Re: Complete axiomatization of relational algebra

Neil Nelson wrote:
>
> Any algebra will be complete for what it does, but maybe the object
> is to be `complete' as that word is used in logic.

Yes, that is what I meant. The relational algebra is not an abstract algebra in the sense that the domain and the operations are specified in set theory and the equalities are derived afterwards. So I can ask the question if all equalities that hold can be derived from a certain finite list of equalities.

By the way, this is as far as I know also a meaningful question for an abstract algebra that is specified only by its equivalence rules; it can be that an equality holds for every interpretation of the algebra, but is not derivable from the equality rules.

> Or do we want the algebra to be `complete' (to faithfully represent)
> for some set of operations that are associated with databases?

That is not what I meant, but also an interesting kind of completeness.

> purpose of the database. If we were to ask: what is the algebra that
> would represent an arbitrary application that could use a database (the
> possible relations on an arbitrary database), then such an algebra is
> merely some Turing complete language.

And Turing-completeness is also an interesting kind of completeness. :-) But it is well known that the relational algebra is not complete in that sense.

> Perhaps we want to know as a standard feature of the database language
> what row contains the smallest value (or nearest, next greatest to some
> value) for a column. We then have a sort or key sequence.

Er, sorting is not possible because the domain is relations and relations do not have an order by definition. But you probably already knew that.

Kind regards,

-- 
  Jan Hidders