Monads and Quantitative Equational Theories for Nondeterminism and Probability

Matteo Mio (1) , Valeria Vignudelli (2)

1 ENS de Lyon - École normale supérieure de Lyon
2 LIP - Laboratoire de l'Informatique du Parallélisme

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.

Mots clés: Monads; Metric Spaces; Quantitative Algebras

Domaines: Logique en informatique [cs.LO]

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⟩