2023Activity reportProject-TeamDEDUCTEAM

6.1.1 Lambdapi

• Keywords:
  Dependent types, Rewriting, Proof assistant
• Functional Description:

  Lambdapi is an interactive proof development system featuring dependent types like in Martin-Lőf’s type theory, but allowing to define objects and types using oriented equations, aka rewriting rules, and reason modulo those equations. This allows to simplify some proofs, and formalize complex mathematical objects that are otherwise impossible or difficult to formalize in more traditional proof systems.

  Lambdapi comes with Emacs and VSCode support.

  Lambdapi can also read and output Dedukti files, and can thus be used as an higher-level intermediate language for translating proofs from one system to Dedukti.

  Lambdapi is a logical framework and does not come with a pre-defined logic. However, it is easy to define a logic by declaring a few symbols and rules. A library of pre-defined logic is also provided.

  Here are some of the features of Lambdapi: - Emacs and VSCode plugins (based on LSP) - support for unicode (UTF-8) and user-defined infix operators - symbols can be declared commutative, or associative and commutative - some arguments can be declared as implicit: the system will try to find out their value automatically - symbol and rule declarations are separated so that one can easily define inductive-recursive types or turn a proved equation into a rewriting rule - support for interactive resolution of typing goals, and unification goals as well, using tactics - a rewrite tactic similar to the one of SSReflect in Coq - the possibility of calling external automated provers - a command is provided for automatically generating an induction principle for (mutually defined) strictly-positive inductive types - Lambdapi can call external provers for checking the confluence and termination of user-defined rewriting rules by translating them to the XTC and HRS formats used in the termination and confluence competitions

• URL:
  https://­github.­com/­Deducteam/­lambdapi
• Contact:
  Frederic Blanqui

6.1.2 Dedukti

• Keyword:
  Logical Framework
• Functional Description:

  Dedukti is a proof-checker for the LambdaPi-calculus modulo. As it can be parametrized by an arbitrary set of rewrite rules, defining an equivalence relation, this calculus can express many different theories. Dedukti has been created for this purpose: to allow the interoperability of different theories.

  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 his project in different files and compile them separately.

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

• URL:
  https://­deducteam.­github.­io/
• Publications:
  hal-01086609, hal-01176715, hal-01441751
• Contact:
  Francois Thire
• Participants:
  Francois Thire, Gaspard Ferey, Guillaume Genestier, Rodolphe Lepigre

6.1.3 personoj

• Keywords:
  PVS, Automated theorem proving, Dedukti, Machine translation
• Functional Description:
  Personoj comprises a set of PVS patches that may be used to export PVS specifications (propositions and definitions) or to export successive sequents of a proof to lambdapi. Another program is able to process these sequents and call automated theorem provers through Why3 to prove the implications of the successive sequents.
• Contact:
  Gabriel Hondet

6.1.4 Agda2Dedukti

• Keywords:
  Compilation, Proof assistant, Higher-order logic, Rewriting systems
• Functional Description:
  Translation of Agda proofs to the Logical Framework Dedukti.
• URL:
  https://­github.­com/­Deducteam/­Agda2Dedukti
• Contact:
  Guillaume Genestier
• Partner:
  Chalmers University

6.1.5 Coqine

• Name:
  Coq In dEdukti
• Keywords:
  Higher-order logic, Formal methods, Proof
• Functional Description:
  CoqInE is a plugin for the Coq software translating Coq proofs into Dedukti terms. It provides a Dedukti signature file faithfully encoding the underlying theory of Coq (or a sufficiently large subset of it). Current development is mostly focused on implementing support for Coq universe polymorphism. The generated ouput is meant to be type-checkable using the latest version of Dedukti.
• URL:
  http://­www.­ensiie.­fr/­~guillaume.­burel/­blackandwhite_coqInE.­html.­en
• Contact:
  Guillaume Burel

6.1.6 Krajono

• Keyword:
  Proof
• Functional Description:
  Krajono translates Matita proofs into Dedukti[CiC] (encoding of CiC in Dedukti) terms.
• Contact:
  Francois Thire

6.1.7 Holide

• Keyword:
  Proof
• Functional Description:
  Holide translates HOL proofs to Dedukti[OT] proofs, using the OpenTheory standard (common to HOL Light and HOL4). Dedukti[OT] being the encoding of OpenTheory in Dedukti.
• URL:
  https://­github.­com/­Deducteam/­Holide
• Contact:
  Guillaume Burel

6.1.8 Logipedia

• Name:
  Logipedia
• Keywords:
  Formal methods, Web Services, Logical Framework
• Functional Description:

  Logipedia is composed of two distinct parts: 1) A back-end that translates proofs expressed in a theory encoded in Dedukti to other systems such as Coq, Lean or HOL 2) A front-end that prints these proofs in a "nice way" via a website. Using the website, the user can search for a definition or a theorem then, download the whole proof into the wanted system.

  Currently, the available systems are: Coq, Matita, Lean, PVS and OpenTheory. The proofs comes from a logic called STTForall.

  In the long run, more systems and more logic should be added.

• Release Contributions:
  This is the beta version of Logipedia. It implements the functionalities mentioned above.
• URL:
  http://­www.­logipedia.­science
• Contact:
  Francois Thire

6.1.9 nubo

• Name:
  Nubo
• Keywords:
  Interoperability, Proof
• Functional Description:
  Nubo is a repository of formal proofs for computer scientists and mathematicians. Nubo aims to leverage the interoperability issues raised by the substantial quantity of proof systems. To do so, it relies on a formalism in which many proofs of other systems can be stated. This formalism allows to translate formal developements to and fro foreign systems. Nubo stores, classifies and serves those formal developments expressed in this general formalism. As such, developers may exchange their proofs, whatever their favourite system is.
• URL:
  https://­github.­com/­Deducteam/­nubo
• Contact:
  Gabriel Hondet

6.1.10 Zenon Modulo

• Keywords:
  First-order logic, Automated theorem proving, Deduction Modulo
• Functional Description:
  Zenon Modulo is an extension of the automated theorem prover Zenon. Compared to Super Zenon, it can 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.
• URL:
  https://­github.­com/­Deducteam/­zenon_modulo
• Contact:
  Pierre Halmagrand

6.1.11 SKonverto

• Name:
  SKonverto
• Keywords:
  Skolemization, First-order logic, Proof assistant
• Functional Description:
  SKonverto is a tool that transforms Lambdapi proofs containing Skolem symbols into proofs without these symbols.
• URL:
  https://­github.­com/­Deducteam/­SKonverto
• Contact:
  Mohamed Yacine El Haddad

6.1.12 Predicativize

• Name:
  Predicativize
• Keywords:
  Dedukti, Proof assistant, Interoperability
• Functional Description:
  Predicativize is a tool allowing for the translation of proofs from a core impredicative type theory to a core predicative theory featuring universe polymorphism. It works by calculating constraints between universe levels, which are then solved using universe level unification, generating then a predicative universe polymorphic definition. The theory behind the tool is provided in the paper "Translating proofs from an impredicative type system to a predicative one", by Thiago Felicissimo, Frédéric Blanqui and Ashish Kumar Barnawal. Predicativize was used to translate Matita's arithmetic library to Agda.
• URL:
  https://­github.­com/­Deducteam/­predicativize
• Contact:
  Thiago Felicissimo Cesar

6.1.13 KaMeLo

• Name:
  KaMeLo
• Keywords:
  K Framework, Matching Logic, Semantics, Rewriting systems
• Functional Description:
  Translation of the K framework to the Logical Framework Dedukti. The input is written in Matching Logic.
• URL:
  https://­gitlab.­com/­semantiko/­kamelo
• Contact:
  Amelie Ledein

6.1.14 MM2DK

• Keywords:
  Metamath, Logical Framework
• Functional Description:
  Translation of the K framework to the Logical Framework Dedukti. The input is written in Matching Logic
• URL:
  https://­gitlab.­com/­semantiko/­mm2dk/­translator
• Contact:
  Amelie Ledein
• Participant:
  Elliot Butte

6.1.15 BiTTs

• Keywords:
  Dependent types, Logical Framework
• Functional Description:
  This is an implementation of the generic bidirectional typing algorithm presented in the paper "Generic bidirectional typing for dependent type theories".
• URL:
  https://­github.­com/­thiagofelicissimo/­BiTTs
• Contact:
  Thiago Felicissimo Cesar

6.1.16 pogtranslator

• Keywords:
  Formal methods, Proof
• Functional Description:
  Translator of Atelier B proof obligations (in the POG format) to the TPTP or SMT-LIB format.
• Contact:
  Claude Stolze

6.1.17 sniper

• Keywords:
  Coq, Automated deduction
• Functional Description:
  Sniper is a Coq plugin that improves its automation.
• URL:
  https://­github.­com/­smtcoq/­sniper
• Contact:
  Chantal Keller
• Partner:
  Université Paris-Saclay

6.1.18 hol2dk

• Keywords:
  Interoperability, Proof
• Functional Description:
  Tool making HOL-Light generate proofs, simplifying those proofs, and translating those proofs to Dedukti, Lambdapi and Coq.
• URL:
  https://­github.­com/­Deducteam/­hol2dk
• Contact:
  Frederic Blanqui

6.1.19 commutative-diagrams

• Name:
  Commutative diagrams proof assistant
• Keyword:
  Proof assistant
• Functional Description:
  A coq plugin enabling to progress categoretical proofs graphically. It can infer the diagram from the proof context, and display it graphically to the user. The user's action on the diagram are then converted into Coq proofs.
• URL:
  https://­github.­com/­dwarfmaster/­commutative-diagrams
• Contact:
  Luc Chabassier

6.1.20 dkpltact

• Keywords:
  Coq, Interoperability, Proof
• Functional Description:
  A tool to translate proofs from a Dedukti encoding of Predicate logic to the tactic language of Coq. It takes Dedukti files whose terms comply with this encoding and produces the corresponding Coq files.
• URL:
  https://­gitlab.­crans.­org/­geran/­dkpltact
• Contact:
  Yoan Geran

7.1.1 Lambdapi

Participants: Frédéric Blanqui.

Lambdapi has been improved and extended in various ways. The most notable novelties are:

• Lambdapi can now translate to Coq any Dedukti or Lambdapi files using a user-defined encoding of higher-order logic. Moreover, some Dedukti or Lambdapi symbol can be renamed or replaced by Coq expressions in order to align those symbols to the one already defined in the Coq standard library.
• Claudio Sacerdoti from the University of Bologna added commands for indexing constants, definitions and rewrite rules; searching such items matching some patterns and conditions; running a web server for answering such requests.

7.2.1 Confluence and levels

Participants: Corentin Chabanol, Jean-Pierre Jouannaud, Gilles Dowek.

In a dependently typed lambda calculus, subject reduction, confluence and termination are inter-dependent, which makes difficult to add dependently typed higher-order rewrite rules, as needed is some complex encodings. It then makes sense to check confluence in the untyped lambda-calculus. The case of left-linear rewrite rules is treated in 36: confluence is preserved by adding terminating rewrite rules whose critical pairs are joinable by Van Oostrom's decreasing diagrams. Unfortunately, the use of higher-order rewrite rules with non-linear left-hand sides destroys the confluence property of the untyped lambda-calculus, this is the case with very simple critical pair free rewrite rules like F(x) -> x. In 38, it is shown that confluence is preserved on a subset of layered terms, provided "nested critical pairs" are joinable by some "layer non-increasing" van Oostrom decreasing diagram. A yet open question is under which assumptions the set of layered terms contains all typable terms of interest, a property that happens to be true in some practical cases. In a yet unpublished work, we have described a way to layer even more terms by a simpler definition of layering which is at the same time more easily implementable, a first simple step towards a solution to this question.

7.2.2 Generic bidirectional typing for dependent type theories

Participants: Thiago Felicissimo, Frédéric Blanqui, Gilles Dowek.

Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be used. Bidirectional typing has been fruitfully studied and bidirectional systems have been developed for many type theories. However, the formal development of bidirectional typing has until now been kept confined to specific theories, with general guidelines remaining informal. In this work 28, we give a generic account of bidirectional typing for a general class of dependent type theories.

As a practical outcome, we obtain a theory-independent bidirectional typechecker that has been implemented in a prototype and used in practice with many theories. The use of bidirectionality allows in particular the omission of many type annotations, proividing a much more succint syntax when compared with fully-annotated presentations of type theory as available in logical frameworks. As a result, we expect our implementation to provide important performance gains when compared with Dedukti. This work has been accepted at ESOP 2024.

7.3.1 Universes

Participants: Yoan Géran, Rishikesh Vaishnav, Olivier Hermant, Gilles Dowek, Frédéric Blanqui.

The imax operator defined by $imax(x,0)=0$ and $imax(x,s(y)=max(x,s\left(y\right))$ is used to represent universes in impredicative theories. Yoan Géran has given a canonical form for the term of the $imax$-successor algebra, leading to a decision procedure for the equality and inequality problem in this algebra 29. Rishikesh Vaishnav implemented it in lean2dk (see below).

7.3.2 Set theory

Participants: Thomas Traversié, Valentin Blot, Gilles Dowek, Claude Stolze, Catherine Dubois, Olivier Hermant, Alessio Coltellacchi.

We are currently expressing two set-based specification formalisms used in industry, B and TLA+ and their proof tools. A translator, called pogtranslator, has been developed: it translates proof obligations generated by Atelier B expressed in the framework of the B set theory, into TPTP proof obligations, expressed in first-order logic.

TLAPS, the TLA+ proof system, is a proof assistant that mechanically checks TLA+ proofs by calling automatic provers such as veriT, cvc4, cvc5, or Zenon, on proof obligations. In collaboration with Stephan Merz (Loria), we are developing a ckecker for these proofs by reconstructing a proof term from a trace in the new Alethe proof format 34. The term produced uses the encoding of TLA+ in Dedukti as defined by Stephan Merz.

7.3.3 Cubical Type Theory

Participants: Nicolas Margulies, Bruno Barras.

During his internship supervised by Bruno Barras, Nicolas Margulies has integrated the various elements of an proof import procedure from Cubical to Dedukti. He has mainly worked on two components. Firstly, he has updated the encoding of Cubical Type Theory to follow the minor evolutions of this language. He also adapted the work of Luc Chabassier (translation from extensional to intensional type theory inside Dedukti), to translate Cubical proofs in their usual presentation into the encoding of Cubical Type Theory as a 2-level Type Theory. This adaptation appeared to be tedious but most of it has been implemented.

7.4.1 From Isabelle to Dedukti

Participants: Frédéric Blanqui.

In the framework of his PHC Sakura project, Frédéric Blanqui, together with Jérémy Dubut and Akihisa Yamada (AIST Tokyo, Japan) continued to improve isabelle_dedukti, the translator from Isabelle to Dedukti and Lambdapi. It is now possible to export most of the Isabelle/HOL standard library, as well as some libraries of the Archive of Formal Proofs (AFP). Frédéric Blanqui started also to work on the translation of the obtained Dedukti files to Coq.

7.4.2 From HOL-Light to Lambdapi and Coq

Participants: Frédéric Blanqui, Anthony Bordg.

hol2dk is a new software making HOL-Light to generate proofs, simplifying them, and translating them to Dedukti and Lambdapi, and in turn to Coq by using the new export feature of Lambdapi described above. To translate the proofs generated by HOL-Light, which can be quite big, it is necessary to simplify them, prune useless proofs and translate them in parallel. hol2dk can currently handle the whole base library of HOL-Light as well as some other libraries. Some further improvement is necessary to handle all the HOL-Light libraries. For the obtained Coq theorems to be usable, it is necessary to align the definitions of the types and functions of HOL-Light to those given in the Coq standard library. We did this for natural numbers and several common mathematical functions on natural numbers. The obtained Coq library is available in the Opam package coq-hol-light. Our goal is to make this alignement up to real numbers, so as to allow Coq users to import and reuse the large library of real analysis of HOL-Light to Coq.

7.4.3 From Lean to Dedukti

Participants: Rishikesh Vaishnav, Frédéric Blanqui.

For his PhD thesis started in March, Rishikesh Vaishnav started to write a framework implementation for translating Lean code to Dedukti (lean2dk) that reads in Lean code, elaborates, runs a translation function, and prints out the translated Dedukti code. He began the implementation of a Dedukti library for the encoding of Lean (generally following an interpretation of Lean as a Pure Type System). He added debugging utilities and various command line options to lean2dk control what code is translated from the input file, and wrote code to test the translation and various aspects of the rewrite systems. He worked with Yoan on the implemenation and theory of a rewrite system for deciding impredicative universe terms, and integrated this system into lean2dk. Finally, he implemented the translation of a number of features of Lean including universe impredicativity, let expressions, inductive types and recursors.

7.4.4 From impredicative to predicative type theory

Participants: Thiago Felicissimo, Frédéric Blanqui, Gilles Dowek.

As the development of formal proofs is a time-consuming task, it is important to devise ways of sharing the already written proofs to prevent wasting time redoing them. One of the challenges in this domain is to translate proofs written in proof assistants based on impredicative logics, such as Coq, Matita and the HOL family, to proof assistants based on predicative logics like Agda, whenever impredicativity is not used in an essential way.

In 2022, we proposed an algorithm to do such a translation between a core impredicative type system and a core predicative one allowing prenex universe polymorphism like in Agda. It was implemented in the tool Predicativize and then used to translate semi-automatically many non-trivial developments from Matita's arithmetic library to Agda, including Bertrand's Postulate and Fermat's Little Theorem, which were not available in Agda yet.

In 2023, this work has been published at the conference Computer Science Logic 2023 (CSL 23) 19. An extended version of this work is currently under submission for the special issue of CSL at Logical Methods in Computer Science  37.

7.4.5 From Predicate logic to the tactic language of Coq

Participants: Yoan Géran, Olivier Hermant, Gilles Dowek.

dkpltact is a software that translates proof from Predicate Logic, expressed in Dedukti, into the tactic language of Coq. Thus, it permits to obtain proof that are more readable and lighter than proof terms.

7.4.6 From the $𝕂$ Framework to Dedukti

Participants: Amélie Ledein, Valentin Blot, Catherine Dubois.

An encoding from $𝕂$ to Dedukti via Matching Logic using the $𝕂$ore language, in order to execute programs within Dedukti has been defined and implemented in the tool KaMeLo. We have contributed in particular to a paper formalization of the translation from $𝕂$ into $𝕂$ore 21. We also defined a partial shallow embedding of Matching Logic. The latter is used to check the proof objects generated by $𝕂$’s automatic prover in the particular case of program execution.

7.4.7 From Metamath to Dedukti

Participants: Amélie Ledein, Valentin Blot.

The Metamath formal language for specification of mathematical proofs, comes with a proof checker. A deep and a shallow embedding of Metamath into Dedukti have been defined. With an extended version of the deep encoding, all the proofs of the Metamath standard library have been translated into Dedukti and checked by it using the tool MM2DK  23.

7.4.8 From a variant of extensional type theory using ghost types

Participants: Théo Winterhalter.

We have developed a new version of extensional type theory where equality reflection is restricted to certain types so that the type theory still enjoys desirable properties like type constructor discrimination (the ability to distinguish, e.g. the type of natural numbers from a function type) and termination (although this last point remains a conjecture for now). We show that this theory is conservative over an intensional type theory, without having to rely on the usual axioms of function extensionality and uniqueness of indentity proofs.

We build this restriction by considering ghost dependent types. Values in a ghost type can be safely erased for computation (for instance at extraction), but are nevertheless distinguishable. They thus have a spot in-between propositions (whose proofs are all equal) and relevant data. In the type theory we consider, reflection is restricted to those ghost values. We have written a preprint 32 containing two translations, one from ghost extensional type theory to ghost type theory and one for ghost type theory to the usual intensional one with a universe of definitionally proof-irrelevant propositions (for instance that of Coq or Agda), showing consistency of the two theories.

7.4.9 From rewrite rules to axioms

Participants: Thomas Traversié, Valentin Blot, Gilles Dowek, Théo Winterhalter.

We studied 25 the possibility to transform proofs of the $\lambda \Pi$-calculus modulo rewriting so that we replace the use of user-defined rewrite rules by the use of equational axioms instead. This work has been published in Foundations of Software Science and Computation Structures 2024 (FoSSaCS 2024). This result paves the way for its implementation in Dedukti, that would allow one to get rid of rewrite rules used for one encoding of a theory in order to produce a proof in a different system without these rules.

7.5.1 Automation for the Coq proof assistant

Participants: Valentin Blot, Louise Dubois de Prisque, Chantal Keller.

In order to automatize the Coq proof assistant, Valentin Blot and Louise Dubois de Prisque, with the external collaboration of Chantal Keller, develop the Sniper plugin 17 (see 6.1.17).

The plugin contains:

• a library of fine-grained certifying logical transformations
• a tactic that combines these transformations in order to translate a subset of Coq goals into first-order logic, then calls external SMT solvers (through the SMTCoq plugin).

The use of modular and independent transformations allows incremental development. A rewriting of the orchestrator that combines them, in order to make the tactic more powerful and more efficient, is under progress.

7.5.2 Extensions of proof assistants with rewrite rules

Participants: Yann Leray, Théo Winterhalter.

We have started an implementation of user-defined rewrite rules in the Coq proof assistant, which, although still at an experimental stage, is waiting to be integrated in a coming official release. This practical was conducted in parallel to a formalisation of the meta-theory of Coq extended with rewrite rules as part of the MetaCoq project which contains a specification of Coq's type theory, theorems about its meta-theory and a certified implementation of type checker. This is still work in progress, but we identified a criterion to ensure confluence of whole system and proceeded with its formal proof of correctness.

7.5.3 Diller-Nahm bar recursion

Participants: Valentin Blot.

Valentin Blot described an interpretation of the double-negation shift (and hence of the classical axiom of countable choice and of second-order arithmetic) in the Diller-Nahm variant of the Dialectica interpretation 18. Using the Diller-Nahm variant allows in particular for non-decidable atomic formulas, and provides a naturally structured interpretation.

7.5.4 Quantum Computing

Participants: Gilles Dowek, Alejandro Díaz-Caro.

Alejandro Díaz-Caro and Gilles Dowek are investingting applications of proof-theory to the design of quantum progrmming languages. More precisely they try to understand in which way propositional logic must be extended or restricted in such a way that its proof-term language is a quantum programming language. First, their 2021 work on the extension of propostional logic with a non-harmonious connective "sup" (for "superposition") has been published in a journal. A linear restriction of this calculus has been presented in 2022. The final version of this paper has been published in a journal 13.

A new work has been started on new introduction rues for the disjunction, that allow a better elimination process for comuting cuts. The obtained calculus has some similarities with the sup-calculus. This work will be submitted for publication in 2024.

7.5.5 Category theory in Dedukti

Participants: Luc Chabassier, Bruno Barras.

Luc Chabassier and Bruno Barras have explored the potential of using dedukti powerful definitional equality to work around the complexities of the use of dependent types in category theory formalisations. Indeed, the intrisically dependent nature of category theory means any formalisation suffers from the drawbacks of dependent types. To work around that without going to a full extensional theory, they implemented some categories in dedukti such that the rewrite system of Dedukti perfectly captured the equality on morphisms of those categories. However, despite some success on simple categories, the approach failed to generalize to more complex categories.

7.5.6 Rewriting with graphs

Participants: Jean-Pierre Jouannaud.

Jean-Pierre Jouannaud and two external collaborators (Nachum Dershowitz, Tel Aviv University, and Fernando Orejas, Universitat Politecnica de Catalugna) have developed a new algebraic framework for rewriting term-graphs equiped with variables, seen as input ports, and roots, seen as output ports of some computation. Term-graphs are just graphs whose every vertex is labeled by a function symbol whose arity dictates the number of its outgoing edges. They describe an algorithm for unification and use it for deciding local confluence (hence confluence under a termination assumption) in 16. They have recently improved their framework and shown that it now encodes faithfully first-order term rewriting, which has been a long standing open problem only solved in particular cases so far 26. The next, ongoing step is the generalization of this framework to arbitrary graphs equiped with variables and roots, that is, whose number of outgoing edges at a given vertex can be arbitrary.

7.5.7 Ethics and logic

Participants: Gilles Dowek.

Gilles Dowek has published a paper 14 showing a paralelism between the notion of explanation used in ethics and the notion of cut used in logic.

9.1.1 Participation in other International Programs

9.2.1 Visits of international scientists

9.2.2 Visits to international teams

9.3.1 Other european programs/initiatives

Frédéric Blanqui is the chair of the COST action CA20111 EuroProofNet 2022-2025 which is a research network on proofs gathering more than 400 members from 43 different countries.

9.4.1 ICSPA

Participants: Guillaume Burel, Gilles Dowek, Catherine Dubois, Olivier Hermant, Claude Stolze.

The ANR project (2022-2025) ICSPA (Interoperable and Confident Set-based Proof Assistants) has been accepted in the context of the AAPG 2021 call. It is coordinated by Catherine Dubois and has the following academic partners Samovar – Inria Grand Est – Inria Paris-Saclay – LIRMM – IRIT with the industrial partner Clearsy. The project starts on January 1st 2022. This project aims at reinforcing the confidence in proofs carried out mechanically for the set-based specification formalisms B, Event-B, and TLA+ that are used in industry.This will be done by verifying these proofs formally and independently with the proof verifier Dedukti. The project also aims at designing and implementing an exchange framework, through which those three systems can share their proofs and theories, making them effectively interoperable.

9.4.2 PROGRAMme

Participants: Gilles Dowek.

The ANR PROGRAMme is an ANR for junior researcher Liesbeth Demol (CNRS, UMR 8163 STL, University Lille 3) to which G. Dowek participates. The subject is: “What is a program? Historical and Philosophical perspectives”. This project aims at developing the first coherent analysis and pluralistic understanding of “program” and its implications to theory and practice.

10.1.1 Scientific events: organisation

10.1.2 Scientific events: selection

10.1.3 Invited talks

Frédéric Blanqui gave an invited talk at the 16th Conference on Intelligent Computer Mathematics.

Frédéric Blanqui gave a talk at the annual meeting of the IFIP WG1.6 on rewriting.

10.1.4 Leadership within the scientific community

Frédéric Blanqui is member of the IFIP WG1.6 on rewriting.

10.1.5 Research administration

Frédéric Blanqui was elected member of the Evaluation committee of Inria until August 2023.

Frédéric Blanqui is member of the Scientific committee of Inria Saclay.

Frédéric Blanqui is the chair of the COST action CA20111 EuroProofNet 2022-2025 which is a research network on proofs gathering more than 400 members from 43 different countries.

Catherine Dubois is one of the two co-chairs of Groupement de Recherche Génie de la Programmation et du Logiciel (Gdr GPL).

10.2.1 Teaching

• Master: Frédéric Blanqui, formal languages, 21h, M1, ENSIIE, France
• Master: Frédéric Blanqui, rewriting theory, 14h, M1, ENS Paris-Saclay, France
• Master: Théo Winterhalter, Proof Assistants, 12h, M2, MPRI, France
• Master: Amélie Ledein, Software Engineering, 30h, M1, ENS Paris-Saclay, France
• License: Amélie Ledein, Compilation project, 15h, L3, ENS Paris-Saclay, France
• License: Amélie Ledein, Logic project, 22h30, L3, ENS Paris-Saclay, France
• License: Luc Chabassier, Logique, L3, 30h, ENS Paris-Saclay, France
• License: Luc Chabassier, Projet base de données, 22h30, L3, ENS Paris-Saclay, France
• License: Luc Chabassier, Architecture et système, 22h30, L3, ENS Paris-Saclay, France
• License: Nicolas Margulies, Compilation project, 15h, L3, ENS Paris-Saclay, France
• License: Nicolas Margulies, Architecture et système, 22h30, L3, ENS Paris-Saclay, France
• License: Yoan Géran, Compilation project, 15h, L3, ENS Paris-Saclay, France
• License: Yoan Géran, Projet Programmation, 30h, L3, ENS Paris-Saclay, France
• IUT: Luc Chabassier, C++ R101-2, première année, 38h30, IUT d'Orsay, France
• IUT: Luc Chabassier, Projet C++ S102, première année, 10h30, IUT d'Orsay, France
• IUT: Claude Stolze, C++ R101-2, première année, 33h, IUT d'Orsay, France
• Engineering school: Thomas Traversié, Algorithmique et complexité, 18h, first-year engineering school, CentraleSupélec, France
• Engineering school: Thomas Traversié, Modélisation logique - Langages et automates, 12h, third-year engineering school, CentraleSupélec, France

10.2.2 Supervision

• Valentin Blot and Chantal Keller are supervising the PhD of Louise Dubois de Prisque.
• Catherine Dubois and Valentin Blot are supervising the PhD of Amélie Ledein.
• Catherine Dubois and Burkhart Wolff are supervising the PhD of Benoit Ballenghien.
• Bruno Barras and Gilles Dowek are supervising the PhD of Luc Chabassier.
• Bruno Barras and Gilles Dowek are supervising the PhD of Nicolas Margulies.
• Frédéric Blanqui is supervising the PhD of Rishikesh Vaishnav.
• Frédéric Blanqui and Gilles Dowek are supervising the PhD of Thiago Felicissimo.
• Olivier Hermant and Gilles Dowek are supervising the PhD of Yoan Géran.
• Marc Aiguier and Gilles Dowek are supervising the PhD of Thomas Traversié.
• Stephan Merz and Gilles Dowek are supervising the PhD of Alessio Coltellacci.

10.2.3 Juries

• Catherine Dubois was the president of the jury for the PhD defence of Rosalie Defourné (Université de Lorraine), on 7 November 2023.
• Catherine Dubois was the president of the jury for the PhD defence of Wendlasida Ouédrago (Institut Polytechnique de Paris), on 15 September 2023.
• Théo Winterhalter was an examiner for the PhD defence of Enzo Crance (Nantes Université), 21 December 2023.
• Gilles Dowek was an examiner for the PhD defence of Julie Cailler, December 2023 (Université de Montpellier).

10.3.1 Education

Gilles Dowek has been appointed at the Conseil Supérieur des Programmes, in charge of defining the curricula for K-12 education on all topics.

International journals

• 12 articleF.Frédéric Blanqui, G.Gilles Dowek, E.Emilie Grienenberger, G.Gabriel Hondet and F.François Thiré. A modular construction of type theories.Logical Methods in Computer Science191February 2023HALDOI
• 13 articleA.Alejandro Díaz-Caro and G.Gilles Dowek. A New Connective in Natural Deduction, and its Application to Quantum Computing.Theoretical Computer Science9572023, 113840HALDOIback to text
• 14 articleG.Gilles Dowek. Explanation: from ethics to logic.Annals of the Japan Association for Philosophy of Science322023, 16HALback to text
• 15 articleP.Philipp Haselwarter, E.Exequiel Rivas, A.Antoine van Muylder, T.Théo Winterhalter, C.Carmine Abate, N.Nikolaj Sidorenco, C.Cătălin Hriţcu, K.Kenji Maillard and B.Bas Spitters. SSProve: A Foundational Framework for Modular Cryptographic Proofs in Coq.ACM Transactions on Programming Languages and Systems (TOPLAS)453September 2023, 1-61HALDOI
• 16 articleJ.-P.Jean-Pierre Jouannaud and F.Fernando Orejas. Unification of Drags and Confluence of Drag Rewriting.Journal of Logical and Algebraic Methods in Programming131February 2023, 26HALDOIback to text

International peer-reviewed conferences

• 17 inproceedingsV.Valentin Blot, D.Denis Cousineau, E.Enzo Crance, L.Louise Dubois de Prisque, C.Chantal Keller, A.Assia Mahboubi and P.Pierre Vial. Compositional pre-processing for automated reasoning in dependent type theory.CPP 2023 - Certified Programs and ProofsBoston, United States2023, 1-15HALDOIback to text
• 18 inproceedingsV.Valentin Blot. Diller-Nahm Bar Recursion.FSCD 2023 - 8th International Conference on Formal Structures for Computation and Deduction260LIPIcsRome, ItalyJuly 2023, 32:1-32:16HALDOIback to text
• 19 inproceedingsT.Thiago Felicissimo, F.Frédéric Blanqui and A.Ashish Kumar Barnawal. Translating proofs from an impredicative type system to a predicative one.31st EACSL Annual Conference on Computer Science Logic (CSL 2023)Warsaw, Poland2023HALDOIback to text
• 20 inproceedingsG.Gaëtan Gilbert, Y.Yann Leray, N.Nicolas Tabareau and T.Théo Winterhalter. The Rewster: The Coq Proof Assistant with Rewrite Rules.TYPES 2023 - 29th International Conference on Types for Proofs and ProgramsValencia, Spain2023, 1-3HAL
• 21 inproceedingsA.Amélie Ledein, V.Valentin Blot and C.Catherine Dubois. A semantics of K into dedukti.TYPES 2022 - 28th International Conference on Types for Proofs and ProgramsTYPES 2022 - 28th International Conference on Types for Proofs and Programs (TYPES)Nantes, FranceSchloss Dagstuhl - Leibniz-Zentrum für Informatik2023HALDOIback to text

National peer-reviewed Conferences

• 22 inproceedingsA.Amélie Ledein, V.Valentin Blot and C.Catherine Dubois. Vers une traduction de K en Dedukti.JFLA 2022 - Journées Francophones des Langages ApplicatifsJFLA 2022 - Journées Francophones des Langages Applicatifs (JFLA)Saint-Médard-d'Excideuil, FranceSchloss Dagstuhl - Leibniz-Zentrum für Informatik2023HAL
• 23 inproceedingsA.Amélie Ledein and E.Elliot Butte. Traduire l'univers des mathématiques en Dedukti, sans univers.JFLA 2023 - 34èmes Journées Francophones des Langages ApplicatifsPraz-sur-Arly, FranceJanuary 2023, 172-189HALback to text

Reports & preprints

• 24 reportF.Frédéric Blanqui, A.Anne Canteaut, H.Hidde de Jong, S.Sébastien Imperiale, N.Nathalie Mitton, G.Guillaume Pallez, X.Xavier Pennec, X.Xavier Rival and B.Bertrand Thirion. Recommandations sur les « éditeurs de la zone grise ».InriaJanuary 2023, 1-3HAL
• 25 miscV.Valentin Blot, G.Gilles Dowek, T.Thomas Traversié and T.Théo Winterhalter. From Rewrite Rules to Axioms in the λΠ-Calculus Modulo Theory.February 2024HALback to text
• 26 miscN.Nachum Dershowitz, J.-P.Jean-Pierre Jouannaud and F.Fernando Orejas. Drag Rewriting.June 2023HALback to text
• 27 miscG.Gilles Dowek. A theory independent Curry-De Bruijn-Howard correspondence.April 2023HAL
• 28 miscT.Thiago Felicissimo. Generic bidirectional typing for dependent type theories.November 2023HALback to text
• 29 miscY.Yoan Géran. Encoding impredicative hierarchy of type universes with variables.November 2023HALback to text
• 30 miscM.Matthieu Sozeau, Y.Yannick Forster, M.Meven Lennon-Bertrand, J. B.Jakob Botsch Nielsen, N.Nicolas Tabareau and T.Théo Winterhalter. Correct and Complete Type Checking and Certified Erasure for Coq, in Coq.April 2023HAL
• 31 miscC.Claude Stolze, O.Olivier Hermant and R.Romain Guillaumé. Towards Formalization and Sharing of Atelier B Proofs with Dedukti.January 2024HAL
• 32 miscT.Théo Winterhalter. Extensionality of Ghost Dependent Types for Free.July 2023HALback to text