2026-07-22T14:16:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12840 2024-03-06T10:50:49Z ddc:004 open_access

Monads and Quantitative Equational Theories for Nondeterminism and Probability Mio, Matteo Vignudelli, Valeria Computational Effects Monads Metric Spaces Quantitative Algebras 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Matteo Mio and Valeria Vignudelli 2020 Is Part Of LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2020.28 urn:nbn:de:0030-drops-128407 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.28 eng https://creativecommons.org/licenses/by/3.0/legalcode