A BRICS Mini-Course
September 4 and 6, 2002
Glynn Winskel, Glynn.Winskel@cl.cam.ac.uk
Computer Laboratory, University of Cambridge, UK
Classical domain theory and denotational semantics, pioneered by Dana Scott and Christopher Strachey, has been inspirational in suggesting programming languages, their types and ways to understand them. Domain theory has played a much lesser role in research in interactive/concurrent/distributed computation. One reason perhaps is that classical domain theory has not scaled up to the more intricate models we find used in concurrency.
In the first half of the course (Tuesday) I will describe what I see as the aims, challenges, and promising approaches to a domain theory for concurrency. This will make a case for replacing domains as partial orders of information by categories, and outline what I see as the primary current problems.
In the second half of the course (Thursday), I will introduce an approach to category theory which stands alone, but is particularly useful when domains are categories because it often provides swift calculations to show the continuity of functors (i.e., their limit and colimit preserving properties). The power of the approach derives from its early use of ends and coends.
The first half of the mini-course (Tuesday) will touch on many areas (inevitably somewhat quickly), though will begin with a simple, if not well-known, domain theory for concurrency. The second half of the mini-course (Thursday) will be more self-contained and will only assume a nodding acquaintance with category theory; in particular, I will try to give an accessible introduction to ends and coends.
(The mini-course is based on joint work with Luca Cattani and Mikkel Nygaard Hansen (Tuesday), and Mario Caccamo (Thursday)-see my web page and, in particular, Lecture Notes on Category Theory at www.brics.dk/ mcaccamo. Further references will be given during the course. )