Commutative Monads for Probabilistic Programming Languages

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...

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Vydáno v:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 14
Hlavní autoři: Jia, Xiaodong, Lindenhovius, Bert, Mislove, Michael, Zamdzhiev, Vladimir
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 29.06.2021
Témata:
Calculus
Computer languages
Computer science
Cost accounting
Probabilistic logic
Semantics
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Shrnutí: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.
DOI:10.1109/LICS52264.2021.9470611