The Extended Probabilistic Powerdomain Monad over Stably Compact Spaces

  • Ben Cohen
  • Martin Escardo
  • Klaus Keimel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


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.


Compact Space Scalar Multiplication Topological Vector Space Algebra Homomorphism Continuous Domain 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ben Cohen
    • 1
  • Martin Escardo
    • 2
  • Klaus Keimel
    • 1
  1. 1.Fachbereich MathematikTechnische UniversitätDarmstadtGermany
  2. 2.School of Computer ScienceUniversity of BirminghamBirminghamUK

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