The troublesome probabilistic powerdomain

The Extended Probabilistic Powerdomain Monad over Stably Compact Spaces

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...

QRB-Domains and the Probabilistic Powerdomain

Is there any cartesian-closed category of continuous domains that would be closed under Jones and Plotkin’s probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higher-order languages. We relax the question, and look for quasi-continuous dcpos instead. We introduce a natural class of such quasi-continuous dcpos, the !QRB-dom...

A Probabilistic Powerdomain of Evaluations

We give a probabilistic powerdomain construction on the category of inductively complete partial orders; it is the partial order of continuous [0, 11-valued evaluations on the Scott topology. By means of a theory of integration with respect to such evaluations, the powerdomain is shown to be a monad, and indeed one gets a model for Moggi’s computational lambda-calculus. One can also solve recur...

Domain Theory and its Applications

Michael Baldamus An Elementary Set–Theoretic Semantics for the π–Calculus . . . . . . . . . . . 6 Andrej Bauer Recursive Analysis in PER(PN) . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Eike Best Relational Semantics Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Marcello Bonsague Infinitary Logic of Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Lawson-compactness for the Probabilistic Powerdomain