We propose a new tactic language for the system goq, which is intended to enrich the current tactic combinators (tacticals). This language is based on a functional core with recursors and matching operators for goq terms but also for proof contexts. It can be used directly in proof scripts or in toplevel denitions (tactic denitions). We show that the implementation of this language involves considerable changes in the interpretation of proof scripts, essentially due to the matching operators. We give some examples which solve small proof parts locally and some others which deal with non-trivial problems. Finally, we discuss the status of this metalanguage with respect to the goq language and the implementation language of goq. hvidFhelhyedinriFfr, httpXGGoqFinriFfrG£delhyeG.
Abstract. We propose an extension of the tableau-based first order automated theorem prover Zenon to deduction modulo. The theory of deduction modulo is an extension of predicate calculus, which allows us to rewrite terms as well as propositions, and which is well suited for proof search in axiomatic theories, as it turns axioms into rewrite rules. We also present a heuristic to perform this latter step automatically, and assess our approach by providing some experimental results obtained on the benchmarks provided by the TPTP library, where this heuristic is able to prove difficult problems in set theory in particular. Finally, we describe an additional backend for Zenon that outputs proof certificates for Dedukti, which is a proof checker based on the λΠ-calculus modulo.
We introduce an encoding of the set theory of the B method using polymorphic types and deduction modulo, which is used for the automated verification of proof obligations in the framework of the BWare project. Deduction modulo is an extension of predicate calculus with rewriting both on terms and propositions. It is well suited for proof search in theories because it turns many axioms into rewrite rules. We also present the associated automated theorem prover Zenon Modulo, an extension of Zenon to polymorphic types and deduction modulo, along with its backend to the Dedukti universal proof checker, which also relies on types and deduction modulo, and which allows us to verify the proofs produced by Zenon Modulo. Finally, we assess our approach over the proof obligation benchmark provided by the BWare project.
We introduce BWare, an industrial research project that aims to provide a mechanized framework to support the automated verification of proof obligations coming from the development of industrial applications using the B method and requiring high integrity. The adopted methodology consists in building a generic verification platform relying on different automated theorem provers, such as first order provers and SMT (Satisfiability Modulo Theories) solvers. Beyond the multi-tool aspect of our methodology, the originality of this project also resides in the requirement for the verification tools to produce proof objects, which are to be checked independently. In this paper, we present some preliminary results of BWare, as well as some current major lines of work.
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