Re: domains for typed lambda calculi

Michal Przybylek <mrp@xxxxxxxxxxxx> wrote:
JohnF <john@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
That's exactly what I was looking for.

If so (i.e. if you are really interested in categorical models),
then I strongly suggest you to read
"An introduction to fibrations, topos theory, the effective
topos and modest sets" by Wesley Phoa (you will find this article
here:
http://www.lfcs.inf.ed.ac.uk/reports/92/ECS-LFCS-92-208)
and
"Categorical Logic and Type Theory" by Bart Jacobs.

Thanks for the recommendations, Michal, which I'll look at soon.
However, your instinct is right that I was actually hoping for
models based on domain equations, like D=[D-->D] for the untyped
lambda calculus. Can anything like that be constructed?
Any references along those lines?

Michal Przybylek <mrp@xxxxxxxxxxxx> wrote:
JohnF <john@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
Any suggestions for online or journal or textbook
references discussing domains for typed lambda calculi?

The standard book is the following:
"Domains and Lambda-Calculi" by Amadio and Curien. But if you
are not used to serious math, this book could be difficult for you.

Well, after looking at a library copy, it definitely ain't easy (for me).
I can follow the math with a little effort, but the lack of intuitive
motivation for most of it makes the book a hard read (for me), indeed.
Much more my speed is "Mathematical Theory of Domains" by
Viggo Stoltenberg-Hansen and Ingrid Lindstrom and Edward Griffor,
Cambridge UP, 1994, ISBN 0-521-38344-7. Any recommendations more
at that level? Thanks again,
--
John Forkosh ( mailto: j@xxxxx where j=john and f=forkosh )
.