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Monads and Quantitative Equational Theories for Nondeterminism and Probability

Authors Matteo Mio, Valeria Vignudelli

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Matteo Mio
  • Université Lyon, CNRS, ENS Lyon, UCB Lyon 1, LIP, France
Valeria Vignudelli
  • Université Lyon, CNRS, ENS Lyon, UCB Lyon 1, LIP, France

Funding

Both authors have been partially supported by the French project ANR-16-CE25-0011 REPAS. Vignudelli has been partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 programme (CoVeCe, grant agreement No 678157) and by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

Acknowledgements

The authors are grateful to the anonymous reviewers and to the authors of [Giorgio Bacci et al., 2018] for their useful comments and suggestions.

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Matteo Mio and Valeria Vignudelli. Monads and Quantitative Equational Theories for Nondeterminism and Probability. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CONCUR.2020.28

Abstract

The monad of convex sets of probability distributions is a well-known tool for modelling the combination of nondeterministic and probabilistic computational effects. In this work we lift this monad from the category of sets to the category of extended metric spaces, by means of the Hausdorff and Kantorovich metric liftings. Our main result is the presentation of this lifted monad in terms of the quantitative equational theory of convex semilattices, using the framework of quantitative algebras recently introduced by Mardare, Panangaden and Plotkin.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Axiomatic semantics
  • Theory of computation → Categorical semantics
Keywords
  • Computational Effects
  • Monads
  • Metric Spaces
  • Quantitative Algebras

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