Monads and Quantitative Equational Theories for Nondeterminism and Probability - Archive ouverte HAL
Conference Papers Year : 2020

Monads and Quantitative Equational Theories for Nondeterminism and Probability

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.
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Dates and versions

hal-03028173 , version 1 (27-11-2020)

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Matteo Mio, Valeria Vignudelli. Monads and Quantitative Equational Theories for Nondeterminism and Probability. CONCUR 2020, Sep 2020, Vienna (on line), Austria. ⟨10.4230/LIPIcs.CONCUR.2020.28⟩. ⟨hal-03028173⟩
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