Re: RA with MV attributes

Bob Badour wrote:

[snip]

> >>A similar
> >>thing seems to be true for a relation - it is more than its set of
> >>tuples. Note in any case that I defined a tuple to be a mapping on
> >>A(r), so therefore you can't really disconnect the tuple from the set
> >>of attributes anyway.
> >
> >
> > I'm not proposing "disconnecting" them per se; I'm trying to emphasize
> > that type and value may exist at different phases in computation. They
> > remain intimately connected the same way that "3" and "int" are
> > connected.
> > But I would not say that "3" is part of the type nor that "int" is part
> > of
> > the value.
>
> A quibble: If one accepts that a type is a set of values and the
> operations defined on those values, then "3" is "part of the type" as it
> is an element of the value set.

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.

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"

[snip] Received on Thu Jan 18 2007 - 02:32:59 CET