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Date: Sat, 03 Sep 2005 22:01:03 +0200
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Subject: Re: Surprise in array concatenation
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Date: 2005-09-03T22:00:11+02:00
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Dmitry A. Kazakov wrote:

> Just try to rewrite your program to make it working for any array type.

A rewrite for any array (I presume: any index) will fail only where
mathematically subtracting 4 from 3 will fail in N.

> C++. But *programming* in C++ is an immense problem. See any parallel?

Are you saying that C++ is less mathematical than Ada?

> What about zero radius? If you want to play a Luddite, then start with
> prohibiting empty strings. Do a writer need empty texts?

Writers have used empty texts. Programmers frequently use empty
strings, for I/O.

> Do computers something which cannot be described using
> mathematics?

Yes, most real computers, if not all of them, cannot at all be shown to
be a Turing machine equivalent. We do not even know whether or not the
world's most often sold CPU works properly, at least not in a
mathematically satisfying sense ("yes" or "no").
Now think of the peripherals, etc. A real computer is a statistically
reliable device, but you cannot mathematically show that your desktop
computer does what we believe it does.

> That is not what you are saying. Then what?

Another problem with computer mathematics is that it largely neglects
continuous time, and bare I/O operations. Time is transformed into
ticks, I/O is reduced to 'Valid plus compiler magic built on top of
OS routines which mostly work - for whatever reason.
Who can show, in mathematically sufficient detail, the way of
some bits generated by a partition running on computer A sent
to a partition running on computer B? (Who *wants* to do this? :)

This requires statistics, rules of thumb, and experiments.

> A trivial analysis shows inconsistency of A'First..A'First-1.

The inconsistency of A'First..A'First - 1, if any, is relative
to a set of definitions.

It seem that off-bounds indices are a ubiquituous feature, found in
several programming languages' algorithms and data structures.
The indices avoid, for one thing, a proliferation of conditionals
like
  if x'length = 0 then ... else perform(...) end if;
Without the special test, you can unconditionally say

  forall things in x | P ...

or

  as-soon-as cursor is off things in x | P ...

Something that I think is frequently found in math literature ;-)