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Domains for denotational semantics

  • Dana S. Scott
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 140)

Abstract

The purpose of the theory of domains is to give models for spaces on which to define computable functions. The kinds of spaces needed for denotational sematics involve not only spaces of higher type (e.g. function spaces) but also spaces defined recursively (e.g. reflexive domains). Also required are many special domain constructs (or functors) in order to create the desired structures. There are several choices of a suitable category of domains, but the basic one which has the simplest properties is the one sometimes called consistently complete algebraic cpo's. This category of domains is studied in this paper from a new, and it is to be hoped, simpler point of view incorporating the approaches of many authors into a unified presentation. Briefly, the domains of elements are represented set theoretically with the aid of structures called information systems. These systems are very familiar from mathematical logic, and their use seems to accord well with intuition. Many things that were done previously axiomatically can now be proved in a straightfoward way as theorems. The present paper discusses many examples in an informal way that should serve as an introduction to the subject.

Keywords

Topological Space Data Object Finite Subset Approximable Mapping Domain Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Dana S. Scott
    • 1
  1. 1.Department of Computer ScienceCarnegie-Mellon UniversityPittsburghUSA

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