Monads and their presentations via equational theories provide a tool for reasoning about programs with computational effects. In recent works, we have studied monads resulting from the combination of nondeterminism, probabilities, and termination, as well as their extensions to the category of metric spaces. In this talk, we'll introduce this framework and show applications to proving equivalences and distances of nondeterministic and probabilistic systems.

Bibliography:

Bonchi, Sokolova, Vignudelli. The theory of traces for systems with nondeterminism and probabilities. LICS 2019. Available at: https://arxiv.org/abs/1808.00923

Mio, Vignudelli. Monads and quantitative equational theories for nondeterminism and probabilities. CONCUR 2020. Available at: https://arxiv.org/abs/2005.07509

Mio, Sarkis, Vignudelli. Combining nondeterminism, probability, and termination: equational and metric reasoning. LICS 2021. Available at: https://arxiv.org/abs/2012.00382