Re: Notions of Type

Keith H Duggar wrote:
> Marshall wrote:
> > Very true. Of the various relational operators that have
> > been identified over the years, only a few, like union,
> > are really algebraic.

Except that union applies to relations of the same arity only. Compare it to "normal" algebras where operations have one exeption only (like division by 0). Are operations with multiple exceptions more complicated than those with none, or single one? You bet.

> > RESTRICT, PROJECT, etc. aren't.
> > Nonetheless people call it an algebra because it's an
> > algebra in spirit
>
> 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.

Correct. Keep in mind, however, that "multi-sorted" in practice means "2-sorted". In RA case we have:

Relations,
Sets of attribute names (projection),
Pairs of attributes (renaming),
Predicate expressions (selection)

• 4 sorts at least. Are multisorted algebras more complicated than normal algebras? You bet.