David Delahaye

Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM) | LIRMM · Informatics Department

We discuss the practical results obtained by the first generation of automated theorem provers based on Deduction modulo theory. In particular, we demonstrate the concrete improvements such a framework can bring to first-order theorem provers with the introduction of a rewrite feature. Deduction modulo theory is an extension of predicate calculus w...

Software product line engineering is a reuse-driven paradigm for developing families of similar products from a generic product backbone with identified options. A customised product is then derived by combining the artefacts implementing the backbone with the ones implementing the chosen options. Variability analysis and representation is a centra...

We propose an automation-friendly set theory for the B method. This theory is expressed using first order logic extended to polymorphic types and rewriting. Rewriting is introduced along the lines of deduction modulo theory, where axioms are turned into rewrite rules over both propositions and terms. We also provide experimental results of several...

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...

We propose an extension of a tableau-based calculus to deal with linear arithmetic. This extension consists of a smooth integration of arithmetic deductive rules to the basic tableau rules, so that there is a natural interleaving between arithmetic and regular analytic rules. The arithmetic rules rely on the general simplex algorithm to compute sol...

We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and uses the principles of superdeduction, among which the theory is used to enrich the deduction system with new de...

Proceedings of the first workshop about Sets and Tools, SETS 2014, affiliated to ABZ 2014

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 diff...

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 p...

We present the certifying part of the Zenon Modulo automated theorem prover, which is an extension of the Zenon tableau-based first order automated theorem prover 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 sea...

This talk is about several experiments of automated deduction with 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. In particular, we present two ext...

Proof assistants based on type theory allow the user to adopt either a functional style, or a relational style (e.g., by using inductive types). Both styles have pros and cons. Relational style may be preferred because it allows the user to describe only what is true, discard momentarily the termination question, and stick to a rule-based descripti...

We propose a method which allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to p...

We propose a formal and mechanized framework which consists in verifying proof rules of the B method, which cannot be automatically proved by the elementary prover of Atelier B and using an external automated theorem prover called Zenon. This framework contains in particular a set of tools, named BCARe and developed by Siemens IC-MOL, which relies...

egalement g en er ee en Focalize. ABSTRACT. We propose a method of generation of functional code from inductive specications in the framework of the Focalize environment. This method consists of

We present the formalization of regulations intended to ensure airport security in the framework of civil aviation. In particular, we describe the formal models of two standards, one at the international level and the other at the European level. These models are expressed using the Focal environment, which is an object-oriented specification and p...

We introduce the Focal environment, which is an integrated development environment, offering functional and object-oriented features, and designed to build certified components using theorem proving. In Focal, inheritance provides a suit-able notion of refinement, allowing us to go step by step (in an incremental approach) from abstract specificati...

This paper describes the Integrated Development Environ- ment Focal together with a brief proof of usability on the formal devel- opment of access control policies. Focal is an IDE providing powerful functional and object-oriented features that allow to formally express specification and to go step by step (in an incremental approach) to design and...

We present the formalization of regulations intended to ensure airport security in the framework of civil aviation. In particular, we describe the formal models of two standards, one at the international level and the other at the European level. These models are expressed using the Focal environment, which is an object-oriented specification and p...

We propose an automatic transformation of focal specifications to UML class diagrams. The main motivation for this work lies within the framework of the EDEMOI project, which aims to integrate and apply several requirements engineering and formal methods techniques to analyze regulations in the domain of airport security. The idea is to provide a g...

We propose an automatic transformation of Focal specifications to UML class diagrams. The main motivation for this work lies within the framework of the EDEMOI project, which aims to integrate and apply several requirements engineering and formal methods techniques to analyze airport security regulations. The idea is to provide a graphical document...

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 di...

We propose a method to extract purely functional contents from logical inductive types in the context of the Calculus of Inductive Constructions. This method is based on a mode consistency analysis, which verifies if a computation is possible w.r.t. the selected inputs/outputs, and the code generation itself. We prove that this extraction is sound...

We present the validation of regulations intended to ensure airport security in the framework of civil aviation. In particular, we describe the proofs of correctness/completeness for two standards, one at the international level and the other at the European level, and we show how the properties of the European level refines those of the internatio...

We present the formalization of regulations intended to ensure airport security in the framework of civil aviation. In particular, we describe the formal models of two standards, one at the international level and the other at the European level. These models are expressed using the Focal environment, which is also briefly presented. Focal is an ob...

We propose a decision procedure for algebraically closed fields based on a quantifier elimination method. The procedure is intended to build proofs for systems of polynomial equations and inequations. We describe how this procedure can be carried out in a proof assistant using a Computer Algebra system in a purely skeptical way. We present an imple...

We present the proof of Diophantus' 20th problem (book VI of Diophantus' Arithmetica), which consists in wondering if there exist right triangles whose sides may be measured as integers and whose surface may be a square. This problem was negatively solved by Fermat in the 17th century, who used the "wonderful" method (ipse dixit Fermat) of infinite...

Cet article presente l'emploi de l'outil d'aide a la preuve Coq aupres d'etudiants de DESS (3e cycle universitaire). D'abord, dans le cadre d'un cours de semantique des langages, Coq facilite l'appropriation par les etudiants de notions souvent jugees abstraites en leur permettant de les relier a des termes plus concrets. Ensuite, un projet informa...

We describe an interface between the Coq proof assistant and the Maple symbolic computation system, which mainly consists in importing, in Coq, Maple computations regarding algebraic expressions over fields. These can either be pure computations, which do not require any validation, or computations used during proofs, which must be proved (to be co...

We present the proof of Diophantus’ 20th problem (book VI of Diophantus’ Arithmetica), which consists in wondering if there exist right triangles whose sides may be measured as integers and whose surface may be a square. This problem was negatively solved by Fermat in the 17th century, who used the wonderful method (ipse dixit Fermat) of infinite d...

In this article, we present the use of the Coq proof assistant with DESS (Master thesis) students. First, in the framework of a course of programming language semantics, Coq greatly helps the students to understand formal and abstract notions, such as induction, by binding them to more concrete terms. Next, a computer science project shows that Coq...

We describe a proof dedicated meta-language, called tac, in the context of the Coq proof assistant. This new layer of meta-language is quite appropriate to write small and local automations. tac, is essentially a small functional core with recursors and powerful pattern-matching operators for Coq terms but also for proof contexts. As tac, is not co...

We propose a new proof language based on well-known existing styles such as procedural and declarative styles but also using terms as proofs, a specific feature of theorem provers based on the Curry-Howard isomorphism. We show that these three styles are really appropriate for specific domains and how it can be worth combining them to benefit from...

We describe a proof dedicated meta-language, called tac, in the context of the Coq proof assistant. This new layer of meta-language is quite appropriate to write small and local automations. tac, is essentially a small functional core with recursors and powerful pattern-matching operators for Coq terms but also for proof contexts. As tac, is not co...

We propose a new tactic language for the system Coq, which is intended to enrich the current tactic combinators (tacticals). This language is based on a functional core with recursors and matching operators for Coq terms but also for proof contexts. It can be used directly in proof scripts or in toplevel definitions (tactic definitions). We show th...

We propose a method to search for a lemma in a Coq proof library by using the lemma type as a key. The method is based on the concept of type isomorphism developed within the functional programming framework. We introduce a theory which is a generalization of the axiomatization for the simply typed γ-calculus (associated with Closed Cartesian Categ...

In this article, we present the use of the Coq proof assistant with DESS (Master thesis) students. First, in the framework of a course of programming language semantics, Coq greatly helps the students to understand formal and abstract notions, such as induction, by binding them to more concrete terms. Next, a computer science project shows that Coq...