Re: The Fact of relational algebra (was Re: Clean Object Class Design -- What is it?)

"Bob Badour" <bbadour_at_golden.net> wrote in message news:3hIv7.676$as.19014753_at_radon.golden.net...
> > I think completeness means that the language can express any 'computable
> > function'. For example, it can express the square of a number, since
that
> is
> > computable.
>
> "You think". "You seem to remember." "I can't remember"
>
> Have you considered discussing what you know and remember? Above, are you

I studdied maths & philosopy a long time ago. Its all a bit hazy now, even more than it was when I studdied it ;-) In the past I have used relational and object databases, and did quite a lot of busness modelling using oo techniques. Thats my background.

> referring to Turing Computability? If you are, what makes you think
database
> management requires it?

As for Truing Computability, no dbms do not require it, as rdbms have shown.

> > > What "fundamental concepts" do you think that relational algebra
> > redefines?
> >
> > I found this definition of "relation" on a maths page on the net:
> >
> > *** relation : (logic, set theory)
> > a correspondence between two sets (say A, B) represented
by
> > a set of ordered pairs, each containing one element from
> > A and one from B.
> >
> > Implying you have to normalise everything into binary relations before
it
> > looks anything like the above definition.
>
> I am not sure where you found the above definition, but my highschool
> _Relations, Transformations and Statistics_ textbook gives a less
> restrictive definition of relation. Even though the textbook only covers
> binary relations and frequently uses "relation" to mean "binary relation",
> it makes it clear on the first page that other types of relations exist.
You
> wouldn't want to base your entire argument on a highschool-level pedagogic
> simplification, would you?

In my short and not very glorious time as a maths/philosophy undergraduate, we also used the binary definition.

> > A good example of a relation is the greater-or-equal-to sign >=
> > It would be 'implemented' in set theory as an infinite set containing
all
> > the numbers,
> >
> > {(0,0),(0,1),(0,2),.......(1,1),(1,2),(1,3),...........}
> >
> > Of course we don't have infinitely big sets in computers, so we
implement
> it
> > using an algorithm.
> >
> > Daniel
>
> Define "good example".
>
> In the relational model, one would ordinarily implement the above
> truth-valued binary function as a domain operation represented by the >=
> operator. One might express the predicate for a relation using the above
> operator, in which case one would constrain the values in two columns with
> respect to each other.

In a 'pure' relational way of representing the world, eveything is a relation, including the >= operator. Functions are also relations. But I think this is just talking syntax.

Cheers

Daniel Received on Tue Oct 09 2001 - 10:55:46 CEST