Discrete random variables over domains

Abstract

In this paper we explore discrete random variables over domains. We show that these lead to a continuous endofunctor on the categories R B (domains that are retracts of bifinite domains), and FS (domains where the identity map is the directed supremum of deflations finitely separated from the identity). The significance of this result lies in the fact that there is no known category of continuous domains that is closed under the probabilistic power domain, which forms the standard approach to modeling probabilistic choice over domains. The fact that RB and FS are cartesian closed and also are closed under the discrete random variables power domain means we can now model, e.g., the untyped lambda calculus extended with a probabilistic choice operator, implemented via random variables. © Springer-Verlag Berlin Heidelberg 2005.