2022/07/21 by Gilles Barthe, Raphaëlle Crubillé, Barthe, Gilles +5 · 1 citation
Computer Science · #Advanced Database Systems and Queries #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Programming Languages (cs.PL)
paper · pdf · doi:10.48550/arxiv.2207.10590
openalex publication_date 2022/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the nature of applicative bisimilarity in λ-calculi endowed with operators for sampling from continuous distributions. On the one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide with contextual equivalence when real numbers can be manipulated only through continuous functions. The key ingredient towards this result is a novel notion of Feller-continuity for labelled Markov processes, which we believe of independent interest, being a broad class of LMPs for which coinductive and logically inspired equivalences coincide. On the other hand, we show that if no constraint is put on the way real numbers are manipulated, characterizing contextual equivalence turns out to be hard, and most of the aforementioned notions of equivalence are even unsound.