Abstract
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.,i¾?density as well as algorithmically i.e.,i¾?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.
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