Abstract

In this collection we try to give anoverview of some selected topics in Domain Theory and Denotational Semantics. In doing so, we rst survey the mathematical universes which have been used as semantic domains. The emphasis is on those ordered structures which have beenintroduced by Dana Scott in 1969 and which gure under the name (Scott-) domains. After surveying developments in the concrete theory of domains we describe two newer developments, the axiomatic and the synthetic approach. In the second part we look at three computational phenomena in detail, namely, sequential computation, polymorphism, and mutable state, and at the challenges that these pose for a mathematical model. This presentation does by no means exhaust the various approaches to denotational semantics and it certainly does not describe all possible mathematical techniques which havebeen used to describe various aspects of programs. We hope that, nevertheless, it illustrates how a particular challenge (namely the modelling of recursive de nitions) has given rise to an immensely rich theory, both in its general parts and in its applications.

Citations