Re: Notions of Type

Bob Badour wrote:
> Marshall wrote:
>
> > paul c wrote:
> >
> >>Marshall wrote:
> >>
> >>>erk wrote:
> >>>
> >>>>Sorry if this is obvious to everyone else, but does an algebra include
> >>>>only operations defined on values of the type in question?
> >>>
> >>>Yes.
> >>>
> >>>
> >>>>I ask
> >>>>because in relational algebra, at least the rename operator involves a
> >>>>different type ("attribute name") than the "core type" (relation).
> >>>
> >>>Very true. Of the various relational operators that have been
> >>>identified over the years, only a few, like union, are really
> >>>algebraic. RESTRICT, PROJECT, etc. aren't. ...
> >>
> >>Just a quick question - is your reason for making that statement that
> >>restrict, project, etc. result in a relation that doesn't necessarily
> >>have all the attributes of the operand relations?
> >
> >
> > No; that's actually not a problem.
> >
> > The problem is the operands. Strictly speaking, an algebraic operator
> > would be one which had the type
> >
> > op: 'a, 'a -> 'a
> >
> > ("The thing named "op" has the type: function taking operands of
> > type some-a and some-a and returning a value of type some-a.")
> >
> > So the algebra of the integers has operators like:
> >
> > +: int, int -> int
> >
> > Consider PROJECT:
> >
> > PROJECT: Relation, Set-of-attributes -> Relation
> >
> > So for PROJECT of an x,y point over x, we pass it two
> > things:
> >
> > 1) A relation defined over attributes x and y
> > 2) ???
> > and it returns
> > 3) A relation defined over attribute x (aka "profit")
> >
> > Whoops! Doesn't fit the template. The second argument isn't
> > a relation. So, strictly speaking, this is not an algebraic operator,
> > because it isn't closed over the type Relation. Exercise for the
> > reader: what *is* the type of the other argument? This should
> > make your head hurt a least a little bit.
>
> It is a relation of degree 1 and cardinality N representing a set of N
> attribute names.

Must it be a relation, given that its tuples aren't used at all? And if one uses a relation, isn't the degree N and the cardinality 0? (I'm basing this on TABLE_DEE (true) being degree zero, cardinality one and TABLE_DUM (false) being degree zero, cardinality zero). Received on Thu Aug 17 2006 - 20:04:48 CEST