What is Expressiveness in a Computer Language

Marshall marshall.spight at gmail.com
Wed Jun 21 20:58:47 CEST 2006

Andreas Rossberg wrote:
> Chris Uppal wrote:
> >
> > I have never been very happy with relating type to sets of values (objects,
> > whatever).
> Indeed, this view is much too narrow. In particular, it cannot explain
> abstract types, which is *the* central aspect of decent type systems.

What prohibits us from describing an abstract type as a set of values?

> There were papers observing this as early as 1970.


> (There are also theoretic problems with the types-as-sets view, because
> sufficiently rich type systems can no longer be given direct models in
> standard set theory. For example, first-class polymorphism would run
> afoul the axiom of foundation.)

There is no reason why we must limit ourselves to "standard set theory"
any more than we have to limit ourselves to standard type theory.
Both are progressing, and set theory seems to me to be a good
choice for a foundation. What else would you use?

(Agree with the rest.)


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