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Introduction to Domain Theory
Graham Hutton School of Computer Science and IT University of Nottingham
Domain theory has its roots in the seminal work of Scott and
Strachey in the 1970s on denotational semantics, in particular
on solving the technical problems that arise in giving semantics
to recursively defined programs and types. As well as being one
of the most fascinating topics in the foundations of computing
science, domain-theoretic ideas are used in many branches of
modern research on programming languages and their semantics. The aim
of this course is to teach the basic concepts of domain theory.
The course comprises five lectures, each with exercises:
Background and motivation
(denotational semantics, non-termination and bottom,
partially-ordered sets, monotonic functions);
Recursively defined functions
(chains, directed sets, least upper bound, cpos and
continuous functions, the fixpoint theorem);
Constructions on types
(sums, products, function-spaces, lifting, lazyness
vs strictness, axiomatisations, functors);