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Commutative Monads for Probabilistic Programming Languages

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A long-standing open problem in the semantics of programming languages supporting probabilistic choice is to find a commutative monad for probability on the category DCPO. In this paper we present three such monads and a general construction for finding even more. We show how to use these monads to provide a sound and adequate denotational semantics for the Probabilistic FixPoint Calculus (PFPC) - a call-by-value simply-typed lambda calculus with mixed-variance recursive types, term recursion and probabilistic choice. We also show that in the special case of continuous dcpo's, all three monads coincide with the valuations monad of Jones, and we fully characterise the induced Eilenberg-Moore categories by showing that they are all isomorphic to the category of continuous Kegelspitzen of Keimel and Plotkin.

Dates and versions

hal-03519225 , version 1 (10-01-2022)



Xiaodong Jia, Bert Lindenhovius, Michael Mislove, Vladimir Zamdzhiev. Commutative Monads for Probabilistic Programming Languages. LICS 2022 - 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2021, Rome, Italy. pp.1-14, ⟨10.1109/LICS52264.2021.9470611⟩. ⟨hal-03519225⟩
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