date: 2005-09-02T21:47:37+02:00
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On Fri, 02 Sep 2005 16:23:23 +0200, Georg Bauhaus wrote:

> Dmitry A. Kazakov wrote:
>> On Fri, 02 Sep 2005 12:43:24 +0200, Georg Bauhaus wrote:
>> 
>>>Dmitry A. Kazakov wrote:
>>>
>>>>>>The problem with the current (Ada 83) design is that it tries to abstract
>>>>>>away trivial mathematical facts:
>>>>>
>>>>>As does a computer :-)
>>>>
>>>>It does what you tell it. Computers do not have free will! (:-))
>>>
>>>So why do you want to tell it about non-computer mathematics?
>> 
>> Huh, there is only mathematics and non-mathematics!
> 
> Not at all. Mathematics is not even a well defined term in a formal
> sense of the word "definition". (Notice the recursion :-)
>
> Thus computer-mathematics (as in theory of real, operating hardware)
> if used in a PL context has to start from some description
> of the real computer to be used with a PL program.

So you add another adjective to get: "ill-defined computer mathematics."
(:-))
 
> Real computers executing (non-empty) programs translated from Ada text
> cannot but transorm a finite number (> 0) of finite (non-empty) sets
> of discrete "fantasies" of electro-magnetic values, somehow coping
> with the effects of one or more "times".
> 
> That excludes infinity and no-bits from real-computer mathematics,
> for a start. Likewise, forget about non-discrete numbers.

This is plain wrong. You can deal with all sorts of infinity in a finite
program. Because there is no limitation on how the set of computation
states (finite) have to be mapped onto the application domain set
(potentially infinite). There is no any problem to associate one state with
Pi, another with an empty set and third with aleph-twenty.

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