Re: Relational lattice
Date: 9 Mar 2005 18:41:40 -0800
Message-ID: <1110422500.323466.99120_at_f14g2000cwb.googlegroups.com>
Jan Hidders wrote:
> Vadim Tropashko wrote:
> >
> > I'm confused what does it mean for a set of operators to be
> > relationally complete. Is it
> >
> > 1. All the classic operators should be expressed in terms of the
new
> > ones. More precisely, given an expression in terms of projection,
> > selection, CP, union, and minus, then one have to be able to
exhibit an
> > equivalent expression in terms of generalized union and join.
> >
> > or
> >
> > 2. Given a set of equations in terms of classic operators, one have
to
> > exhibit an equivalent set of equations in new terms.
>
> The first, but the second one is also Ok provided that you give a
> syntactic characterization of which sets of equations express
queries,
> i.e., which ones have always a unique solution.
Is it possible to express transitive closure in a finite set of equations as well?
BTW, I just came across
http://c2.com/cgi/wiki?RelationalAlgebra
describing the "simplified algebra in the Third Manifesto". (I confess
that I don't have a copy of any manifesto book:-). The AND operator is
a natural join, but the OR is defined differently! It is immediate,
that the Third Manifesto definition doesn't respect the absorption law:
A OR (A AND B) header should be the union of the A and B headers,
therefore the result can't be A. Without absorption law the structure
is merely a semilattice, where the order induced by the meet operation
-- OR -- is different from the order induced by the join. The nice
feature of the manifesto algebra is that it respects distributive law.
Received on Thu Mar 10 2005 - 03:41:40 CET