Re: more algebra
Date: Thu, 8 Apr 2010 08:59:10 -0700 (PDT)
Message-ID: <34caf7aa-7d3f-4746-8cc2-755583d35ac8_at_x3g2000yqd.googlegroups.com>
On Apr 8, 6:47 am, Sampo Syreeni <de..._at_iki.fi> wrote:
> On Apr 7, 3:05 am, paul c <toledobythe..._at_oohay.ac> wrote:
>
> > ( r GROUP ( { N } AS n ) ) = ( EXTEND r ADD ( RELATION { TUPLE { N
> > } AS n ) { K, n }
>
> How about A join project_K(A)=A?
This is not a constraint. [Natural] join (aka D&D <AND>, or in less sloppy notation "^") is a semilattice operation, so that it induces a partial order "<" (which is essentially subset order generalized from unary relations into n-ary relations) via equivalence:
x ^ y = x <-> x < y
Projection is a generalized union ("v") -- a complementary operation which elevates semilattice into lattice. Therefore, the constraint becomes
A < A v K
which holds in a lattice trivially. The other way to see it is to rewrite the constraint
A join project_K(A)=A
in the lattice terms as
A ^ (K v A) = A
which trivially holds by absorption law. Received on Thu Apr 08 2010 - 17:59:10 CEST