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Semantics of higher-order probabilistic programs with conditioning

Published:20 December 2019Publication History
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Abstract

We present a denotational semantics for higher-order probabilistic programs in terms of linear operators between Banach spaces. Our semantics is rooted in the classical theory of Banach spaces and their tensor products, but bears similarities with the well-known semantics of higher-order programs a la Scott through the use of ordered Banach spaces which allow definitions in terms of fixed points. Our semantics is a model of intuitionistic linear logic: it is based on a symmetric monoidal closed category of ordered Banach spaces which treats randomness as a linear resource, but by constructing an exponential comonad we can also accommodate non-linear reasoning. We apply our semantics to the verification of the classical Gibbs sampling algorithm.

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        cover image Proceedings of the ACM on Programming Languages
        Proceedings of the ACM on Programming Languages  Volume 4, Issue POPL
        January 2020
        1984 pages
        EISSN:2475-1421
        DOI:10.1145/3377388
        Issue’s Table of Contents

        Copyright © 2019 Owner/Author

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 20 December 2019
        Published in pacmpl Volume 4, Issue POPL

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