2019-10-10: Radu Mardare (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Radu Mardare (MSP)

Quantitative algebras: towards a quantitative theory of effects

Abstract

We develop a quantitative analogue of equational reasoning meant to provide metric semantics for stochastic/probabilistic/quantitative systems and programming languages. Quantitative algebras are algebras over metric spaces defined by these quantitative equational theories, and they implicitly define monads over the category of (extended) metric spaces. We have a few relevant examples of such algebras, where the induced free algebras correspond to well-known structures; among these are Hausdorff metrics from quantitive semilattices, p-Wasserstein metrics (hence also the Kantorovich metric) from barycentric algebras, the total variation metrics from a variant of barycentric algebras, and more.

The talk is based on a series of joint works with Prakash Panangaden and Gordon Plotkin. The main results have been presented at LICS'16, LICS'17 and LICS'18.

2019-10-10 13:30:00 UTC
LT1310