Re: Storing data and code in a Db with LISP-like interface

From: Dmitry A. Kazakov <mailbox_at_dmitry-kazakov.de>
Date: Sun, 7 May 2006 20:40:37 +0200
Message-ID: <gkdc148xuejk$.1956b3jutqton.dlg@40tude.net>

On 6 May 2006 16:18:03 -0700, vc wrote:

> Dmitry A. Kazakov wrote:
> [...]

>>>> Neither it states *how* to construct union or intersection.
>>>
>>> That is correct,  but the union axiom has a clear and intuitive
>>> constructive interpretation that the powerset axiom lacks.
>>
>> It has a quite intuitive interpretation when sets are finite.

>
> Go ahead and provide one in the first-order language.

Why should I? Is the above the definition of "intuitive"?

> [...]

>>. What about (a, b, c, d ) <--> { a, b, c, d } ?

>
> What about it ?

Indeed. Can you transpose a table?

>> I don't care about construction of a set, if I can denote the set.

>
> If you do not care about constructing a structure, how do you intend
> to use something that you have not constructed in any programming
> language ?
>

>> Example:
>> 1.3 of R.

>
> And this shows what exactly ?

It shows that 1.3 is a much better abstraction level for dealing with R than Dedekind's cuts traced down to ZF.

>>pi is also
>> not an approximation, it is pi. I am free to choose a representation where
>> pi were exact.

>
> I'd be curious to see such representation.

enum R { Pi }; // See assembler listing for representation of Pi.

If you had an oscilloscope and some old computer with ferromagnetic coils, you could also directly see its representation in the memory. Fascinating, isn't it? I don't have oscilloscope and, definitely, I don't have time and much desire to drill rather expensive memory chips, so I just write "Pi."

>> But anyway, approximate value + error bounds gives an
>> infinite set. I can deal with. In a pure set-based model I have to present
>> the set.

>
> For example ?

1.2 +/- 0.5

>>>>> In RM, Z is a predefined elementary type,
>>>>
>>>> Why do you need elementary types? Set theory does not need them. If you
>>>> guys claim that 1) set theory is everything one needs, 2) your RM perfectly
>>>> embodies the theory, then a naive listener (like me) could come a
>>>> conclusion that 1 & 2 => integers, floats, strings are all constructed
>>>> using sets.
>>>
>>> They are,  we just use prepackaged products (as any computational model
>>> does),
>>
>> But that means that RM isn't based on set theory! It is on set theory
>> *plus* some "prepackaged products."

>
> That's a bizzare statemen akin to saying that functions, or any math
> structure for that matter, for are not based on the set theory because
> they are used ready-made.

Ask Bob Badour, that was his logic I used, not mine...

>>>>> there is no need to
>>>>> construct it.  Besides,  can you construct Z *anywhere* ?
>>>>
>>>> Any finite subset of, in any language that supports ADTs.
>>>
>>> Go ahead and oblige us with an example.
>>
>> Take bit strings, Algorithms for +, -, * can be found in any text book on
>> computer design.

>
> Could you elaborate ? I am not sure what you are trying to say here.
> You were supposed to construct integers as I recall.

For further reading see "CPU", "Turing Machine", "bignum."

>>> [...]
>>>>>>>>  In mathematics you can go either way. Is integer
>>>>>>>> number rational? How different pairs (1,1),(6,6) can both be 1?
>>>>>>>
>>>>>>> You are confused, amigo.  In the secondary school algebra,  one learns
>>>>>>> that an integer number ain't no rational.
>>>>>>
>>>>>> That depends on construction, they could well be. In the secondary school
>>>>>> one learns that this does *not* matter.
>>>>>
>>>>> What does not matter ? What alternative rationals do you have in mind ?
>>>>
>>>> I can add new elements to Z instead of constructing a set of pairs and then
>>>> choosing subsets there.
>>>
>>> What's that supposed to mean ?
>>
>> Take Z. Add elements denoted as "1/p", for each p, prime number. Postulate
>> them as multiplicative inverses for p. Add all: 1/pq, where p>=q, prime.
>> Postulate. Do same with 3, 4, 5, etc primes. When finished start to add
>> elements which are "multiplies" of new elements to primes. Use only
>> multiplies of primes not used in the denominator. Add an additive inverse
>> for each new element. Done.

>
> That is funny. Regardless of what you are doing with integers, you
> cannot do that as you do not have integers yet.

Your question was about construction Q in which Z were a proper subset. I presented such.

> You said that you'd
> 'inherit' integers from rationals, so rationals should be your
> primordial soup presumably. What's the point of inheriting integers
> from rationals if you already have them ? Besides you did not
> construct integers either. Please retry if you can.

It seems that you don't understand difference between mathematical objects and their computer models. CPU doesn't have Z, Q or R. It has a lot of silicon, copper and stuff like that...

>> Not necessarily. You need not to inherit each implementation. In
>> particular, you don't need to inherit data representation, because it is
>> not "is-a" anymore. Both can have completely different representations. You
>> can even have rational abstract (i.e. no representation at all).

>
> If you have 'abstract rationals' whtever that is, they are not really
> rationals one came to expect from one's school years,

That's for sure. Those rationals were built out of chalk, washed away long time ago...

> they are surely
> something else by virtue of being unusable since they are 'abstract'.

Yep, they are, as much as abstract algebra.

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

Received on Sun May 07 2006 - 13:40:37 CDT