An Application of Computable Distributions to the Semantics of Probabilistic Programming Languages

Most probabilistic programming languages for Bayesian inference give either operational semantics in terms of sampling, or denotational semantics in terms of measure-theoretic distributions. It is important that we can relate the two, given that practitioners often reason both analytically (e.g., density) as well as algorithmically (i.e., in terms of sampling) about distributions. In this paper, we give denotational semantics to a functional language extended with continuous distributions and show that by restricting attention to computable distributions, we can realize a corresponding sampling semantics.