Re: RA with MV attributes

Marshall wrote:
> On Jan 17, 5:32 pm, "David" <davi..._at_iinet.net.au> wrote:

> > Note that thinking of a type this way reminds us that it's
> > nonsensical to say that the set of attributes of a relation (directly)
> > represents its type. The type "relation" has more to do with the
> > set of all possible sets of tuples.
>
> If we know the set of attributes and their types, do we not
> also know the set of all possible sets of tuples? What's
> the difference?

They are different sets.

> > Marshall is correct in saying that the type of a relation can (if we
> > desire) be parameterized on the attributes, and that this may indeed by
> > useful sometimes. However, I don't think it's so useful in the
> > mathematical definition of a relation. For example a join would no
> > longer be regarded as a binary operation.
> >
> > From Wikipedia : "... a binary operation on a set S is a binary
> > function from S and S to S"
>
> Natural join is a binary operation closed over the set of all
> relations.

The very idea to put all relations of all "types" into a single set suggests that the "type" has now become a property of the relation value.

Let's ignore sub-typing because it's not relevant. When we write set<T> we assume all elements have the *same* type T. If we want to support inhomogeneous collections then we need to introduce tagged unions (say) and then the element "type" indicator is really just a property of the elements. Received on Thu Jan 18 2007 - 07:27:45 CET