Domain Theory

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BA in Computer Science BA in Mathematics & Computer Science MSc in Computer Science MSc in Mathematics and the Foundations of Computer Science

16 lectures HT Professor Samson Abramsky

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Overview

Domain theory is a mathematical theory of information and computation. It is based on the idea of states of (in general) partial information, ordered by how much information they contain. On this basis, a beautiful mathematical theory has been developed, with deep applications to many topics in Computer Science, in particular to the semantics of programming languages. In this course, we shall develop both the mathematical theory, and the applications. Particular themes will: the ideas of continuity and approximation supported by domain theory, which has important connections with topology, and gives a basis for computation with infinite objects; the development of a rich theory of fixpoints, as a foundation for recursive definitions; developing a rich set of data type constructions, and recursive definitions of domains themselves; and powerdomains, to support ideas of non-deterministic and probabilistic computation.

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