# Re: completeness of the relational lattice

Date: Fri, 22 Jun 2007 18:20:50 -0000

Message-ID: <1182536450.083309.219960_at_o61g2000hsh.googlegroups.com>

On 22 jun, 19:36, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:

> On Jun 22, 3:08 am, Jan Hidders <hidd..._at_gmail.com> wrote:

*>
**> > > > We cannot distribute in general, but we have a specific distribution rule:
**>
**> > > > (1) r /\ ((s \/ [H]) \/ (t\/[H])) = r /\ (s \/ [H]) \/ r*(t \/ [H])
**>
**> > > Which is BTW a very limited case embraced by Spight criteria.
**>
**> > Indeed. But it is a simple equation, no premises.
**>
**> Your premise is that H is a set of attributes which is a subset of
**> attributes of relations s and t
*

No, any set of attributes H will do.

> > > BTW, why don't we define square brackets [R] as an unary operator,

*> > > expressed in my notation as
**>
**> > > [R] = R /\ 00
**>
**> > What is R? In [R] it is a set of attributes. So a set of attributes is
**> > a valid expression in your syntax? I'm not sure what that means.
*

Sorry, I missed your point there. The problem with [R] is that is doesn't allow me to define a projection for an arbitrary set of attributes.

> > Could

*> > you give a complete definition of your syntax just like I did?
**>
**> - R : a relation name
**> - Expr /\ Expr : the natural join
**> - Expr \/ Expr : the inner union
**> - 00 : the empty relation with empty header
**> - 01 : the relation with the empty tuple and empty header
**> - 10 : the empty relation with the set of all attributes as header
**> - 11 : the relation with all tuples over all attributes
**> - E : the "universal" equlity relation
*

And extended with [R] I assume. Can you prove that you can express all queries in UCQ?

> Once again, I'm not convinced about syntax until I see a convincing

*> set of axioms.
*

- Jan Hidders