Domain dependence

From: Vadim Tropashko <vadimtro_invalid_at_yahoo.com>
Date: Tue, 19 Jun 2007 15:19:50 -0700
Message-ID: <1182291590.251299.251930@q19g2000prn.googlegroups.com>

On Jun 19, 2:58 pm, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> > {(x,z)| (exists y: A(x,y) & exists y: B(y,z) -> forall y : A(x,y) <->
> > B(y,z) }
>
> Ditto.

There is some mystery about domain (in)dependence. In this case it was such a nice expression

{(x,z)| forall y : A(x,y) <-> B(y,z) }

And now it is ugly.

The other example from
http://vadimtropashko.wordpress.com/why-relational-division-is-so-uncommon/ is a set union query

{y | exists x: R(x,y) }

A naive attempt to write set intersection query as a dual of the above

{y | forall x: R(x,y) }

fails because of domain dependence. One have to write much less intuitive

{s | forall x ( (exists y R(x,y)) -> R(x,s) )} Received on Tue Jun 19 2007 - 17:19:50 CDT