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

"Daniel Poon" <spam_at_spam.com> wrote in message news:1002196323.271647_at_kang.qonos...
>
> "Leandro Guimarães Faria Corsetti Dutra" <leandrod_at_mac.com> wrote in
message
> news:3BBBBEEE.30906_at_mac.com...
> > > I seem to remember the rdbms guys redefined 'completeness', to
something
> > > that has no bearing on mathematical compeletness (which I cant
remember
> the
> > Can you expand on that?
>
> 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 referring to Turing Computability? If you are, what makes you think database management requires it?

> > 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?

I prefer the definition you gave earlier involving polyadic predicates. It is much more general and matches "relation" as used in the relational model -- except that the relational model uses relation for monadic predicates as well.

http://www.earlham.edu/~peters/courses/log/terms3.htm

> 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. Received on Sat Oct 06 2001 - 20:43:12 CEST