An Introduction to Domain Theory Notes for a Short Course

This set of notes arises from a short course given at the Universita Degli Studi Udine, given in May, 2003. The aim of the short course is to introduce both undergraduate and PhD students to domain theory, providing some of its history, as well as some of its most recent advances. 1 Outline of the Course The aim of this course is to present some of the basic results about domain theory. This will include the historically most signiflcant contribution of the theory { the use of domains to provide a model of the untyped ‚-calculus of Church and Curry. The course will proceed with the following sections: (i) Some aspects of the ‚-calculus, for motivation. (ii) Some results from universal algebra and category theory for background. (iii) !-complete partial orders. (iv) Solving domain equations, and, in particular, building a model of the untyped ‚-calculus. The last part of the course will include lectures that survey additional