Foundational (co)datatypes and (co)recursion for higher-order logic

We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction. In contrast with other systems offering codatatypes, no additional axioms or logic extensions are necessary with our approach

Semantic Foundations of Higher-Order Probabilistic Programs in Isabelle/HOL

Higher-order probabilistic programs are used to describe statistical models and machine-learning mechanisms. The programming languages for them are equipped with three features: higher-order functions, sampling, and conditioning. In this paper, we propose an Isabelle/HOL library for probabilistic programs supporting all of those three features. We extend our previous quasi-Borel theory library in Isabelle/HOL. As a basis of the theory, we formalize s-finite kernels, which is considered as a theoretical foundation of first-order probabilistic programs and a key to support conditioning of probabilistic programs. We also formalize the Borel isomorphism theorem which plays an important role in the quasi-Borel theory. Using them, we develop the s-finite measure monad on quasi-Borel spaces. Our extension enables us to describe higher-order probabilistic programs with conditioning directly as an Isabelle/HOL term whose type is that of morphisms between quasi-Borel spaces. We also implement the qbs prover for checking well-typedness of an Isabelle/HOL term as a morphism between quasi-Borel spaces. We demonstrate several verification examples of higher-order probabilistic programs with conditioning

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic

Journées Francophones des Langages Applicatifs 2018

National audienceLes 29èmes journées francophones des langages applicatifs (JFLA) se déroulent en 2018 à l'observatoire océanographique de Banyuls-sur-Mer. Les JFLA réunissent chaque année, dans un cadre convivial, concepteurs, développeurs et utilisateurs des langages fonctionnels, des assistants de preuve et des outils de vérification de programmes en présentant des travaux variés, allant des aspects les plus théoriques aux applications industrielles.Cette année, nous avons sélectionné 9 articles de recherche et 8 articles courts. Les thématiques sont variées : preuve formelle, vérification de programmes, modèle mémoire, langages de programmation, mais aussi théorie de l'homotopieet blockchain