A probabilistic powerdomain of evaluations

A probabilistic power domain construction is given for the category of inductively complete partial orders. It is the partial order of continuous [0,1]-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 a model for the Moggi computational lambda calculus is obtained. It is also possible to solve recursive domain equations involving the powerdomain, and all this gives a metalanguage for programming languages with probabilistic features. This is used to give the semantics of a language with a probabilistic parallel construct. it is shown that the construction generalizes previous work on partial orders of measures