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Deduction modulo is a theoretical framework for reasoning modulo a congruence on propositions. Computational steps are thus removed from proofs, thus allowing a clean separatation of computational and deductive steps. A sequent calculus modulo has been defined in (Dowek et al., 2003) as well as a resolution-based proof search method, in which the… (More)

We present Zenon, an automated theorem prover for first order classical logic (with equality), based on the tableau method. Zenon is intended to be the dedicated prover of the Focal environment, an object-oriented algebraic specification and proof system, which is able to produce OCaml code for execution and Coq code for certification. Zenon can directly… (More)

Deduction modulo is a theoretical framework designed to introduce computational steps in deductive systems. This approach is well suited to automated theorem proving and a tableau method for first-order classical deduction modulo has been developed. We reformulate this method and give an (almost constructive) semantic completeness proof. This new proof… (More)

- Pascal Cuoq, Julien Signoles, Patrick Baudin, Richard Bonichon, Géraud Canet, Loïc Correnson +3 others
- ICFP
- 2009

This experience report describes the choice of OCaml as the implementation language for Frama-C, a framework for the static analysis of C programs. OCaml became the implementation language for Frama-C because it is expressive. Most of the reasons listed in the remaining of this article are secondary reasons, features which are not specific to OCaml… (More)

Deduction modulo is a theoretical framework which allows the introduction of computational steps in deductive systems. This approach is well suited to automated theorem proving. We describe a proof-search method based upon tableaux for Gentzen's intuitionistic LJ extended with rewrite rules on propositions and terms. We prove its completeness with respect… (More)

In the power generation industry, digital control systems may play an important role in plant safety. Thus, these systems are the object of rigorous analyzes and safety assessments. In particular, the quality , correctness and dependability of control systems software need to be justified. This paper reports on the development of a tool-based methodology to… (More)

We prove the syntactic soundness of classical tableaux with free variables and on-the-fly Skolemization. Soundness proofs are usually built from semantic arguments, and this is to our knowledge, the first proof that appeals to syntactic means. We actually prove the soundness property with respect to cut-free sequent calculus. This requires great care… (More)

This paper describes two syntactic extensions to Smt-Lib scripts: lambda-expressions and poly-morphism. After extending the syntax to allow these expressions, we show how to update the typing rules of the Smt-Lib to check the validity of these new terms and commands. Since most Smt-solvers only deal with many-sorted first-order formulas, we detail a… (More)

This article describes an efficient persistent mergeable data structure for mapping intervals to values. We call this data structure rangemap. We provide an example of application where the need for such a data structure arises (abstract interpretation of programs with pointer casts). We detail different solutions we have considered and dismissed before… (More)