Re: domains for typed lambda calculi

Hello,

Chapters 2 and 8 of

Andrea Asperti, Giuseppe Longo. Categories, Types and Structures.
M.I.T. Press, 1991

available at

http://www.di.ens.fr/users/longo/download.html
http://www.cs.unibo.it/~asperti/PAPERS/book.pdf

discuss the (categorical) semantics of typed-lambda calculus
based on Scott domains (domains = types, continuous functions = terms).
Chapter 8 can be read just after section 2.4, or even 2.3 (no need to
learn complex categorical notions). This semantics is based on the
work of Plotkin,

Gordon D. Plotkin. Pisa Notes (On Domain Theory).
Department of Computer Science, University of Edinburgh, 1983

available at

http://homepages.inf.ed.ac.uk/gdp/publications/Domains.ps

Chapters 7 and 8 of

Jaap Van Oosten. Basic Category Theory.
http://www.math.uu.nl/people/jvoosten/syllabi/catsmoeder.ps.gz
http://www.math.uu.nl/people/jvoosten/syllabi/catsmoeder.pdf

also contain similar material, but Van Oosten is definitely more
mathematical and much less "computer-oriented".

There are many more texts available on the web on this topic,
but these are my preferred ones (PS. Be aware that the Asperti/Longo
text contains some errata in the exercises).

Kind regards.

--
Jose Juan Mendoza Rodriguez

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.