Re: Generic Package

[Markus E Leypold <development-2006-8ecbb5cc8aREMOVETHIS@ANDTHATm-e-leypold.de>]

"Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> writes:

> On Fri, 27 Apr 2007 13:43:58 +0200, Markus E Leypold wrote:
>
>> "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> writes:
>> 
>>> On Thu, 26 Apr 2007 22:52:58 +0100, Simon Wright wrote:
>>>
>>>> "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> writes:
>>>> 
>>>>> You cannot iterate a relational table, because there is no order
>>>>> defined on it.
>>>> 
>>>> Why would that stop me iterating over all the rows?
>>>
>>> Because iterating presumes following an order. If there is no *any* order,
>>> which one would you follow? 
>> 
>> None. Iteration gives the values in a certain sequence,
>
> "Sequence" is defined as an ordered [and countable] set.

So what? 

Both, 1,2,3 aand 3,1,2 are possible sequences suitable for iterating
over the set "all positive numbers below 4". One even needn't to get
the same sequence on every iteration which somewhat disqualifies the
idea that the set would have to be ordered so that I could iterate
over it.

Your implication was, that is impossible to "iterate" over the
components/elements of structures/compounds which are not
ordered. Admittedly the implementation is introducing an ad hoc order
at the moment and for the moment the iteration takes place, but
actually I don't care and a massively parallel machine might even
choose to perform operations on single elements in parallel. But your
point was that it is __impossible__ to iterate over such "unordered"
structures, which is -- in my eyes -- patent nonsense. Every actual
sequence of iteration would suffice and I think that the sentence
"iterate over the set ..."  could be well applied in this case under
every useful meaning (and it can even be defined formally).

But of course YMMV: People like me who do not think that every real
programs are trivial, might not grasp your logic completely and not
achieve your precision of definition.

>>> It is clear that we could enumerate anything on
>>> a real computer, but that would be same as Unchecked_Conversion, it would
>>> break the abstraction. 
>> 
>> So I'm having an unchecked operation if I enumerate elements of a set
>> (sets are unordered). How embarrasing.
>
> Yes, because that set is a representation [model] of some other [domain
> space] set which could be fundamentally unordered and/or uncountable. As an

Uncountable is another issue. You're ditching the original issue again
(how familiar this has become to me ...). You said "one cannot iterate
over realtional tables, because they are unordered". Realtional tables
are not uncountable, so stick to the issue at hand, Dmitry. 

<snipped off topic "example">

> After interating reals we could proceed to complex numbers...

Which has nothing at all to do  with relational tables. 

I'd be really indebted to you, if you stuck to the topic you
introduced (can one iterate over relational tables) and didn't give in
to the brainstorm of completely unrelated fragments from mathematics
and computer science that seems to afflict you every time one starts
to discuss with you topics from computer science you yourself
introduced.

BTW: Your best way out of the corner into which you painted yourself
again might be to define "relational tables" as tables with an
uncountable number of tuples/rows -- in quite the style in which you
defined "trivial program".

Regards -- Markus