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I think this is all an unfortunate misunderstanding.
Jonathan, Dare and I were talking about static types (I also use the term "imperative types") in our discussion before XQuery formal semantics were brought up. I dropped out of the discussion at that point because I have not read this document, but I think it's reasonable to assume that Dare was continuing to talk about static types when he said "types". This is a very common abbreviation among programmers (though I wish it weren't), and you yourself later on admitted you probably understood Dare as such. It's also useful to remember that the use of the word "class" in object oriented development is very different from its more general use.
I do have a formal background in Comp Sci, and I have read Tarski (a few years ago), but I completely reject the notion that one must read Tarski, or any other staple text of formal logic, in order to have an effective discussion of information systems technologies. I would certainly agree that discrete maths is essential, but then again, I had discrete maths twice in college (in Nigeria and in the U.S.), and I've read discrete maths texts since then, and I can still be caught making elementary errors on discrete maths theory. I think it's fair to say I've managed to be very productive with computer systems nevertheless.
Anyway, back to the main point. I agree with your broader definition of types as being defined by constraints, and this is *precisely* why I am always ridiculing the W3C efforts which put so much effort into static typing at the behest of their SQL and procedural programming backgrounds (I guess). Programmers don't need to become pure mathematicians to appreciate this: Bertrand Meyer provides much of the essence in his own writing about object-oriented development.
Also, I explore a bit of this in one of my Thinking XML column installments. I purposefully use lay/programmer language in it because the column is specifically billed as being for programmers, not philosophers.
Uche Ogbuji Fourthought, Inc.
http://uche.ogbuji.net http://4Suite.org http://fourthought.com
Track chair, XML/Web Services One (San Jose, Boston): http://www.xmlconference.com/
DAML Reference - http://www.xml.com/pub/a/2002/05/01/damlref.html
RDF Query using Versa - http://www-106.ibm.com/developerworks/xml/library/x-think10/index.html
XML, The Model Driven Architecture, and RDF @ XML Europe - http://www.xmleurope.com/2002/kttrack.asp#themodel