research-article

Commutative monads for probabilistic programming languages

Authors:

Bert Lindenhovius,

Michael Mislove,

Vladimir ZamdzhievAuthors Info & Claims

LICS '21: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science

Article No.: 19, Pages 1 - 14

https://doi.org/10.1109/LICS52264.2021.9470611

Published: 24 November 2021 Publication History

Abstract

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.

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Di Gianantonio PEdalat ASobocinski PLago UEsparza J(2024)A Cartesian Closed Category for Random VariablesProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662126(1-14)Online publication date: 8-Jul-2024
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cover image ACM Conferences

LICS '21: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science

June 2021

1227 pages

ISBN:9781665448956

Conference Chair:
Daniele Gorla
Università di Roma "La Sapienza"

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SIGLOG: ACM Special Interest Group on Logic and Computation

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EACSL: European Association for Computer Science Logic
IEEE-CS: Computer Society

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Association for Computing Machinery

New York, NY, United States

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Published: 24 November 2021

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LICS '21

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SIGLOG

LICS '21: 36th Annual ACM/IEEE Symposium on Logic in Computer Science

June 29 - July 2, 2021

Rome, Italy

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Overall Acceptance Rate 215 of 622 submissions, 35%

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Cited By

Di Gianantonio PEdalat ASobocinski PLago UEsparza J(2024)A Cartesian Closed Category for Random VariablesProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662126(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662126
Goubault-Larrecq JJia XThéron C(2023)A Domain-theoretic Approach to Statistical Programming LanguagesJournal of the ACM10.1145/361166070:5(1-63)Online publication date: 11-Oct-2023
https://dl.acm.org/doi/10.1145/3611660
Avanzini MMoser GPechoux RPerdrix SZamdzhiev V(2022)Quantum Expectation Transformers for Cost AnalysisProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533332(1-13)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533332
Jia XKornell ALindenhovius BMislove MZamdzhiev V(2022)Semantics for variational Quantum programmingProceedings of the ACM on Programming Languages10.1145/34986876:POPL(1-31)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498687
de Amorim PKozen DMardare RPanangaden PRoberts MGorla D(2021)Universal semantics for the stochastic λ-calculusProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470747(1-12)Online publication date: 29-Jun-2021
https://dl.acm.org/doi/10.1109/LICS52264.2021.9470747

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