Re: Logical equivalence of simple and complex types under the relational model?

"Neo" <neo55592_at_hotmail.com> wrote in message news:4b45d3ad.0412010715.16279bd_at_posting.google.com...
> > > What is a type?
> >
> > A type is a set of values supporting the same operations.
>
> Can a type itself be a value in another set supporting same/similar ops.
> For example, ... -1, 0, 1, ... are integers
> and 1.2, 3.57, 68.888 are floats.
> and integers, floats, fractions are data types.

Some type systsems support this. For example the numerical tower in Common Lisp.

There is a type 'number' which includes all numbers.

There are also types that subtypes of this type. For examples Integer.

The total numerical tower is quite complicated.

> What is the ultimate type, or least the one that would include data types?

I think this is likely to be type system specific, and that in a lot of type systems that there is no ultimate type.

In common lisp the ultimate type is 't' (short for true) which all values are a members of.

Note that it only makes sense to talk about type membership for first class objects.
For example in most languages parameters themselves, or namespaces are not things that "stand by themselves" as values, and hence one does not speak of type membership.

Rene. Received on Wed Dec 01 2004 - 16:37:31 CET