Algebras of the Extended Probabilistic Powerdomain Monad

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...

The troublesome probabilistic powerdomain

In [12] it is shown that the probabilistic powerdomain of a continuous domain is again continuous. The category of continuous domains, however, is not cartesian closed, and one has to look at subcategories such as RB, the retracts of bifinite domains. [8] offers a proof that the probabilistic powerdomain construction can be restricted to RB. In this paper, we give a counterexample to Graham’s p...

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...

The probabilistic powerdomain for stably compact spaces

This paper reviews the one-to-one correspondence between stably compact spaces (a topological concept covering most classes of semantic domains) and compact ordered Hausdorff spaces. The correspondence is extended to certain classes of real-valued functions on these spaces. This is the basis for transferring methods and results from functional analysis to the non-Hausdorff setting. As an applic...

Lawson-compactness for the Probabilistic Powerdomain