Re: monotonic subtype relations?

To: clem@echo.canberra.edu.au, John.Reynolds@proof.ergo.cs.cmu.edu
Cc: types@theory.lcs.mit.edu
Date: Wed, 10 Apr 91 18:53:15 PDT

It wasn't clear from the original request whether the notion of "subtype"
referred to was the notion of subtype treated in object oriented
programming.  John Reynold's response (very carefully) referred to the
notion of "subdomain" rather than "subtype".  In case the original request
really had to do with the object-oriented notion, let me put in a strong
caution that the OOL notion of "subtype" is usually quite distinct from a
notion of ordering used, for example, to find fixed points or solve domain
equations.  For instance, the ordering of types in the finitary projection
model of the second order lambda calculus seems to have no relevance (alas!)
to the notions of subtype for OOL's.  If such a model were to be extended
to support subtypes, an entirely different ordering would be required for
the subtype hierarchy.

If the original enquiry had nothing to do with OOL's, ignore this caution.
Otherwise, beware!

	Kim Bruce