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A convenient category of domains

Authors Ingo Battenfeld, Matthias Schröder, Alex Simpson



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Ingo Battenfeld
Matthias Schröder
Alex Simpson

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Ingo Battenfeld, Matthias Schröder, and Alex Simpson. A convenient category of domains. In Computational Structures for Modelling Space, Time and Causality. Dagstuhl Seminar Proceedings, Volume 6341, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)
https://doi.org/10.4230/DagSemProc.06341.2

Abstract

We motivate and define a category of "topological domains", whose objects are certain topological spaces, generalising the usual $omega$-continuous dcppos of domain theory. Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations. It also supports the construction of free algebras for (in)equational theories, provides a model of parametric polymorphism, and can be used as the basis for a theory of computability. This answers a question of Gordon Plotkin, who asked whether it was possible to construct a category of domains combining such properties.
Keywords
  • Domain theory
  • topology of datatypes

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