Re: Notions of Type

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.
> Nonetheless people call it an algebra because it's an
> algebra in spirit

For certain your type theory knowledge is superior to mine, so I'm unsure what you are saying above. Because I'm almost certain that algebraic structures are not limited to a single set.

For example, Linear Algebra is an algebraic structure over a vector space and a field. The entire family of multi-sorted algebras are defined over two or more different subsets of a particular set.

In other words I thought

  algebraic structure : a set of function signatures and   axioms defined over /one or more/ sets.

Is this not the case? And if not, what does the above definition define?

• Keith -- Fraud 6