Quantitative Equational Reasoning

Giorgio Bacci, Radu Mardare, Prakash Panangaden, Gordon D. Plotkin

Publikation: Bidrag til bog/antologi/rapport/konference proceedingBidrag til bog/antologiForskningpeer review


Equational logic has been a central theme in mathematical reasoning and in reasoning about programs. We introduce a quantitative analogue of equational reasoning that allows one to reason about approximate equality. The equality symbol is annotated with a real number that describes how far apart two terms can be. We develop the counterparts of standard results of equational logic, in particular, a completeness theorem. We define quantitative algebras and free quantitative algebras which yield monads on categories of metric spaces. We show that key examples of probability metrics, in particular, the Kantorovich metric and the Wasserstein p-metrics, arise from simple quantitative theories. Finally we develop a quantitative version of the theory of effects in programming languages.

TitelFoundations of Probabilistic Programming
RedaktørerGilles Barthe, Joost-Pieter Katoen, Alexandra Silva
ForlagCambridge University Press
Publikationsdatodec. 2020
ISBN (Trykt)9781108488518
ISBN (Elektronisk)9781108770750
StatusUdgivet - dec. 2020


Dyk ned i forskningsemnerne om 'Quantitative Equational Reasoning'. Sammen danner de et unikt fingeraftryk.