The extended probabilistic powerdomain monad over stably compact spaces

Authors:
Ben Cohen;Martin Escardo;Klaus Keimel
Affiliations:
Fachbereich Mathematik, Technische Universität, Darmstadt, Germany;School of Computer Science, University of Birmingham, Birmingham, UK;Fachbereich Mathematik, Technische Universität, Darmstadt, Germany
Venue:
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Year:
2006

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Abstract

For the semantics of probabilistic features in programming mainly two approaches are used for building models. One is the Giry monad of Borel probability measures over metric spaces, and the other is Jones’ probabilistic powerdomain monad [6] over dcpos (directed complete partial orders). This paper places itself in the second domain theoretical tradition. The probabilistic powerdomain monad is well understood over continuous domains. In this case the algebras of the monad can be described by an equational theory [6, 9,5]. It is the aim of this work to obtain similar results for the (extended) probabilistic powerdomain monad over stably compact spaces. We mainly want to determine the algebras of this powerdomain monad and the algebra homomorphisms.