Quantitative Algebraic Reasoning: An overview

In this talk I will review the basic definitions, constructions and key results presented in three works, namely Mardare at al. LICS16, LICS17, and Bacci et al. LICS18, which constitute the first steps of the more ambitious the program of understanding the algebraic properties of computational effects on categories enriched over (extended) metric spaces. During the talk I will provide several motivating examples to offer a general pragmatic picture of how algebraic reasoning works and how it can be used. Finally, I will conclude by presenting a list of open problems and initial ideas on how to address them.