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

Dmitry A. Kazakov wrote:
> On 5 May 2006 04:18:44 -0700, vc wrote:
>
> > Dmitry A. Kazakov wrote:
> > [...]
> >>But ADTs have far less problems with set theory as the application
> >> domain than RM. Trivial examples are:
> >>
> >> 1. Power set operation
> >> 2. Set complement in an infinite universal set
> >> 3. Infinite sets modeled by finite classes of equivalences
> >
> > The paragraph above does make any obvious sense. Could you elaborate ?
>
> Above are set operations. Take SQL, and create power set of a table column,
> row, table, set of tables.

That's a silly request since it's widely know that ZFC does not state *how* to construct a powerset, and constructive set theories do not even have the powerset axiom (Martin-Lof). What about (2) and (3) ?

>Can you create Z in RM?

In RM, Z is a predefined elementary type, there is no need to construct it. Besides, can you construct Z *anywhere* ? "Die ganze Zahl schuf der liebe Gott, alles Übrige ist Menschenwerk"

> Use the standard
> procedure to create first 100 naturals:
>
> {Ø}, {{Ø}}, {{{Ø}}}, ...

You are confused again, those are not naturals, those are Von Neumann numerals.

>
> > [...]
> >> 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 ?

>
> > Rationals are the set of
> > equivalence classes of pairs of integers. The pairs (1,1) and (6,6)
> > simply belong to the same equivalence class,
>
> Welcome in club...

What's that supposed to mean ?

>
> > there is no need to use
> > 'inheritance' or some other OOP mumbo-jumbo when talking anout this
> > sort of things.
>
> That mumbo-jumbo expresses algebraic properties. Integer is a subtype of
> Rational in the same sense as a ring exists in a field.

So using your favourite OOP mumbo-jumbo, how would you go about constructing rationals?

>The point is that
> subtyping relation has nothing to do with subsets of values. It deals with
> properties. In OO it is called "behavior".
>
> --
> Regards,
> Dmitry A. Kazakov
> http://www.dmitry-kazakov.de
Received on Fri May 05 2006 - 18:54:03 CEST