Re: Notions of Type

"paul c" <toledobythesea_at_oohay.ac> wrote in message news:sj7Fg.426224$IK3.379801_at_pd7tw1no...

> Earlier, Bob B said about the "set of attributes": "It is a relation of
> degree 1 and cardinality N representing a set of N attribute names".
> Maybe you are right and saying that isn't necessary, but his stance
> seems to me to obviate the question.
>
> (I don't know if it matters that if his approach is right, projection
> wouldn't depend on whatever the name of the single attribute is - I
> presume that it would have the same name and type as all headers in the
> db, eg., just another axiom in the form of the catalog.)

I tend to think like a computer person and not like a mathematician. What follows reflects this.

A relation has a header (definition) and set of tuples (content). If we look inside the relation header we find.... by golly!.... a set of attributes!

so

PROJECT spaceof(<relation>) spaceof (<set of attributes>) -> PROJECTION

is really more like

PROJECT spaceof(attributeset(<relation>) spaceof(<set of attributes>) -> PROJECTION. PROJECT is just a function that returns a function. Spaceof is just a function that makes a space out of a set of attributes. Attribute set is just a function that pulls the attribute set out of the relation definition.

Then

PROJECTION <relation> -> <relation>

is something we can look at in terms of closure. Received on Fri Aug 18 2006 - 07:20:16 CDT