The team investigates applications of recent results in proof theory to the design of proof-checkers and automated theorem proving systems. It develops the Dedukti proof-checker and the iProver modulo and Zenon modulo automated theorem proving systems.

*Deduction modulo* is a formulation of predicate logic
where deduction is performed modulo an equivalence relation defined on
propositions. A typical example is the equivalence relation relating
propositions differing only by a re-arrangement of brackets around
additions, relating, for instance, the propositions *purely computational*.

Deduction modulo was proposed at the end of the 20th century as a tool to simplify the completeness proof of equational resolution. Soon, it was noticed that this idea was also present in other areas of logic, such as Martin-Löf's type theory, where the equivalence relation is definitional equality, Prawitz' extended natural deduction, etc. More generally, Deduction modulo gives an account on the way reasoning and computation are articulated in a formal proof, a topic slightly neglected by logic, but of prime importance when proofs are computerized.

The early research on Deduction modulo focused on the design of general proof search methods—Resolution modulo, tableaux modulo, etc.—that could be applied to any theory formulated in Deduction modulo, to general proof normalization and cut elimination results, to the definitions of models taking the difference between reasoning and computation into account, and to the definition of specific theories—simple type theory, arithmetic, some versions of set theory, etc.—as purely computational theories.

A new turn with Deduction modulo was taken when the idea of reasoning modulo an
arbitrary equivalence relation was applied to typed

This led to the development of a general proof-checker based on the

Dedukti proofs can also be exported to other systems, in particular to the MMT format .

A thesis, which is at the root of our research effort,
and which was already formulated by the team of the Logical Framework
is that
proof-checkers should be theory independent. This is for instance
expressed in the title of our invited talk at Icalp 2012: *A
theory independent Curry-De Bruijn-Howard correspondence*.

Using a single prover to check proofs coming from different provers naturally led to investigate how these proofs could interact one with another. This issue is of prime importance because developments in proof systems are getting bigger and, unlike other communities in computer science, the proof-checking community has given little effort in the direction of standardization and interoperability. On a longer term we believe that, for each proof, we should be able to identify the systems in which it can be expressed.

Deduction modulo has originally been proposed to solve a problem in
automated theorem proving and some of the early work in this area
focused on the design of an automated theorem proving method called
*Resolution modulo*, but this method was so complex that it was
never implemented. This method was simplified in 2010
and it could
then be implemented. This implementation that builds on the
iProver effort is called iProver modulo.

iProver modulo gave surprisingly good results , so
that we use it now to search for proofs in many areas: in the theory
of classes—also known as *B* set theory—, on finite
structures, etc. Similar ideas have also been implemented for the
tableau method with in particular several extensions of the *Zenon*
automated theorem prover. More precisely, two extensions have been
realized: the first one is called *Super Zenon* and is an
extension to superdeduction (which is a variant of Deduction modulo), and
the second one is called
*Zenon Modulo* , and is an
extension to Deduction modulo. Both extensions have been extensively
tested over first order problems (of the TPTP library), and also
provide good results in terms of number of proved problems. In
particular, these tools provide good performances in set theory, so
that *Super Zenon* has been successfully applied to verify *B* proof
rules of *Atelier B* (work in collaboration with
*Siemens*). Similarly, we plan to apply *Zenon Modulo* in the framework of
the *BWare* project to verify *B* proof obligations coming from
the modeling of industrial applications.

More generally, we believe that proof-checking and automated theorem proving have a lot to learn from each other, because a proof is both a static linguistic object justifying the truth of a proposition and a dynamic process of proving this proposition.

The idea of Deduction modulo is that computation plays a major role in the foundations of mathematics. This led us to investigate the role played by computation in other sciences, in particular in physics. Some of this work can be seen as a continuation of Gandy's on the fact that the physical Church-Turing thesis is a consequence of three principles of physics, two well-known: the homogeneity of space and time, and the existence of a bound on the velocity of information, and one more speculative: the existence of a bound on the density of information.

This led us to develop physically oriented models of computations.

In parallel with this effort in logic and in the development of proof checkers and automated theorem proving systems, we always have been interested in using such tools. One of our favorite application domain is the safety of aerospace systems. Together with César Muñoz' team in Nasa-Langley, we have proved the correctness of several geometric algorithms used in air traffic control.

This has led us sometimes to develop such algorithms ourselves, and sometimes to develop tools for automating these proofs.

Set theory appears to be an appropriate
theory for automated theorem provers based on Deduction modulo, in
particular the several extensions of *Zenon* (*Super Zenon* and
*Zenon Modulo*). Modeling techniques using set theory are therefore good
candidates to assess these tools. This is what we have done with the
*B* method whose formalism relies on set theory. A collaboration
with *Siemens* has been developed
to automatically verify the *B*
proof rules of *Atelier B* . From this work
presented in the Doctoral dissertation of Mélanie Jacquel,
the
*Super Zenon*
tool has been designed
in order to be able to reason modulo the *B* set theory. As a sequel of
this work, we contribute to the *BWare* project whose aim is to provide a
mechanized framework to support the automated verification of *B*
proof obligations coming from the development of industrial
applications. In this context, we have recently designed
*Zenon Modulo* ,
(Pierre Halmagrand's PhD thesis, which has started on October 2013) to
deal with the *B* set theory. In this work, the idea is to
manually transform the *B* set theory into a theory modulo and
provide it to *Zenon Modulo* in order to verify the proof obligations of the
*BWare* project.

Termination is an important property to verify, especially in critical applications. Automated termination provers use more and more complex theoretical results and external tools (e.g. sophisticated SAT solvers) that make their results not fully trustable and very difficult to check. To overcome this problem, a language for termination certificates, called CPF, has been developed since several years now. Deducteam develops a formally certified tool, Rainbow, based on the Coq library CoLoR, that is able to automatically verify the correctness of such termination certificates.

Dedukti is a
proof-checker for the

Dedukti's core is based on the standard algorithm for type-checking semi-full pure type systems and implements a state-of-the-art reduction machine inspired from Matita's and modified to deal with rewrite rules.

Dedukti's input language features term declarations and definitions (opaque or not) and rewrite rule definitions. A basic module system allows the user to organize its project in different files and compile them separately.

Dedukti now features matching modulo beta for a large class of patterns called Miller's patterns, allowing for more rewriting rules to be implemented in Dedukti.

Dedukti has been developed by Mathieu Boespflug, Olivier Hermant, Quentin Carbonneaux and Ronan Saillard. It is composed of about 2500 lines of OCaml.

Dedukti comes with four companion tools: Holide, an embedding of HOL
proofs through the OpenTheory format , Coqine, an embedding of Coq
proofs, Focalide, an embedding of FoCaLiZe certified programs,
and Sigmaid, a type-checker for the simply-typed

A preliminary version of Coqine supports the following features of Coq: the raw Calculus of Constructions, inductive types, and fixpoint deﬁnitions. Coqine is currently being rewritten to support universes. Coqine has been developed by Mathieu Boespﬂug, Guillaume Burel, and Ali Assaf.

Holide supports all the features of HOL, including ML-polymorphism, constant deﬁnitions, and type deﬁnitions. It is able to translate all of the OpenTheory standard theory library. Holide has been developed by Ali Assaf.

Focalide has been improved to support FoCaLiZe proofs found by Zenon using the Dedukti backend for Zenon developped by Frédéric Gilbert. This backend has been improved by a simple typing mechanism in order to work with Focalide. Focalide has also been updated again to work with the latest version of FoCaLiZe.

Sigmaid implements a shallow embedding of the simply-typed

Focalide and Sigmaid have been developed by Raphaël Cauderlier.

Translators from Version 2.0 of the SMT-LIB standard and from the SMT-solver veriT have been initiated. They are currently developed by Frédéric Gilbert.

iProver Modulo is an extension of the automated theorem prover iProver originally developed by Konstantin Korovin at the University of Manchester. It implements Ordered polarized resolution modulo, a refinement of the Resolution method based on Deduction modulo. It takes as input a proposition in predicate logic and a clausal rewriting system defining the theory in which the formula has to be proved. Normalization with respect to the term rewriting rules is performed very efficiently through translation into OCaml code, compilation and dynamic linking. Experiments have shown that Ordered polarized resolution modulo dramatically improves proof search compared to using raw axioms. iProver modulo is also able to produce proofs that can be checked by Dedukti, therefore improving confidence. iProver modulo is written in OCaml, it consists of 1,200 lines of code added to the original iProver.

A tool that transforms axiomatic theories into polarized rewriting systems, thus making them usable in iProver Modulo, has also been developed. Autotheo supports several strategies to orient the axioms, some of them being proved to be complete, in the sense that Ordered polarized resolution modulo the resulting systems is refutationally complete, some others being merely heuristics. In practice, autotheo takes a TPTP input file and transforms the axioms into rewriting rules, and produces an input file for iProver Modulo.

iProver Modulo and autotheo have been developed by Guillaume Burel. iProver Modulo is released under a GPL license.

Several extensions of the *Zenon* automated theorem prover (developed
by Damien Doligez at *Inria* in the *Gallium* team) to Deduction
modulo have been studied. These extensions intend to be applied in the
context of the automatic verification of proof rules and obligations
coming from industrial applications formalized using the *B*
method.

The first extension, developed by Mélanie Jacquel and David Delahaye,
is called *Super Zenon*
and is an extension of *Zenon* to superdeduction, which can be seen
as a variant of Deduction modulo. This extension is a generalization
of previous experiments together with
Catherine Dubois and Karim Berkani (*Siemens*), where *Zenon* has
been used and extended to superdeduction to deal with the *B* set
theory and automatically prove proof rules of *Atelier B*. This
generalization consists in allowing us to apply the extension of
*Zenon* to superdeduction to any first order theory by means of a
heuristic that automatically transforms axioms of the theory into
rewrite rules. This work is described
in , which also
proposes a study of the possibility of recovering intuition from
automated proofs using superdeduction.

The second extension, developed by Pierre Halmagrand, David Delahaye,
Damien Doligez, and Olivier Hermant, is called *Zenon Modulo* and is an
extension of *Zenon* to Deduction modulo. Compared to *Super Zenon*, this
extension allows us to deal with rewrite rules both over propositions
and terms. Like *Super Zenon*, *Zenon Modulo* is able to deal with any first order
theory by means of a similar heuristic. To assess the approach of
*Zenon Modulo*, we have applied this extension to the first order problems
coming from the TPTP library. An increase of the number of proved
problems has been observed, with in particular a significant increase
in the category of set theory. Over these problems of the TPTP
library, we have also observed a significant proof size reduction,
which confirms this aspect of Deduction modulo. These results are
gathered into two
publications , .

The third extension, developed by Guillaume Bury and David Delahaye,
is an extension of *Zenon* to (rational and integer) linear
arithmetic (using the simplex algorithm), that has been integrated
to *Zenon Modulo* by Guillaume Bury and Pierre Halmagrand, in order to be
applied in the framework of the *B* set theory to the
verification of proof obligations of
*Atelier B* . Experiments have been
conducted over the benchmarks of the *BWare* project, and it turns
out that more than 95% of the proof obligations are proved thanks
to this extension.

Zipperposition is an implementation of the superposition method; it relies on the library Logtk for basic logic data structures and algorithms. Zipperposition is designed as a testbed for extensions to superposition, and can currently deal with polymorphic typed logic, integer arithmetic, and total orderings; an extension to handle structural induction is being worked on by Simon Cruanes.

Those pieces of software also depend on many smaller tools and libraries developped by Simon Cruanes in OCaml. In particular, efficient iterators were key to implementing arithmetic rules successfully, and a lightweight extension to the standard library has been developped steadily and released regularly.

CoLoR is a Coq library on rewriting theory and termination of more than 83,000 lines of code . It provides definitions and theorems for:

Mathematical structures: relations, (ordered) semi-rings.

Data structures: lists, vectors, polynomials with multiple variables, finite multisets, matrices, finite graphs.

Term structures: strings, algebraic terms with symbols of fixed arity,
algebraic terms with varyadic symbols, pure and simply typed

Transformation techniques: conversion from strings to algebraic terms, conversion from algebraic to varyadic terms, arguments filtering, rule elimination, dependency pairs, dependency graph decomposition, semantic labelling.

Termination criteria: polynomial interpretations, multiset ordering, lexicographic ordering, first and higher order recursive path ordering, matrix interpretations.

CoLoR is distributed under the CeCILL license. It is currently developed by Frédéric Blanqui and Kim-Quyen Ly, but various people participated to its development since 2006 (see the website for more information).

HOT is an automated termination prover for higher-order rewrite systems based on the notion of computability closure and size annotation . It won the 2012 competition in the category “higher-order rewriting union beta”. The sources (5000 lines of OCaml) are not public. It is developed by Frédéric Blanqui.

Moca is a construction functions generator for OCaml data types with invariants.

It allows the high-level definition and automatic management of complex invariants for data types. In addition, it provides the automatic generation of maximally shared values, independently or in conjunction with the declared invariants.

A relational data type is a concrete data type that declares invariants or relations that are verified by its constructors. For each relational data type definition, Moca compiles a set of construction functions that implements the declared relations.

Moca supports two kinds of relations:

predefined algebraic relations (such as associativity or commutativity of a binary constructor),

user-defined rewrite rules that map some pattern of constructors and variables to some arbitrary user's define expression.

The properties that user-defined rules should satisfy (completeness, termination, and confluence of the resulting term rewriting system) must be verified by a programmer's proof before compilation. For the predefined relations, Moca generates construction functions that allow each equivalence class to be uniquely represented by their canonical value.

Moca is distributed under QPL. It is written in OCaml (14,000 lines) It is developed by Frédéric Blanqui, Pierre Weis (EPI Pomdapi) and Richard Bonichon (CEA).

Rainbow is a set of tools for automatically verifying the correctness of termination certificates expressed in the CPF format used in the termination competition. It contains:

a tool `xsd2coq` for generating Coq data types for
representing XML files valid wrt some XML Schema,

a tool `xsd2ml` for generating OCaml data types and
functions for parsing XML files valid wrt some XML Schema,

a tool for translating a CPF file into a Coq script,

a standalone Coq certified tool for verifying the correctness of a CPF file.

Rainbow is distributed under the CeCILL license. It is developed in OCaml (10,000 lines) and Coq (19,000 lines). It is currently developed by Frédéric Blanqui and Kim-Quyen Ly. See the website for more information.

mSAT is a modular, proof-producing, SAT and SMT core based on Alt-Ergo Zero, written in OCaml. The solver accepts user-defined terms, formulas and theory, making it a good tool for experimenting. This tool produces resolution proofs as trees in which the leaves are user-defined proof of lemmas.

An encoding of tableaux rules as a theory for SMT solvers has been implemented and tested in mSAT. mSat has also been extended to implement model constructing satisfiability calculus, a variant of SMT solvers in which assignment of variables to values are propagated along with the usual boolean assignment of litterals.

In the framework of the *BWare* project, Pierre Halmagrand,
David Delahaye, Damien Doligez, and Olivier Hermant designed a new
version of the *B* set theory using deduction modulo, in order
to automatically verify a large part of the proof obligations of the
benchmark of *BWare*, which consists of proof obligations coming
from the modeling of industrial applications (about 13,000 proof
obligations). Using this *B* set theory modulo with *Zenon Modulo*, as
well as some other extensions of *Zenon*, such as typed proof
search and arithmetic (implemented by Guillaume Bury), we are able
to automatically verify more than 95% of the proof obligations of
*BWare*, while the regular version of *Zenon* is only able to
prove less than 1% of these proof obligations. This is a real
breakthrough for the *BWare* project, but also for automated
deduction in general, as it tends to show that deduction modulo is
the way to go when reasoning modulo theories.

Frédéric Blanqui, together with Jean-Pierre Jouannaud (Univ. Paris
11) and Albert Rubio (Technical University of Catalonia), have
finished their work on a new version of the higher-order recursive
path ordering (HORPO) , , a
decidable monotone well-founded relation that can be used for
proving the termination of higher-order rewrite systems by checking
that rules are included in it. This new version, called the
computability path ordering (CPO), appears to be the ultimate
improvement of HORPO in the sense that this definition captures the
essence of computability arguments *à la* Tait and Girard
, therefore explaining the name of the
improved ordering. It has been shown that CPO allows to consider
higher-order rewrite rules in a simple type discipline with
inductive types, that most of the guards present in the recursive
calls of its core definition cannot be relaxed in any natural way
without losing well-foundedness, and that the precedence on function
symbols cannot be made more liberal anymore. This new result is
described in a 41-pages papers available on Frédéric Blanqui's web
page which has been submitted to a journal for publication. A Prolog
implementation of CPO is also available on Albert Rubio's web page.

Frédéric Blanqui revised his work on the compatibility of Tait and
Girard's notion of computability for proving the termination of
higher-order rewrite systems when matching is done modulo

Frédéric Blanqui did some historical investigations on fixpoint theorems in posets used for instance for defining the semantics of non-basic inductive types (i.e. types with constructors taking functions as arguments) and the termination of functions defined by induction on such non-basic inductive types. These theorems assume the function either extensive or monotone. However, as shown by Salinas in , these two conditions can be subsumed by a more general one. Frédéric Blanqui slightly improved this condition further by using results by Hartogs, Rubin and Rubin, and Abian and Brown. This work is described in a 10-pages note available on his web page .

Kim Quyen Ly finished the development of a new version faster, safer (proved correct in Coq) and standalone version of Rainbow, based on Coq extraction mechanism. She defended her PhD thesis on the automated verification of termination certificates in October.

Ali Assaf defined a sound and complete embedding of the cumulative universe
hierarchy of the *calculus of inductive constructions* (CIC) in the

Frédéric Gilbert and Olivier Hermant defined new encodings from classical
to intuitionistic first-order logic. These encodings, based on the
introduction of double negations in formulas, are tuned to satisfy two purposes jointly:
basing their specifications on the definition of *classical connectives*
inside intuitionistic logic – which is the property of *morphisms*,
and reducing their impact on the shape and size of formulas,
by limiting as much as possible the number of negations
introduced. This paper has been submitted.

Raphael Cauderlier and Catherine Dubois defined a shallow embedding
of an object calculus (formalized by Abadi and
Cardelli), in the

Ali Assaf, Olivier Hermant and Ronan Saillard defined a rewrite system such that all strongly normalizable proof term can be typed in Natural Deduction modulo this rewrite system. This work is inspired by Statman's work , and can be understood as an encoding of intersection types.

Guillaume Burel showed how to get rewriting systems that admit cut
by using standard saturation techniques from automated theorem
proving, namely ordered resolution with selection, and
superposition. This work relies on a view of proposition rewriting
rules as oriented clauses, like term rewriting rules can be seen as
oriented equations. This also lead to introduce an extension of
deduction modulo with *conditional* term rewriting rules. This
work was presented at the RTA-TLCA conference in
Vienna .

Gilles Dowek, has generalized the notion of super-consistency to the lambda-Pi-calculus modulo theory and proved this way the termination of the embedding of various formulations of Simple Type Theory and of the Calculus of Constructions in the Lambda-Pi calculs modulo theory.

Gilles Dowek and Alejandro Díaz-Caro have finished their work on the extension of Simply Typed Lambda-Calculus with Type Isomorphisms. This work has been presented at the Types meeting and recently accepted for publication in the Theoretical Computer Science journal .

Gilles Dowek and Ying Jiang have given a new proof of the decidability of reachability in alternating pushdown systems, based on a cut-elimination theorem.

Vaston Costa presented to the group a new structure to represent proofs through references rather than copy. The structure, called Mimp-graph, was initially developed for minimal propositional logic but the results have been extended to first-order logic. Mimp-graph preserves the ability to represent any Natural Deduction proof and its minimal formula representation is a key feature of the mimp-graph structure, it is easy to distinguish maximal formulas and an upper bound in the length of the reduction sequence to obtain a normal proof. Thus a normalization theorem can be proved by counting the number of maximal formulas in the original derivation. The strong normalization follow as a direct consequence of such normalization, since that any reduction decreases the corresponding measures of derivation complexity. Sharing for inference rules is performed during the process of construction of the graph. This feature is very important, since we intend to use this graph in automatic theorem provers.

Guillaume Bury defined a sound and complete extension of the tableaux method to handle linear arithmetic. The rules are based on a variant of the simplex algorithm for rational and real linear arithmetic, and a Branch&Bound algorithm for integer arithmetic.

Guillaume Bury defined an encoding of analytical tableaux rules as a theory for smt solvers. The theory acts like a lazy cnf conversion during the proof search and allows to integrate the cnf conversion into the resolution proof for unsatisfiable formulas. This work was implemented in mSAT.

Simon Cruanes added many improvements to Logtk, in particular a better algorithm to reduce formulas to Clausal Normal Form. A presentation of its design and implementation has been made at PAAR 2014. He also used Zipperposition as a testbed for integer linear arithmetic; a sophisticated inference system for this fragment of arithmetic was designed and implemented in Zipperposition, including many redundancy criteria and simplification rules that make it efficient in practice. The arithmetic-enabled Zipperposition version entered CASC-J7, the annual competition of Automated Theorem Provers, in the first-order theorems with linear arithmetic division where it had very promising results (on integer problems only, since Zipperposition doesn't handle rationals).

Another extension of Zipperposition has been performed by Julien Rateau,
Simon Cruanes, and David Delahaye, in order to deal with a fragment of set
theory in the same vein as the *STR $\dot{+}$VE$\subseteq $* prover . This
extension relies on a specific normal form of literal, which only involves
the

The current effort of research on Zipperposition focuses on extending superposition to handle structural induction, following the work from . The current prototype is able to prove simple properties on natural numbers, binary trees and lists.

Kailiang Ji defined a set of rewrite rules for the equivalence between
CTL formulas (denote them as

Ali Assaf, Alejandro Díaz-Caro, Simon Perdrix, Christine Tasson, and Benoit
Valiron completed a journal paper covering results on different algebraic
extensions of the *algebraic
$\lambda $-calculus* and the

We are coordinators of the ANR-NFSC contract Locali with the Chinese Academy of Sciences.

We are members of the ANR *BWare*, which started on September 2012
(David Delahaye is the national leader of this project). The aim of
this project is to provide a mechanized framework to support the
automated verification of proof obligations coming from the
development of industrial applications using the *B* method. The
methodology used in this project consists in building a generic
platform of verification relying on different theorem provers, such as
first order provers and SMT solvers. We are in particular involved in
the introduction of Deduction modulo in the first order theorem
provers of the project, i.e. *Zenon* and *iProver*, as well as in
the backend for these provers with the use of *Dedukti*.

The ANR mid-term review of the project took place in October 2014 and the members of the project received very positive feedbacks from the reviewers. A more detailed report is expected from the reviewers in early 2015.

We are members of the ANR Tarmac on models of computation, coordinated by Pierre Valarcher.

Olivier Hermant was an invited researcher at the Natal University (UFRN, Brazil) in December 2014.

Catherine Dubois was a general chair of the GDR GPL national days, and the
AFADL'14, CAL'14, and CIEL'14 conferences, organized at *Cnam* in Paris.

David Delahaye was a member of the organizing committee of the GDR GPL
national days, and the AFADL'14, CAL'14, and CIEL'14 conferences,
organized at *Cnam* in Paris.

Olivier Hermant and Florian Rabe organized the 2nd KWARC-Deducteam workshop in Bremen, Germany (May 2014).

Gilles Dowek is a member of the steering committees of RTA and TLCA. Catherine Dubois is the chair of the steering committee of TAP.

Gilles Dowek has been the PC chair of RTA-TLCA.

David Delahaye and Catherine Dubois were co-chairs of the SETS'14 workshop (affiliated to ABZ'14).

David Delahaye was a co-chair of the

Catherine Dubois was a co-chair of the F-IDE'14 workshop (affiliated to ETAPS'14). She was also a PC co-chair of the AFADL'2014 national conference.

Olivier Hermant was member of the program committee of the RTA-TLCA 2014 conference (July 2014).

Frédéric Blanqui reviewed a paper submitted to the post-proceedings of TYPES'14.

Alejandro Díaz-Caro reviewed a paper submitted to the FSTTCS'14 conference.

Ronan Saillard reviewed a paper submitted to the RTA'14 conference.

David Delahaye is a member of the editorial board of the Global Journal of Advanced Software Engineering (GJASE).

David Delahaye reviewed one paper for the Global Journal of Advanced Software Engineering (GJASE) and one paper for the Requirements Engineering (RE) journal.

Alejandro Díaz-Caro reviewed a paper submitted to Elsevier's “Science of Computer Programming” journal.

Olivier Hermant reviewed a paper submitted to the journal “Theoretical Computer Science”.

CPGE: Simon Cruanes, Mathématiques-Informatiques en MPSI, 64 HETD, MPSI, Lycée Saint-Louis, France.

Licence : Raphaël Cauderlier, Eléments de programmation 2, 63 HETD, L1, UPMC, France.

License: Ali Assaf, Algorithmique et programmation, 36 HETD, L3, Ecole Polytechnique, France.

License: Ali Assaf, Les bases de la programmation et de l’algorithmique, 36 HETD, L3, Ecole Polytechnique, France.

Licence : Alejandro Díaz-Caro, Mathématiques 2, 18 HETD, L1, Université Paris-Ouest Nanterre La Défense, France.

Licence : Alejandro Díaz-Caro, Méthodologie de la mesure en sciences humaines, 48 HETD, L1, Université Paris-Ouest Nanterre La Défense, France.

Licence : Alejandro Díaz-Caro, Statistiques et probabilités, 18 HETD, L2, Université Paris-Ouest Nanterre La Défense, France.

Licence : Alejandro Díaz-Caro, Probabilités, 36 HETD, L2, Université Paris-Ouest Nanterre La Défense, France.

Licence : Alejandro Díaz-Caro, Probabilités, 36 HETD, L2, Université Paris-Ouest Nanterre La Défense, France.

Licence: Ronan Saillard, Programmation Orientée Objet en Java, 27 HETD, Telecom ParisTech, France.

Licence: Guillaume Burel, Programmation avancée, 25.5 HETD, L3, ENSIIE, France

Licence: Guillaume Burel, Logique, 10.5 HETD, L3, ENSIIE, France

Licence: Guillaume Burel, Projet informatique, 22.75 HETD, L3, ENSIIE, France

Master: Guillaume Burel, Systèmes et langages formels, 17.5 HETD, M1, ENSIIE, France

Master: Guillaume Burel, Compilation, 33.25 HETD, M1, ENSIIE, France

Licence: Guillaume Burel is in charge of the 4th, 5th, and 6th semesters of the engineering degree at ENSIIE.

Licence: Pierre Halmagrand, Initiation à la Programmation en JAVA, 48.75 HETD, L1, CNAM, France

Master: Pierre Halmagrand, Initiation à la Méthode B, 53.7 HETD, M2, CNAM, France

Master: Gilles Dowek has given invited classes at Supelec, Centrale, INSA-Lyon.

PhD : Kim-Quyen Ly, Automated verification of termination certificates , University Joseph Fourier, Grenoble, 9 October 2014, Jean-François Monin and Frédéric Blanqui.

PhD in progress : Ronan Saillard, Systèmes de Types Modulo, Oct 2012, Olivier Hermant and Pierre Jouvelot.

PhD in progress : Pierre Halmagrand, “Automated Deduction Modulo”, from Oct. 2013, David Delahaye, Olivier Hermant, and Damien Doligez.

PhD in progress : Guillaume Bury, “SMT Modulo”, Oct. 2014, David Delahaye.

PhD in progress : Ali Assaf, Interoperability of Proof Systems, Oct. 2012, Gilles Dowek and Guillaume Burel.

PhD in progress : Simon Cruanes, Automated reasoning modulo theories, August 2012, Gilles Dowek and Guillaume Burel.

PhD in progress : Kailiang Ji, Model Checking and Automated Theorem Proving, October 2012, Gilles Dowek.

David Delahaye reviewed the PhD thesis of Hernán Vanzetto, supervised by Stephan Merz and Kaustuv Chaudhuri, and defended in Dec. 2014 in Nancy.

David Delahaye was part of the HDR jury of Stéphane Lengrand, defended in Dec. 2014 at École Polytechnique in Palaiseau.

Gilles Dowek has been part of the HDR committee of Philippe Malbos.

Catherine Dubois reviewed the HDR thesis of Oum-El-Kheir Aktouf, defended in July 2014 in Valence.

Gilles Dowek is the president of the scientific board of the “Société Informatique de France” (SIF).

Gilles Dowek is a member of the scientific board of “La Main à la Pâte”.

Raphaël Cauderlier, Simon Cruanes, Pierre Halmagrand et Ronan Saillard ont participé à l'animation du stand Inria au Salon Culture et Jeux Mathématiques les 24 et 25 mai

Ali Asaf, Raphaël Cauderlier, Simon Cruanes et Pierre Halmagrand ont participé à l'animation du stand Inria lors de la Fête de la Science les 9 et 10 octobre 2014 à Paris

Gilles Dowek has given a talk at Mathenjeans.

Alejandro Díaz-Caro is member of the scientific board of “Ensemble”, a journal of the Maison Argentina at Cité Universitaire in Paris, ISSN 1852–5911.