Re: Surprise in array concatenation

[Georg Bauhaus <bauhaus@futureapps.de>]

Dmitry A. Kazakov wrote:
> On Fri, 02 Sep 2005 12:42:06 +0200, Georg Bauhaus wrote:
> 
> 
>>Dmitry A. Kazakov wrote:
>>
>>>On 01 Sep 2005 12:04:17 -0400, Robert A Duff wrote:
>>
>>>>Heh?  You want this:
>>>>
>>>>   procedure Put(S: String) is
>>>>   begin
>>>>       for I in S'First..S'Last loop -- equivalent to S'Range
>>>>           Put_Char(S(I));
>>>>
>>>>to crash when S = ""?
>>>
>>> 
>>>Yes.
>>
>>What is your approach to subranges then?
>>
>>   function h(s: String) return Unsigned_32 is
>>      prefix: String renames
>>         s(s'first .. s'first + Integer'min(3, s'length - 1));
>>      result: Unsigned_32 := 0;
>>   begin
>>      for k in prefix'range loop
>>         result := result or Shift_Left(Character'pos(prefix(k)),
>>                                        (k - prefix'first) * 8);
>>      end loop;
>>      return result;
>>   end h;
>>
>>(If you could assume for the moment that there is no
>>Unchecked_Conversion and not a different/better algorithm etc.)
> 
> 
> I don't see any problem, so far. Subrange of an empty range is empty.

But earlier you said that s'first .. ... should crash when
s = "".

> As
> for the checksum of an empty string it is to be extra defined.
> 
> You cannot in general case reverse any possible sequence S1, S2, S3, ... to
> deduce S0.

This requirement being generated by arbitrarily applying
the mathematical habit of starting things, deducing thing,
extending things to become some general case (not well defined
for real computers), etc. Basic mathematical facts
are basic relative to some starting point from which you perform
mathematical reasoning.


> IF the sequence is a series bound by some operation *:
> SN = x1 * x2 * ...* xN
> 
> AND * is a group operation
> 
> THEN you can take the unit element of the group for S0.

And what does mathematical group theory offer when the computer
executes fine without it? Why don't you start your basic
mathematical theory from things that work, and explain them
first?

If a sphere of negative radius opens many interesting insights
into unforeseen extensions of geometry, will this have an
influence on a pot maker's occupation?

I'm not asking these questions because I believe that mathematics
is the wrong science for approaching real computers. It's not.

However, every once in a while I'm having to defend
that running computers and performing mathematics are two
sets of operations. They have a fair amount of overlap.
But they are not the same set. Yet many mathematicians
seem to view computer programming as if it were nothing but
a way of transforming their mathematical knowledge into programs,
largely ignoring a few issues:

1 - computers perform I/O, in time - no complete simple theory
    here, right?
2 - computers operate non-deterministically ("malfunction")
    ("Malfunctions are the technicians' job. I'm writing
    mathematically correct programs for flawless computers")
3 - computers are finite.
4 - computers cannot operate on no (0) bits.

Why don't they apply their mathematical capacity to problems
that are probably less fun and more dirty but more crucial?
That it, at least consider adapting mathematics to the world
instead of adapting the world to mathematics.


> Now, take something else: let * be max, what would be the maximum of an
> empty array?

A problem of math-think. Like this

... talking to son:

"See this little wood over there? I have counted the trees,
there are 139."

... a little later:

"Remember I told you about this wood having 139 trees, 14
years ago? Now there are only 23 left."

... talking to granddaughter visiting:

"See this little wood over there?" -- "No."
-- "It has 0 trees". -- "Ha, ha."

If there is nothing about which to say anything,
then mathematicians decide to say something about
it: truth. Useful, but in a material setting, you have
to consider whether it makes sense. Using your Max example,
I could ask those mathematicians about the maximum of a
subset of the natural numbers (possibly empty!). I'd venture
a guess that the answer will likely be, "It depends.".

For example, you have given "extra defined". ;-)