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

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

Above are set operations. Take SQL, and create power set of a table column, row, table, set of tables. Can you create Z in RM? Use the standard procedure to create first 100 naturals:

{Ø}, {{Ø}}, {{{Ø}}}, ...

> [...]

>>  In mathematics you can go either way. Is integer
>> number rational? How different pairs (1,1),(6,6) can both be 1?

That depends on construction, they could well be. In the secondary school one learns that this does *not* matter.

> 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...

> 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. 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