Re: The wisdom of the object mentors (Was: Searching OO Associations with RDBMS Persistence Models)

[...]
>The third problem is that
> you need "=" for all things as well as literals for all things. It is a can
> of worms.

Why is it 'a can of worms'?

> Especially function literals aren't easy. What is a literal of
> sine?

You tell us 'what is a literal of sine'. There is no such creature in math.

> Even if they model uncountable sets?

Interesting to know how would you go about 'model[ing] uncountable sets' in your OO tool of choice.

>. In general, when you want to enforce some
> semantics on the resulting function.

What kind of semantics do you have in mind ? Any computer program can be regarded as having say denotational semantics. Is that what you have in mind ? If so, you do not need to 'enforce' anything -- as soon as you've written your program the semantics is already there.

> >> Because in this particular case function is a value and values are outside
> >> the language scope.

That does not make any obvious sense -- how a function can be a value that is outside the language scope ? Surely it depends on the language in question.

> Right. The problem is that mathematical constructs modeled in a
> computational framework might be too large for any finite state machine. So
> an uncountable set of real numbers is replaced by a finite set of
> intervals.

What do you mean by 'a finite set of intervals' ? If you mean the floating point arithmetic, then the numerals in this arithmentic nominally represent members of a finite subset of rational numbers with peculiar operations (+, -, *, /) that are affected by rounding issues.

>That's the gibberish in which I am talking. We can't have all
> the table of real-valued functions.

You do not need one. It's well-known that sine is a Turing-computable function. Otherwise, how would a gadget like your PC produce it ?

> The size of this table is aleph-2!

It is not.

> Where you find a hard disk of this size? Fortunately, from all this table,
> today, I need only sine. So I say let sine be denoted as 0x2.

You are not making much sense here.

>
> Nevertheless, nothing prevents us to formalize these bastards and use
> mathematical rigour to handle them.

What 'bastards' do you intend to formalize ? Could you, like, demonstrate ?

Disagree?
>
> --
> Regards,
> Dmitry A. Kazakov
> http://www.dmitry-kazakov.de
Received on Thu Jun 01 2006 - 21:01:10 CDT