Keywords
 A2.1. Programming Languages
 A2.2. Compilation
 A2.4. Formal method for verification, reliability, certification
 A4.5. Formal methods for security
 A7.2. Logic in Computer Science
 A7.2.1. Decision procedures
 A7.2.2. Automated Theorem Proving
 A7.2.3. Interactive Theorem Proving
 A7.2.4. Mechanized Formalization of Mathematics
 A7.3.1. Computational models and calculability
 A8.1. Discrete mathematics, combinatorics
 A8.11. Game Theory
 B6.1. Software industry
1 Team members, visitors, external collaborators
Research Scientists
 Lutz Strassburger [Team leader, INRIA, Senior Researcher, HDR]
 Beniamino Accattoli [INRIA, Researcher]
 Kaustuv Chaudhuri [INRIA, Researcher]
 Ian Mackie [CNRS, Researcher]
 Dale Miller [INRIA, Senior Researcher]
 Gabriel Scherer [INRIA, Researcher]
Faculty Members
 Benjamin Werner [LIX, Professor, HDR]
 Noam Zeilberger [LIX, Associate Professor]
PostDoctoral Fellows
 Bryce Clarke [Inria, from Mar 2022]
 Peter Faul [Ecole Polytechnique, from Oct 2022]
 Lê Thành Dung Nguyên [Ecole Polytechnique, from Mar 2022 until Sep 2022]
PhD Students
 Farah Al Wardani [Inria]
 Nicolas Blanco [University of Birmingham]
 Pablo Donato [LIX]
 Adrienne Lancelot [Inria, from Oct 2022]
 Olivier Martinot [INRIA]
 Marianela Evelyn Morales Elena [IP Paris]
 Giti Omidvar [INRIA]
 Wendlasida Ouedraogo [SIEMENS MOBILITY]
 Antoine Sere [LIX]
 Alexandros Singh [Université Paris Nord, until Nov 2022]
 JuiHsuan Wu [IP PARIS]
Interns and Apprentices
 Luigi Massacci [Ecole polytechnique, Intern, until Sep 2022]
 Remy Sasseau [Inria, Intern, until Mar 2022, Bachelor Student]
Administrative Assistant
 Michael Barbosa [Inria, from May 2022]
Visiting Scientist
 Victoria Barrett [University of Bath, from Nov 2022 until Nov 2022]
2 Overall objectives
There is an emerging consensus that formal methods must be used as a matter of course in software development. Most software is too complex to be fully understood by one programmer or even a team of programmers, and requires the help of computerized techniques such as testing and model checking to analyze and eliminate entire classes of bugs. Moreover, in order for the software to be maintainable and reusable, it not only needs to be bugfree but also needs to have fully specified behavior, ideally accompanied with formal and machinecheckable proofs of correctness with respect to the specification. Indeed, formal specification and machine verification is the only way to achieve the highest level of assurance (EAL7) according to the ISO/IEC Common Criteria.1
Historically, achieving such a high degree of certainty in the operation of software has required significant investment of manpower, and hence of money. As a consequence, only software that is of critical importance (and relatively unchanging), such as monitoring software for nuclear reactors or flybywire controllers in airplanes, has been subjected to such intense scrutiny. However, we are entering an age where we need trustworthy software in more mundane situations, with rapid development cycles, and without huge costs. For example: modern cars are essentially mobile computing platforms, smartdevices manage our intensely personal details, elections (and election campaigns) are increasingly fully computerized, and networks of drones monitor air pollution, traffic, military arenas, etc. Bugs in such systems can certainly lead to unpleasant, dangerous, or even lifethreatening incidents.
The field of formal methods has stepped up to meet this growing need for trustworthy general purpose software in recent decades. Techniques such as computational type systems and explicit program annotations/contracts, and tools such as model checkers and interactive theorem provers, are starting to become standard in the computing industry. Indeed, many of these tools and techniques are now a part of undergraduate computer science curricula. In order to be usable by ordinary programmers (without PhDs in logic), such tools and techniques have to be high level and rely heavily on automation. Furthermore, multiple tools and techniques often need to marshaled to achieve a verification task, so theorem provers, solvers, model checkers, property testers, etc. need to be able to communicate with—and, ideally, trust—each other.
With all this sophistication in formal tools, there is an obvious question: what should we trust? Sophisticated formal reasoning tools are, generally speaking, complex software artifacts themselves; if we want complex software to undergo rigorous formal analysis we must be prepared to formally analyze the tools and techniques used in formal reasoning itself. Historically, the issue of trust has been addressed by means of relativizing it to small and simple cores. This is the basis of industrially successful formal reasoning systems such as Coq, Isabelle, HOL4, and ACL2. However, the relativization of trust has led to a balkanization of the formal reasoning community, since the Coq kernel, for example, is incompatible with the Isabelle kernel, and neither can directly crossvalidate formal developments built with the other. Thus, there is now a burgeoning cottage industry of translations and adaptations of different formal proof languages for bridging the gap. A number of proposals have also been made for universal or retargetable proof languages (e.g., Dedukti, ProofCert) so that the crossplatform trust issues can be factorized into single trusted checkers.
Beyond mutual incompatibility caused by relativized trust, there is a bigger problem that the proof evidence that is accepted by small kernels is generally far too detailed to be useful. Formal developments usually occurs at a much higher level, relying on algorithmic techniques such as unification, simplification, rewriting, and controlled proof search to fill in details. Indeed, the most reusable products of formal developments tend to be these algorithmic techniques and associated collections of handcrafted rules. Unfortunately, these techniques are even less portable than the fully detailed proofs themselves, since the techniques are often implemented in terms of the behaviors of the trusted kernels. We can broadly say that the problem with relativized trust is that it is based on the operational interpretation of implementations of trusted kernels. There still remains the question of metatheoretic correctness. Most formal reasoning systems implement a variant of a well known mathematical formalism (e.g., MartinLöf type theory, set theory, higherorder logic), but it is surprising that hardly any mainstream system has a formalized metatheory.2 Furthermore, formal reasoning systems are usually associated with complicated checkers for sideconditions that often have unclear mathematical status. For example, the Coq kernel has a builtin syntactic termination checker for recursive fixedpoint expressions that is required to work correctly for the kernel to be sound. This termination checker evolves and improves with each version of Coq, and therefore the most accurate documentation of its behavior is its own source code. Coq is not special in this regard: similar trusted features exist in nearly every mainstream formal reasoning system.
The Partout project is interested in the principles of deductive and computational formalisms. In the broadest sense, we are interested in the question of trustworthy and verifiable metatheory. At one end, this includes the well studied foundational questions of the metatheory of logical systems and type systems: cutelimination and focusing in proof theory, type soundness and normalization theorems in type theory, etc. The focus of our research here is on the fundamental relationships behind the the notions of computation and deduction. We are particularly interested in relationships that go beyond the well known correspondences between proofs and programs.3 Indeed, interpreting computation in terms of deduction (as in logic programming) or deduction in terms of computation (as in rewrite systems or in model checking) can often lead to fruitful and enlightening research questions, both theoretical and practical.
From another end, Partout works on the question of the essential nature of deductive or computational formalisms. For instance, we are interested in the question of proof identity that attempts to answer the following question: when are two proofs of the same theorem the same? Surprisingly, this very basic question is left unanswered in proof theory, the branch of mathematics that supposedly treats proofs as algebraic objects of interest. We also pay particular attention to the combinatorial and complexitytheoretic properties of the formalisms. Indeed, it is surprising that until very recently the $\lambda $calculus, which is the de facto basis of every functional programming language, lacked a good complexitytheoretic foundation, i.e., a cost model that would allow us to use the $\lambda $calculus directly to define complexity classes.
To put trustworthy metatheory to use, the Partout project also works on the design and implementations of formal reasoning tools and techniques. We study the mathematical principles behind the representations of formal concepts ($\lambda $terms, proofs, abstract machines, etc.), with the goal of identifying the relationships and tradeoffs. We also study computational formalisms such as higherorder relational programming that is well suited to the specification and analysis of systems defined in the structural operational semantics (SOS) style. We also work on foundational questions about induction and coinduction, which are used in intricate combinations in metamathematics.
3 Research program
Software and hardware systems perform computation (systems that process, compute and perform) and deduction (systems that search, check or prove). The makers of those systems express their intent using various frameworks such as programming languages, specification languages, and logics. The Partout project aims at developing and using mathematical principles to design better frameworks for computation and reasoning. Principles of expression are researched from two directions, in tandem:

Foundational approaches, from theories to applications: studying fundamental problems of programming and proof theory.
Examples include studying the complexity of reduction strategies in lambdacalculi with sharing, or studying proof representations that quotient over rule permutations and can be adapted to many different logics.

Empirical approaches, from applications to theories: studying systems currently in use to build a theoretical understanding of the practical choices made by their designers.
Examples include studying realistic implementations of programming languages and proof assistants, which differ in interesting ways from their usual highlevel formal description (regarding of sharing of code and data, for example), or studying new approaches to efficient automated proof search, relating them to existing approaches of proof theory, for example to design proof certificates or to generalize them to nonclassical logics.
One of the strengths of Partout is the coexistence of a number of different expertise and points of view. Many dichotomies exist in the study of computation and deduction: functional programming vs logic programming, operational semantics vs denotational semantics, constructive logic vs classical logic, proof terms vs proof nets, etc. We do not identify with any one of them in particular, rather with them as a whole, believing in the value of interaction and crossfertilization between different approaches. Partout defines its scope through the following core tenets:
 An interest in both computation and logic.
 The use of mathematical formalism as our core scientific method, paired with practical implementations of the systems we study.
 A shared belief in the importance of good design when creating new means of expression, iterating towards simplicity and elegance.
More concretely, the research in Partout will be centered around the following four themes:
 Foundations of proof theory as a theory of proofs. Current proof theory is not a theory of proofs but a theory of proof systems. This has many practical consequences, as a proof produced by modern theorem provers cannot be considered independent from the tool that produced it. A central research topic here is the quest for proof representations that are independent from the proof system, so that proof theory becomes a proper theory of proofs.
 Program Equivalence We intend to use our proof theoretical insights to deepen our understanding of the structure of computer programs by discovering canonical representations for functional programming languages, and to apply these to the problems of program equivalence checking and program synthesis.
 Reasoning with relational specifications of formal systems. Formal systems play a central role for proof checkers and proof assistants that are used for software verification. But there is usually a large gap between the specification of those formal systems in concise informal mathematical language and their implementation in ML or C code. Our research goal is to close that gap.
 Foundations of complexity analysis for functional programs. One of the great merits of the functional programming paradigm is the natural availability of highlevel abstractions. However, these abstractions jeopardize the programmer's predictive control on the performance of the code, since many lowlevel steps are abstracted away by higherorder functions. Our research goal is to regain that control by developing models of space and time costs for functional programs.
4 Application domains
4.1 Automated Theorem Proving
The Partout team studies the structure of mathematical proofs, in ways that often makes them more amenable to automated theorem proving – automatically searching the space of proof candidates for a statement to find an actual proof – or a counterexample.
(Due to fundamental computability limits, fullyautomatic proving is only possible for simple statements, but this field has been making a lot of progress in recent years, and is in particular interested with the idea of generating verifiable evidence for the proofs that are found, which fits squarely within the expertise of Partout.)
4.2 Proofassistants
Our work on the structure of proofs also suggests ways how they could be presented to a user, edited and maintained, in particular in “proof assistants”, automated tool to assist the writing of mathematical proofs with automatic checking of their correctness.
4.3 Programming language design
Our work also gives insight on the structure and properties of programming languages. We can improve the design or implementation of programming languages, help programmers or language implementors reason about the correctness of the programs in a given language, or reason about the cost of execution of a program.
5 Highlights of the year
Dale Miller was named an ACM Fellow for contributions to proof theory and computational logic.
Dale Miller was named a Fellow of the AsiaPacific Artificial Intelligence Association (AAIA).
Accattoli has been cochair of the international conference PPDP 2022.
The version 5.0 of the OCaml programming language implementation was released, with participation from Gabriel Scherer.
5.1 Awards
Paper 9 by Accattoli, Dal Lago, and Vanoni received the distinguished paper award of the international conference ICFP 2022.
5.2 Results
 We solved a longstanding open problem by showing that the logic BV and pomset logic are not the same (see 22 and 34).
 Accattoli has two papers 14, 15 in the international conference LICS 2022, one of the top conferences of the area, and both papers have been selected for the special issue of the conference. Moreover, 14 solved a longstanding problem in the theory of $\lambda $calculus, namely how to measure logarithmic space in a way equivalent to Turing machines.
5.3 Grants
 Zeilberger is the scientific coordinator of LambdaComb, a fouryear project financed by the ANR from the beginning of 2022. Broadly, the project aims to deepen connections between lambda calculus and logic on the one hand and combinatorics on the other. One important motivation for the project is the discovery over recent years of a host of surprising links between subsystems of lambda calculus and enumeration of graphs on surfaces, or "maps", the latter being an active subfield of combinatorics with roots in W. T. Tutte's work in the 1960s. Currently, the project involves over 20 researchers distributed across four partner laboratories in France (LIX, LIPN, LIS, and LIGM) and one partner in Poland (Jagiellonian University).
 Accattoli is the PI of the Inria Action Exploratoire CANofGAS (Cost ANalyses of GAme Semantics), led together with Guilhem Jaber (Université de Nantes & Inria Rennes, Gallinette team), which started in 2022 and will continue until 2025. The aim of the project is to merge two lines of research, the one about reasonable cost models for the $\lambda $calculus and the one about game semantics for functional languages.
6 New software and platforms
6.1 New software
6.1.1 MOIN

Name:
MOdal Intuitionistic Nested sequents

Keywords:
Logic programming, Modal logic

Functional Description:
MOIN is a SWI Prolog theorem prover for classical and intuitionstic modal logics. The modal and intuitionistic modal logics considered are all the 15 systems occurring in the modal S5cube, and all the decidable intuitionistic modal logics in the IS5cube. MOIN also provides a protptype implementation for the intuitionistic logics for which decidability is not known (IK4,ID5 and IS4). MOIN is consists of a set of Prolog clauses, each clause representing a rule in one of the three proof systems. The clauses are recursively applied to a given formula, constructing a proofsearch tree. The user selects the nested proof system, the logic, and the formula to be tested. In the case of classic nested sequent and Maeharastyle nested sequents, MOIN yields a derivation, in case of success of the proof search, or a countermodel, in case of proof search failure. The countermodel for classical modal logics is a Kripke model, while for intuitionistic modal logic is a birelational model. In case of Gentzenstyle nested sequents, the prover does not perform a countermodel extraction.
A system description of MOIN is available at https://hal.inria.fr/hal02457240
 URL:
 Publication:

Contact:
Lutz Strassburger
6.1.2 OCaml

Keywords:
Functional programming, Static typing, Compilation

Functional Description:
The OCaml language is a functional programming language that combines safety with expressiveness through the use of a precise and flexible type system with automatic type inference. The OCaml system is a comprehensive implementation of this language, featuring two compilers (a bytecode compiler, for fast prototyping and interactive use, and a nativecode compiler producing efficient machine code for x86, ARM, PowerPC, RISCV and System Z), a debugger, and a documentation generator. Many other tools and libraries are contributed by the user community and organized around the OPAM package manager.
 URL:
 Publications:

Contact:
Damien Doligez

Participants:
Florian Angeletti, Damien Doligez, Xavier Leroy, Luc Maranget, Gabriel Scherer, Alain Frisch, Jacques Garrigue, Marc Shinwell, Jeremy Yallop, Leo White
6.1.3 Abella

Keyword:
Proof assistant

Functional Description:
Abella is an interactive theorem prover for reasoning about computations given as relational specifications. Abella is particuarly well suited for reasoning about binding constructs.
 URL:

Contact:
Kaustuv Chaudhuri

Participants:
Dale Miller, Gopalan Nadathur, Kaustuv Chaudhuri, Mary Southern, Matteo Cimini, Olivier SavaryBélanger, Yuting Wang

Partner:
Department of Computer Science and Engineering, University of Minnesota
6.1.4 ocamlboxroot

Keywords:
Interoperability, Library, Ocaml, Rust

Scientific Description:
Boxroot is an implementation of roots for the OCaml GC based on concurrent allocation techniques. These roots are designed to support a calling convention to interface between Rust and OCaml code that reconciles the latter's foreign function interface with the idioms from the former.

Functional Description:
Boxroot implements fast movable roots for OCaml in C. A root is a data type which contains an OCaml value, and interfaces with the OCaml GC to ensure that this value and its transitive children are kept alive while the root exists. This can be used to write programs in other languages that interface with programs written in OCaml.
 URL:
 Publication:

Contact:
Guillaume Munch

Participants:
Guillaume Munch, Gabriel Scherer
6.1.5 Actema

Name:
Actema

Keywords:
Higherorder logic, Firstorder logic, Proof assistant, GUI (Graphical User Interface), Manmachine interfaces, User Interfaces

Functional Description:
This is a new approach, aiming at making the building of formal proofs more intuitive and convenient. The system is currently at a prototype stage. An interfacing with the Coq proofsystem is under study. The system runs through an html/JS serve.

Release Contributions:
This version can be used online at actema.xyz and comes with explanation videos.

News of the Year:
The logical mechanism at work in Actema have been described in the article https://hal.archivesouvertes.fr/hal03823357
 URL:
 Publication:

Contact:
Benjamin Werner

Participants:
Benjamin Werner, Pablo Donato, PierreYves Strub

Partner:
Ecole Polytechnique
6.1.6 ProfoundIntuitionistic

Name:
Interactive theorem proving by direct manipulation for Intuitionistic Logic

Keywords:
Interactive Theorem Proving, Firstorder logic

Functional Description:
ProfountIntuitionistic (Profint) is a tool for building formal proofs in intuitionistic logic using an interactive direct manipulation based webinterface. The tool can transform the interactive proof into formal proof objects in a variety of backend provers including: Coq, Lean 3, Lean 4, Isabelle/HOL, HOL4, and Abella.

Release Contributions:
This release adds support for proof output in a variety of backend provers including: Coq, Lean 3, Lean 4, Isabelle/HOL, HOL 4, and Abella.
 URL:

Contact:
Kaustuv Chaudhuri
7 New results
7.1 Combinatorial Proofs for Constructive Modal Logic
Participants: Lutz Straßburger.
External Collaborators: Matteo Acclavio (Univ. Luxembourg)
Combinatorial proofs form a syntaxindependent presentation of proofs, originally proposed by Hughes for classical propositional logic. In this paper we present a notion of combinatorial proofs for the constructive modal logics CK and CD, we show soundness and completeness of combinatorial proofs by translation from and to sequent calculus proofs, and we discuss the notion of proof equivalence enforced by these translations.
This work has been published at the AiML 2022 conference 18
7.2 Normalization Without Syntax
Participants: Lutz Straßburger.
External Collaborators: Willem Heijltjes (University of Bath), Dominic Hughes (UC Berkeley)
We present normalization for intuitionistic combinatorial proofs (ICPs) and relate it to the simplytyped lambdacalculus. We prove confluence and strong normalization. Combinatorial proofs, or "proofs without syntax", form a graphical semantics of proof in various logics that is canonical yet complexityaware: they are a polynomialsized representation of sequent proofs that factors out exactly the nonduplicating permutations. Our approach to normalization aligns with these characteristics: it is canonical (free of permutations) and generic (readily applied to other logics). Our reduction mechanism is a canonical representation of reduction in sequent calculus with closed cuts (no abstraction is allowed below a cut), and relates to closed reduction in lambdacalculus and supercombinators. While we will use ICPs concretely, the notion of reduction is completely abstract, and can be specialized to give a reduction mechanism for any representation of typed normal forms.
This work was published at the FSCD 2022 conference 20.
7.3 Combinatorial Flows as Bicolored Atomic Flows
Participants: Giti Omidvar, Lutz Straßburger.
Combinatorial flows are a graphical representation of proofs. They can be seen as a generalization of atomic flows on one side and of combinatorial proofs on the other side. From atomic flows, introduced by Guglielemi and Gundersen, they inherit the close correspondence with open deduction and the possibility of tracing the occurrences of atoms in a derivation. From combinatorial proofs, introduced by Hughes, they inherit the correctness criterion that allows to reconstruct the derivation from the flow. In fact, combinatorial flows form a proof system in the sense of Cook and Reckhow. We show how to translate between open deduction derivations and combinatorial flows, and we show how they are related to combinatorial proofs with cuts.
This work has been published in 23
7.4 BV and Pomset Logic Are Not the Same
Participants: Lutz Straßburger.
External Collaborators: Nguyễn, Lê Thành Dũng (ENS Lyon)
BV and pomset logic are two logics that both conservatively extend unitfree multiplicative linear logic by a third binary connective, which (i) is noncommutative, (ii) is selfdual, and (iii) lies between the "par" and the "tensor". It was conjectured early on (more than 20 years ago), that these two logics, that share the same language, that both admit cut elimination, and whose connectives have essentially the same properties, are in fact the same. In this paper we show that this is not the case. We present a formula that is provable in pomset logic but not in BV.
We also studied the complexity of the two logics. These results are presented in 22 and 34.
7.5 Coqlex, an approach to generate verified lexers
Participants: Lutz Straßburger, Wendlasida Ouedraogo, Gabriel Scherer.
External Collaborators: Danko Ilik (Siemens)
A compiler consists of a sequence of phases going from lexical analysis to code generation. Ideally, the formal verification of a compiler should include the formal verification of every component of the toolchain. In order to contribute to the endtoend verification of compilers, we implemented a verified lexer generator with usage similar to OCamllex. This softwareCoqlexreads a lexer specification and generates a lexer equipped with Coq proofs of its correctness. Although the performance of the generated lexers does not measure up to the performance of a standard lexer generator such as OCamllex, the safety guarantees it comes with make it an interesting alternative to use when implementing totally verified compilers or other language processing tools.
More details on this work can be found here 35
7.6 An Analytic Propositional Proof System On Graphs
Participants: Lutz Straßburger.
External Collaborators: Matteo Acclavio (Univ. Luxembourg), Ross Horne (Univ. Luxembourg)
In this work, published in 11 we present a proof system that operates on graphs instead of formulas. Starting from the wellknown relationship between formulas and cographs, we drop the cographconditions and look at arbitrary (undirected) graphs. This means that we lose the tree structure of the formulas corresponding to the cographs, and we can no longer use standard proof theoretical methods that depend on that tree structure. In order to overcome this difficulty, we use a modular decomposition of graphs and some techniques from deep inference where inference rules do not rely on the main connective of a formula. For our proof system we show the admissibility of cut and a generalization of the splitting property. Finally, we show that our system is a conservative extension of multiplicative linear logic with mix, and we argue that our graphs form a notion of generalized connective.
7.7 A Graphical Proof Theory of Logical Time
Participants: Lutz Straßburger.
External Collaborators: Matteo Acclavio (Univ. Luxembourg), Ross Horne (Univ. Luxembourg), Sjouke Mauw (Univ. Luxembourg)
Logical time is a partial order over events in distributed systems, constraining which events precede others. Special interest has been given to seriesparallel orders since they correspond to formulas constructed via the two operations for "series" and "parallel" composition. For this reason, seriesparallel orders have received attention from proof theory, leading to pomset logic, the logic BV, and their extensions. However, logical time does not always form a seriesparallel order; indeed, ubiquitous structures in distributed systems are beyond current proof theoretic methods. In this paper, we explore how this restriction can be lifted. We design new logics that work directly on graphs instead of formulas, we develop their proof theory, and we show that our logics are conservative extensions of the logic BV.
This work was published at the FSCD 2022 conference 17.
7.8 Taming Bounded Depth with Nested Sequents
Participants: Lutz Straßburger.
External Collaborators: Agata Ciabattoni (TU Wien), Matteo Tesi (SNS Pisa)
Bounded depth refers to a property of Kripke frames that serve as semantics for intuitionistic logic. We introduce nested sequent calculi for the intermediate logics of bounded depth. Our calculi are obtained in a modular way by adding suitable structural rules to a variant of Fitting’s calculus for intuitionistic propositional logic, for which we present the first syntactic cut elimination proof. This proof modularly extends to the new nested sequent calculi introduced in this paper, which has been published at the the AiML 2022 conference 19
7.9 From axioms to synthetic inference rules via focusing
Participants: Dale Miller.
External Collaborators: Sonia Marin (University of Birmingham), Elaine Pimentel (University College of London), and Marco Volpe (Osnabrueck University).
We examine the synthetic inference rules that arise when using theories composed of bipolars in both classical and intuitionistic logics. A key step in transforming a formula into synthetic inference rules involves attaching a polarity to atomic formulas and some logical connectives. Since there are different choices in how polarity is assigned, it is possible to produce different synthetic inference rules for the same formula. We show that this flexibility allows for the generalization of different approaches for transforming axioms into sequent rules present in the literature. We also show how to apply these results to organize the proof theory of labeled sequent systems for several propositional modal logics. This work was published in the Annals of Pure and Applied Logic 13.
7.10 Computational logic based on linear logic and fixed points
Participants: Matteo Manighetti, Dale Miller.
We use $\mu $MALL, the logic that results from adding least and greatest fixed points to firstorder multiplicativeadditive linear logic, as a framework for presenting several topics in computational logic. In particular, we present various levels of restrictions on the roles of fixed points in proofs and show that these levels capture different topics. For example, level 0 of $\mu $MALL captures (generalized) unification problems, level 1 captures Hornclause logic programming, level 2 captures various model checking problems, and level 3 introduces a linearized form of arithmetic. We also show how the proof search interpretation of $\mu $MALL can be used to compute general recursive functions. Finally, we identify several situations where provability in Peano Arithmetic can be replaced by provability in $\mu $MALL. In such situations, the proof theory of $\mu $MALL can be used to study and implement proof search procedures for fragments of Peano Arithmetic.
This work was presented at TLLALinearity 2022 and appears in 33.
7.11 Distributing and trusting proof checking
Participants: Kaustuv Chaudhuri, Dale Miller, Farah Al Wardani.
When a proofchecking kernel completes the checking of a formal proof, that kernel asserts that a specific formula follows from a collection of lemmas within a given logic. We describe a framework in which such an assertion can be made globally so that any other proof assistant willing to trust that kernel can use that assertion without rechecking (or even understanding) the formal proof associated with that assertion. In this framework, we propose to move beyond autarkic proof checkersi.e., selfsufficient provers that trust proofs only when they are checked by their kernelto an explicitly nonautarkic setting. This framework must, of course, explicitly track which agents (proof checkers and their operators) are being trusted when a trusting proof checker makes its assertions. We describe how we have integrated this framework into a particular theorem prover while making minor changes to how the prover inputs and outputs text files. This framework has been implemented using offtheshelf webbased technologies, such as JSON, IPFS, IPLD, and public key cryptography. A preliminary report on this work appears in 31.
7.12 A positive perspective on term representation
Participants: Dale Miller, JuiHsuan Wu.
The focused proof system LJF can be used as a framework for describing term structures and substitution. Since the proof theory of LJF does not pick a canonical polarization for primitive types, two different approaches to term representation arise. When primitive types are given the negative polarity, LJF proofs encode terms as treelike structures in a familiar fashion. In this situation, cut elimination also yields the familiar notion of substitution. On the other hand, when primitive types are given the positive polarity, LJF proofs yield a structure in which explicit sharing of term structures is possible. Such a representation of terms provides an explicit method for sharing term structures. In this setting, cut elimination yields a different notion of substitution. We illustrate these two approaches to term representation by applying them to the encoding of untyped $\lambda $terms. We also exploit concurrency theory techniques—namely traces and simulation—to compare untyped $\lambda $terms using such different structuring disciplines.
This work will be presented as an invited paper at CSL 2023 21.
7.13 Graphical User Interfaces for Formal Proof Construction
Participants: Kaustuv Chaudhuri, Pablo Donato, Benjamin Werner.
Deep Inference can ways to construct proofs steps by pointing to two different locations in the goal and/or hypotheses. This had been described in 36. We have built on this to provide a novel proof interface, Actema, which to construct proofs without textual commands, in a way which is, we beleive, intuitive and userfriendly. A version of the system can be used on the system's web page.This work was published at the CPP 2022 conference 27.
A new version of Actema is under way which allows to use it as a frontend for the Coq proof system.
7.14 Certified Cryptography
Participants: Antoine Séré.
Antoine Séré is conducting his PhD research, with PierreYves Strub as external main adviser, on formally certified cryptography. This year he participated to the formal correctness proof of the Kyber crpytographic primitive (which won the NIST postquantum competition). An article is to be submitted.
7.15 Useful Open CallbyNeed
Participants: Beniamino Accattoli.
External Collaborators: Maico Leberle (ex PhD student in Partout).
This work studies useful sharing, which is a sophisticated optimization for $\lambda $calculi, in the context of callbyneed evaluation (an efficient evaluation strategy) in presence of open terms (a feature needed in the implementation of proof assistants such as Coq). Useful sharing turns out to be harder in callbyneed than for other strategies (such as callbyname or callbyvalue), because callbyneed evaluates inside socalled environments, making it harder to specify when a substitution step is useful. We isolate the key involved concepts and prove the correctness and the completeness of useful sharing in this setting.
This work belongs to the foundations of complexity analysis for functional programs theme of the research program of Partout. It has been published in 16.
7.16 Reasonable Space for the $\lambda $Calculus, Logarithmically
Participants: Beniamino Accattoli.
External Collaborators: Ugo Dal Lago (University of Bologna & Inria), Gabriele Vanoni (University of Bologna & Inria).
Can the λcalculus be considered a reasonable computational model? Can we use it for measuring the time and space consumption of algorithms? While the literature contains positive answers about time, much less is known about space.
This work presents a new reasonable space cost model for the $\lambda $calculus, based on a variant over the Krivine abstract machine, that we call Space KAM. For the first time, this cost model is able to ac commodate logarithmic space, thus our result is the answer to a longstanding open problem in the theory of $\lambda $calculus. Moreover, we study the time behavior of our machine and show how to transport our results to the callbyvalue λcalculus.
This work belongs to the foundations of complexity analysis for functional programs theme of the research program of Partout. It has been published in 14, and it has been selected for the special issue of the conference.
7.17 Multi Types and Reasonable Space
Participants: Beniamino Accattoli.
External Collaborators: Ugo Dal Lago (University of Bologna & Inria), Gabriele Vanoni (University of Bologna & Inria).
This work continues the study of the previous subsection, providing a new system of multi types (a variant of intersection types) and we show how to extract from multi type derivations the space used by the Space KAM, capturing into a type system the space complexity of the abstract machine. Additionally, we show how to capture also the time of the Space KAM, which is a reasonable time cost model, via minor changes to the type system.
This work belongs to the foundations of complexity analysis for functional programs theme of the research program of Partout. It has been published in 9, and it received the distinguished paper award of the conference.
7.18 Exponentials as Substitutions and the Cost of Cut Elimination in Linear Logic
Participants: Beniamino Accattoli.
This work introduces the exponential substitution calculus (ESC), a new presentation of cut elimination for intuitionistic multiplicative and exponential linear logic (IMELL), based on proof terms and building on the idea that exponentials can be seen as explicit substitutions (a formalism for representing sharing in the $\lambda $calculus). The idea in itself is not new, but here it is pushed to a new level, inspired by Accattoli and Kesner’s linear substitution calculus (LSC).
One of the key properties of the LSC is that it naturally models the subterm property of abstract machines, which is the key ingre dient for the study of reasonable time cost models for the $\lambda $calculus. The new ESC is then used to design a cut elimination strategy with the subterm property, providing the first polynomial cost model for cut elimination with unconstrained exponentials.
For the ESC, we also prove untyped confluence and typed strong normalization, showing that it is an alternative to proof nets for an advanced study of cut elimination.
This work belongs to the foundations of complexity analysis for functional programs theme of the research program of Partout. It has been published in 15, and it has been selected for the special issue of the conference.
7.19 The Theory of CallbyValue Solvability
Participants: Beniamino Accattoli.
External Collaborators: Giulio Guerrieri(Edinbugh Research Centre, Huawei, UK).
The denotational semantics of the untyped $\lambda $calculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent notion of meaningless term. The semantics of the untyped callbyvalue $\lambda $calculus (CbV), the variant of the $\lambda $calculus used to model most applications, is instead still in its infancy, because of some inherent difficulties but also because CbV solvable terms are less studied and understood than in callbyname. On the one hand, we show that a carefully crafted presentation of CbV allows us to recover many of the properties that solvability has in callbyname, in particular qualitative and quantitative characterizations via multi types. On the other hand, we stress that, in CbV, solvability plays a different role: identifying unsolvable terms as meaningless induces an inconsistent theory.
This work belongs to the foundations of complexity analysis for functional programs theme of the research program of Partout. It has been published in 10.
7.20 Parsing as a lifting problem and the ChomskySchützenberger Representation Theorem
Participants: Noam Zeilberger.
We begin by explaining how any contextfree grammar encodes a functor of operads from a freely generated operad into a certain "operad of spliced words". This motivates a more general notion of CFG over any category $C$, defined as a finite species $S$ equipped with a color denoting the start symbol and a functor of operads $p:Free\left[S\right]\to W\left[C\right]$ into the operad of spliced arrows in $C$. We show that many standard properties of CFGs can be formulated within this framework, and that usual closure properties of CF languages generalize to CF languages of arrows. We also discuss a dual fibrational perspective on the functor $p$ via the notion of "displayed" operad, corresponding to a lax functor of operads $W\left[C\right]\to Span\left(Set\right)$.
We then turn to the ChomskySchützenberger Representation Theorem. We describe how a nondeterministic finite state automaton can be seen as a category $Q$ equipped with a pair of objects denoting initial and accepting states and a functor of categories $Q\to C$ satisfying the unique lifting of factorizations property and the finite fiber property. Then, we explain how to extend this notion of automaton to functors of operads, which generalize tree automata, allowing us to lift an automaton over a category to an automaton over its operad of spliced arrows. We show that every CFG over a category can be pulled back along a ND finite state automaton over the same category, and hence that CF languages are closed under intersection with regular languages. The last important ingredient is the identification of a left adjoint $C[]:Operad\to Cat$ to the operad of spliced arrows functor, building the "contour category" of an operad. Using this, we generalize the CS representation theorem, proving that any contextfree language of arrows over a category $C$ is the functorial image of the intersection of a $C$chromatic tree contour language and a regular language.
This work has been published in 28.
External Collaborators: PaulAndré Melliès (CNRS)
7.21 An introduction to enriched cofunctors
Participants: Bryce Clarke.
Cofunctors are a kind of map between categories which lift morphisms along an object assignment. In this paper, we introduce cofunctors between categories enriched in a distributive monoidal category. We define a double category of enriched categories, enriched functors, and enriched cofunctors, whose horizontal and vertical 2categories have 2cells given by enriched natural transformations between functors and cofunctors, respectively. Enriched lenses are defined as a compatible enriched functor and enriched cofunctor pair; weighted lenses, which were introduced by Perrone, are precisely lenses enriched in weighted sets. Several other examples are also studied in detail.
A preliminary version of this article was released as the preprint 32. A revised version is in preparation, for journal submission.
External Collaborators: Matthew di Meglio
7.22 Debootstrapping without archeology
Participants: Gabriel Scherer.
External Collaborators: Nathanëlle Courant (INRIA Paris), Julien Lepiller (Yale University)
It is common for programming languages that their reference implementation is implemented in the language itself. This requires a "bootstrap binary": the executable form of a previous version of the implementation is provided along with the sources, to be able to run the implementation itself. Those bootstrap binaries are opaque; they could contain bugs, or even malicious changes that could reproduce themselves when running the source version of the language implementationthis is called the "trusting trust attack". A collective project called Bootstrappable was launched in to remove bootstrap binaries, providing alternative build paths that do not rely on opaque binaries.
Camlboot is our project to debootstrap the OCaml compiler, version 4.07. Using diverse doublecompilation, we were able to prove the absence of trusting trust attack in the existing bootstrap binaries of the standard OCaml implementation.
To our knowledge, our publication 12 is the first scholarly discussion of "tailored" debootstrapping for highlevel programming languages. Debootstrapping recently grew an active community of free software contributors, but so far the interactions with the programming language research community have been minimal. We share our experience on Camlboot, trying to highlight aspects that are of interest to other language designers and implementors; we hope to foster stronger ties between the Bootstrappable project and relevant academic communities. In particular, the debootstrapping experience has been an interesting reflection on language design and implementation..
7.23 Déboîter les constructeurs
Participants: Gabriel Scherer.
External Collaborators: Nicolas Chataing (INRIA Paris), Camille Noûs (laboratoire Cogitamus)
Nous proposons dans 24 une implémentation d'une nouvelle fonctionnalité pour OCaml, l'unboxing de constructeur. Elle permet d'élimineer certains constructeurs de la représentation dynamique des valeurs quand cela ne crée pas d'ambiguité entre différentes valeurs au même type. Nous décrivons:
 l'analyse statique nécessaire pour accepter ou rejeter l'unboxing d'un constructeur,
 l'impact sur la compilation du filtrage de motif, et
 un cas d'usage préliminaire sur les grands entiers où la fonctionnalité améliore les performances de code OCaml idiomatique, éliminant le besoin d'écrire du code nonsûr.
Pour notre analyse statique, nous devons normaliser certaines expressions de type, avec une relation de normalisation qui ne termine pas nécessairement en présence de types mutuellement récursifs; nous décrivons une analyse de terminaison qui garantit la normalisation sans rejeter les déclarations de types qui nous intéressent.
7.24 Backtracking reference stores
Participants: Gabriel Scherer.
External Collaborators: Camille Noûs (laboratoire Cogitamus)
François Pottier's unionfind library is parameterized over an underlying store of mutable references, and provides the usual references, transactional reference stores (for rolling back some changes in case of higherlevel errors), and persistent reference stores. In 26, we extend this library with a new implementation of backtracking reference stores, to get a UnionFind implementation that efficiently supports arbitrary backtracking and also subsumes the transactional interface.
Our backtracking reference stores are not specific to unionfind, they can be used to build arbitrary backtracking data structures. The natural implementation, using a journal to record all writes, provides amortizedconstanttime operations with a space overhead linear in the number of store updates. A refined implementation reduces the memory overhead to be linear in the number of store cells updated, and gives performance that match nonbacktracking references in practice.
7.25 Boxroot, fast movable GC roots for a better FFI
Participants: Gabriel Scherer.
External Collaborators: Guillaume MunchMaccagnoni (INRIA Rennes/Nantes)
In 29 we study the safe manipulation of GCmanaged values inside nonmanaged (foreign) code. Focusing on the problem of implementing a safe and convenient FFI for OCaml in Rust, we propose a new interface and implementation for storing roots for the OCaml GC inside foreign (C and Rust) data structures, along with a typing discipline in Rust's ownership type system, which offer:
 better performance than existing rootregistration interfaces;
 efficient support for multicore OCaml, thanks to a multicorefriendly design;
 a reasoning based on resourcemanagement idioms, enabling an easier OCaml FFI for Rust.
7.26 A OCaml usecase for strong callbyneed reduction
Participants: Gabriel Scherer.
External Collaborators: Nathanëlle Courant (INRIA Paris)
In 30 we detail a usecase for strong callbyneed reduction in the OCaml compiler. Strong callbyneed reduction is a sophisticated reduction strategy for programming languages, and to our knowledge all its practical applications known today are in the field of proof assistants. Our usecase is the first sighting of a use for strong callbyneed reduction outside this specific domain.
8 Bilateral contracts and grants with industry
8.1 Bilateral contracts with industry
8.1.1 CIFRE Thesis Inria  Siemens
Participants: Lutz Straßburger, Wendlasida Ouedraogo.

Title:
Optimization of source code for safetycritical systems

Duration:
2020 – 2022

Scientific Responsible:
Lutz Straßburger

Industrial Partner:
Siemens Mobility, Chatillon

Summary:
The goal of the thesis is to develop ways to optimize the performance of software, while not sacrificing the guarantees of safety already provided for nonoptimized code. The software that Siemens is using for their selfdriving trains (e.g. Metro 14 in Paris) is programmed in Ada. Due to the high safety requirements for the software, the used Ada compiler has to be certified. At the current state of the art, only nonoptimized code fulfils all necessary requirements. Because of higher performance needs, we are interested in producing optimized code that also fulfils these reqirements.
Stated most generally, the aim of the thesis is to assure, at the same time:
 optimization of executiontime of safetycritical software — safetycritical software is more prone to bad executiontime performance, because most of its actions involve performing checks (i.e., CPU branch instructions), and
 maintaining the safety guarantees from the input source code to the produced binary code — in general, as soon as we decide to use a compiler optimization, the qualification of the compiler no longer applies.
8.2 Bilateral grants with industry
8.2.1 OCaml Software Foundation
Participants: Gabriel Scherer.
The OCaml Software Foundation (OCSF),4 established in 2018 under the umbrella of the Inria Foundation, aims to promote, protect, and advance the OCaml programming language and its ecosystem, and to support and facilitate the growth of a diverse and international community of OCaml users.
Since 2019, Gabriel Scherer serves as the director of the foundation.
8.2.2 General OCaml funding from Nomadic Labs
Participants: Gabriel Scherer, Olivier Martinot.
Nomadic Labs, a Parisbased company, has implemented the Tezos blockchain and cryptocurrency entirely in OCaml. In 2019, Nomadic Labs and Inria have signed a framework agreement (“contratcadre”) that allows Nomadic Labs to fund multiple research efforts carried out by Inria groups. Within this framework, we participate to the following grants, in collaboration with the projectteam Cambium at INRIA Paris:
Évolution d’OCaml
This grant is intended to fund a number of improvements to OCaml, including the addition of new features and a possible redesign of the OCaml typechecker. This grant funds the PhD thesis of Olivier Martinot on this topic.
Maintenance d’OCaml
This grant is intended to fund the daytoday maintenance of OCaml as well as the considerable work involved in managing the release cycle.
OCamlRust

Title:
OCaml/Rust bindings

Duration:
20212023

Coordinator:
Gabriel Scherer (INRIA Saclay, EPI Partout)

Participants:
Guillaume MunchMaccagnoni (INRIA Rennes, EPI Galinette), JacquesHenri Jourdan (CNRS, LRI)

Partners:
Inria, Nomadic Labs

Inria contact:
Gabriel Scherer

Summary:
We often want to write hybrid programs with components in several different programming languages. Interfacing two languages typically goes through lowlevel, unsafe interfaces. The OCaml/Rust project studies safer interfaces between OCaml and Rust.

Expected Impact:
We investigated safe lowlevel representations of OCaml values on the Rust side, representing GC ownership, and developed a calling convention that reconciles the OCaml FFI idioms with Rust idioms. We also developed Boxroot, a new API to register values with the OCaml GC, for used when interfacing with Rust (and other programming languages) and possibly when writing concurrent programs. This resulted in novel techniques which can benefit other pairs of languages in the future. These works are now integrated in the ocamlrs interface between OCaml and Rust used in the industry.
9 Partnerships and cooperations
9.1 International initiatives
9.1.1 Inria associate team not involved in an IIL or an international program
COMPRONOM

Title:
Combinatorial Proof Normalization

Duration:
2020 >

Coordinator:
Lutz Strassburger , Willem Heijltjes

Partners:
 Inria Saclay (France)
 Université de Bath (RoyaumeUni)
 University College London (RoyaumeUni)

Inria contact:
Lutz Strassburger

Summary:
This project teams up three research groups, one at Inria Saclay, one at the University of Bath, and one at University College London, who are driven by their joint interest in the development of a combinatorial proof theory which is able to treat formal proofs independently from syntactic proof systems. We plan to focus our research in two major directions: First, study the normalization of combinatorial proofs, with possible applications for the implementation of functional programming languages, and second, study combinatorial proofs for the logic of bunched implications, with the possible application for separation logic and its use in the verification of imperative programs.
9.1.2 STIC/MATH/CLIMAT AmSud projects
DyLoMPC

Title:
Dynamic Logics: Model Theory, Proof Theory and Computational Complexity

Duration:
2020–2022

Coordinator:
Carlos Eduardo Areces

Partners:
 Facultad de Matemática, Astronomía, Física y Computación, Universidad Institution Nacional de Córdoba, Argentina [UNCAR]
 Departamento de Ciência da Computação, Universidade Federal do Rio de Janeiro, Brazil [UFRJBR]
 Equipe Partout, Laboratoire d'Informatique de l'Ecole Polytechnique and Inria Saclay, France [LIXFR]
 Laboratoire Spécification et Vérification, ENS ParisSaclay and CNRS, France [LSVFR]

Inria contact:
Lutz Strassburger

Summary:
During the project we will advance our understanding of a novel family of modal logics called dynamic logics. Dynamic logics are characterized by the inclusion of modal operators that can modify the model in which they are being evaluated. This characteristic made them especially well suited for the description of evolving scenarios like, for example, the temporal evolution of a communication network, where connections are dynamically created and eliminated, constantly changing the actual topology. A number of different dynamic logics have been investigated by members of the project, but a general perspective is still missing, and a number of important open questions remains, ranging from adequate model theoretic characterizations, to a proper understanding of how to define proof calculi for this logics, which are usually not closed under uniform substitutions. The project aims to pull together the strengths of the four international research teams, to unify existing results and attempt to answer these open problems .
9.2 International research visitors
9.2.1 Visits to international teams
Research stays abroad
Beniamino Accattoli

Visited institution:
Huawei Research Center, Edinburgh;

Country:
UK;

Dates:
131 July 2022;

Context of the visit:
collaboration with Dan Ghica on the complexity analyses of program transformations at work in compilers for functional languages;

Mobility program/type of mobility:
research stay.
9.3 National initiatives
LambdaComb

Title:
LambdaComb: a cartographic quest between lambdacalculus, logic, and combinatorics

Duration:
2022 – 2026 (4 years)

Coordinator:
Noam Zeilberger

Partners:
 LIX (Ecole Polytechnique), LIPN (Paris Nord), LIS (Marseille), LIGM (MarnelaVallée)
 Jagiellonian University (Poland)

Summary:
LambdaComb is an interdisciplinary project financed by the Agence Nationale de la Recherche (PRC grant ANR21CE480017). Broadly, the project aims to deepen connections between lambda calculus and logic on the one hand and combinatorics on the other. One important motivation for the project is the discovery over recent years of a host of surprising links between subsystems of lambda calculus and enumeration of graphs on surfaces, or "maps", the latter being an active subfield of combinatorics with roots in W. T. Tutte's work in the 1960s. Using these new links and other ideas and tools, the LambdaComb project aims to:
 develop rigorous logical perspectives on maps and related combinatorial objects; and
 develop precise quantitative perspectives on lambda calculus and related systems.
The project also intersects with and aims to shed new light on other established connections between logic and geometry, notably Joyal and Street's categorical framework of string diagrams as well as Girard's proof nets for linear logic.
REPRO

Title:
REPRO: searching for canonical REpresentations of PROgrams.

Duration:
2021 – 2025 (4 years)

Coordinator:
Gabriel Scherer

Summary:
The REPRO project aims to
 deepen our understanding of the structure of computer programs by discovering canonical representations for fundamental programming languages, and to
 explore the application of canonical representations to the problems of program equivalence checking and program synthesis.
CoREACT

Title:
CoREACT: Coqbased Rewriting: towards Executable Applied Category Theory

Duration:
2023 – 2027 (4 years)

Coordinator:
Nicolas Behr

Partners:
IRIF (Université Paris Cité), LIP (ENSLyon), LIX (Ecole Polytechnique), SophiaAntipolis (Inria)

Local participants:
Benjamin Werner , Noam Zeilberger

Summary:
The main objectives of the CoREACT project include:
 Development of a methodology for diagrammatic reasoning in Coq
 Formalization and certification of a representative collection of axioms and theorems for compositional categorical rewriting theory
 Development of a Coqenabled interactive database and wiki system
 Development of a CoREACT wikibased "proofbypointing" engine
 Executable reference prototype algorithms from categorical structures in Coq (via the use of SMT solvers/theorem provers such as Z3)
10 Dissemination
10.1 Promoting scientific activities
10.1.1 Scientific events: organisation
Member of the organizing committees
 Miller is a member of the Steering Committees of LICS, LFMTP, CPP, FLOPS.
 Accattoli is a member of the Steering Committee of PPDP.
 Zeilberger is a member of the Steering Committee of CLA (Computational Logic and Applications).
 Zeilberger organized the kickoff meeting for the ANR LambdaComb, as a hybrid event at Ecole Polytechnique on April 11, 2022.
 Chaudhuri is a member of the steering committee of the International Joint Conference on Automated Reasoning (IJCAR)
Participating in the organization
 Marianela Morales was student volunteer for the ETAPS 2022 conference
10.1.2 Scientific events: selection
Member of the conference program committees
 Miller was on the program committee of CiE 2022: Computability in Europe 2022 (Swansea, UK, July)
 Miller was on the program committee of HCVS2022: Horn Clauses for Verification and Synthesis (Munich, Germany, April).
 Strassburger was on the program committee of IJCAR 2022: International Joint Conference on Automated Reasoning 2022, August 712, Haifa, Israel (part of FLoC 2022)
 Strassburger was on the program committee of CSL'23: Computer Science Logic 2023, Annual conference of the European Association for Computer Science Logic (EACSL), February 1316, 2023, University of Warsaw, Poland
 Accattoli was cochair of PPDP 2022: International Symposium on Principles and Practice of Declarative Programming 2022, 2022 September 2022, Tbilisi, Georgia.
 Accattoli was on the program committee of APLAS 2022: Asian Symposium on Programming Languages and System, 510 December 2022 Auckland, New Zealand.
 Accattoli was on the program committee of LSFA 2022: International Workshop on Logical and Semantic Frameworks, with Applications, 2324 September 2022, Belo Horizonte, Brazil.
 Chaudhuri was on the program committee of IJCAR 2022
 Scherer was on the program committees of ICFP 2022, LFMTP 2022 and the TyDe workshop 2022
Reviewer
 Strassburger was reviewer for the CSL 2022, IJCAR 2022, AiML 2022, and CSL 2023 conferences
 Marianela Morales was reviewer for the CSL 2023 and FoSSaCS 2023 conferences
 Accattoli reviewed papers for CSL 2023 and LICS 2022 (plus APLAS 2022, PPDP 2022, and LSFA 2022, for which he served on the PC).
10.1.3 Journal
Member of the editorial boards
 Miller is a member of the Advisory Board of the new Diamond Open Access electronic journal TheoretiCS, which publishes research work in all areas of Theoretical Computer Science.
 Miller is a member of the Journal of Automated Reasoning, published by Springer (since May 2011).
 Miller is an area editor for “Type Theory for Theorem Proving Systems” of the Journal of Applied Logic, published by Elsevier (since 2003).
Reviewer  reviewing activities
 Strassburger was reviewer for the journal “Mathematical Structures in Computer Science”, the journal “Logical Methods in Computer Science”, and the “Notre Dame Journal of Formal Logic”
 Accattoli reviewed papers for MSCS, Ann. pure and applied logic, LMCS, TOCL.
 Zeilberger was a reviewer for LMCS.
10.1.4 Invited talks
 Miller was an invited speaker at the StrIP KickOff Workshop, University of Birmingham, June 710, 2022.
 Strassburger was an invited speaker at the workshop on Logic and transdiciplinarity: Mathematics/Computer Science/Philosophy/Linguistics: 711 February 2022 CIRM, Marseille, France. Part of thematic month "Logic and Interactions"
 Strassburger was an invited speaker at the StrIP KickOff Workshop, University of Birmingham, June 710, 2022.
 Zeilberger gave an invited talk for the Topos Institute Colloquium on June 30, 2022.
 Zeilberger was an invited speaker at the 3rd Workshop on Proofs, Computation, and Meaning, held online December 7, 2022.
 Clarke gave an invited talk for the Topos Institute Colloquium on November 3, 2022.
 Chaudhuri was an invited speaker at the ENS Saclay for the seminar organized by the LMF/UPSCaLe (Digicosme) project
10.1.5 Scientific expertise
 Miller reviewed research projects for the Austrian Science Fund (FWF), the Icelandic Research Fund (RANNIS), and the Swiss National Science Foundation.
10.1.6 Involvement in partner institutions
 Benjamin Werner is member of the executive boards (conseils d'administration) of both Ecole polytechnique and Institut Polytechnique de Paris. He is also member of the executive committee of the CS department of Ecole polytechnique.
 Kaustuv Chaudhuri is an elected member of the Conseil de Laboratoire of LIX
 Giti Omidvar is an elected member of the Conseil de Laboratoire of LIX
10.2 Teaching  Supervision  Juries
10.2.1 Teaching
 Strassburger was teaching a course "From Axioms to Rules — The Factory of Modal Proof Systemsrial Proofs" at ESSLLI 2022.

Wendlasida Ouedraogo was teaching assistant for the courses
 INF442  Algorithmes pour l'analyse de données en C++ (10h)
 INF411  Les bases de la programmation et de l'algorithmique (12h)
 INF361  Introduction à l' informatique (40h)
 INF592  Internship in Data Science (2h)
at Ecole Polytechnique
 Miller was an instructor for MPRI (Master Parisien de Recherche en Informatique) in the Course 21: Logique linéaire et paradigmes logiques du calcul. He taught 15 hours during Fall 2022.
 Noam Zeilberger taught the third year undergraduate course "Functional Programming" in the Bachelors program at Ecole Polytechnique, and was a teaching assistant for the second year polytechnicien course INF412 "Fondements de l'informatique".
 Accattoli was an instructor for MPRI (Master Parisien de Recherche en Informatique) in the Course 21: Logique linéaire et paradigmes logiques du calcul. He taught 15 hours.
 Chaudhuri taught the third year undergraduate course "CSE 302: Compiler Design" at the Ecole polytechnique.
 Marianela Morales was teaching assistant at the course Computer Programming at École Polytechnique (CSE101), second semester of Bachelor of Science 1
 Benjamin Werner is responsible for the course INF371 "Mécanismes de la Programation OrientéeObjet" for first year students of the engineering program of Ecole polytechnique (190 students, 8 TAs).
 Benjamin Werner is teaching the CSE203 course "Proofs and Programs" of the Bachelor Program of Ecole polytechnique.
 Gabriel Scherer taught the first year course "Introduction à la Programmation Fonctionnelle" at Université VincennesSaintDenis (Paris 8).
 Gabriel Scherer taught for MPRI in the course 24 (functional programming and type systems).
10.2.2 Supervision
 Miller is supervising three Ph.D. students: Farah Al Wardani, Matteo Manighetti, and JuiHsuan Wu.
 Strassburger is supervising three PhD students: Marianela Morales, Giti Omidvar, Wendlasida Ouedraogo
 Strassburger supervised one Bachelor student: Remy Seassau
 Accattoli is supervising one PhD student, Adrienne Lancelot, since October 2022
 Accattoli supervised the internship of Adrienne Lancelot, MaySeptember 2022.
 Zeilberger has been supervising two PhD students Nicolas Blanco and Alexandros Singh. Singh successfully defended his thesis on November 15, 2022, and Blanco is expected to defend his thesis in February 2023.
 Chaudhuri is cosupervising the PhD student Farah Al Wardani. He is also supervising the Bachelor student Luigi Massacci at the Ecole Polytechnique.
 Scherer is supervising a PhD student, Olivier Martinot.
10.2.3 Juries
 Miller was the present of the jury for Gabriel Hondet, University of ParisSaclay, 27 September 2022.
10.3 Popularization
10.3.1 Internal or external Inria responsibilities
 Strassburger is member of the BCEP at Inria Saclay
 Scherer is a member of the CLHSCT at Inria Saclay
10.3.2 Interventions
 Scherer participated to the "Fête de la science" as an INRIA researcher, introducing computer science concepts to students aged from 10 to 16.
11 Scientific production
11.1 Major publications
 1 articleMulti types and reasonable space.Proceedings of the ACM on Programming Languages6ICFPAugust 2022, 799825
 2 inproceedingsReasonable Space for the λCalculus, Logarithmically.LICS 2022  37th Annual ACM/IEEE Symposium on Logic in Computer ScienceHaifa, IsraelACMAugust 2022, 113
 3 inproceedingsExponentials as Substitutions and the Cost of Cut Elimination in Linear Logic.LICS '22: 37th Annual ACM/IEEE Symposium on Logic in Computer ScienceHaifa Israel, FranceACMAugust 2022, 115
 4 articleAn Analytic Propositional Proof System On Graphs.Logical Methods in Computer Science184October 2022
 5 inproceedingsNormalization Without Syntax.FSCD 2022Haifa, IsraelAugust 2022
 6 articleFrom axioms to synthetic inference rules via focusing.Annals of Pure and Applied Logic1735May 2022, 103091
 7 inproceedingsParsing as a lifting problem and the ChomskySchützenberger representation theorem.MFPS 2022  38th conference on Mathematical Foundations for Programming SemanticsIthaca, NY, United StatesJuly 2022
 8 inproceedingsBV and Pomset Logic Are Not the Same.30th EACSL Annual Conference on Computer Science Logic, CSL 2022Göttingen, GermanyFebruary 2022
11.2 Publications of the year
International journals
 9 articleMulti types and reasonable space.Proceedings of the ACM on Programming Languages6ICFPAugust 2022, 799825
 10 articleThe theory of callbyvalue solvability.Proceedings of the ACM on Programming Languages6ICFPAugust 2022, 855885
 11 articleAn Analytic Propositional Proof System On Graphs.Logical Methods in Computer Science184October 2022
 12 articleDebootstrapping without Archeology.The Art, Science, and Engineering of Programming63February 2022
 13 articleFrom axioms to synthetic inference rules via focusing.Annals of Pure and Applied Logic1735May 2022, 103091
International peerreviewed conferences
 14 inproceedingsReasonable Space for the λCalculus, Logarithmically.LICS 2022  37th Annual ACM/IEEE Symposium on Logic in Computer ScienceHaifa, IsraelACMAugust 2022, 113
 15 inproceedingsExponentials as Substitutions and the Cost of Cut Elimination in Linear Logic.LICS '22: 37th Annual ACM/IEEE Symposium on Logic in Computer ScienceHaifa Israel, FranceACMAugust 2022, 115
 16 inproceedingsUseful Open CallByNeed.CSL 2022  30th EACSL Annual Conference on Computer Science Logic201630th EACSL Annual Conference on Computer Science Logic (CSL 2022)Gottingen, GermanyFebruary 2022
 17 inproceedingsA Graphical Proof Theory of Logical Time.7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)Haifa, IsraelAugust 2022
 18 inproceedingsCombinatorial Proofs for Constructive Modal Logic.Advances in Modal Logic 2022Rennes, FranceAugust 2022
 19 inproceedingsTaming Bounded Depth with Nested Sequents.Advances in Modal Logic 2022Rennes, FranceAugust 2022
 20 inproceedingsNormalization Without Syntax.FSCD 2022Haifa, IsraelAugust 2022
 21 inproceedingsA positive perspective on term representation: Extended paper.CSL 2023: Computer Science LogicWarsaw, PolandFebruary 2023
 22 inproceedingsBV and Pomset Logic Are Not the Same.30th EACSL Annual Conference on Computer Science Logic, CSL 2022Göttingen, GermanyFebruary 2022
 23 inproceedingsCombinatorial Flows as Bicolored Atomic Flows.Logic, Language, Information, and Computation  28th International Workshop, WoLLIC 202213468Lecture Notes in Computer ScienceIaşi, RomaniaSpringer International PublishingSeptember 2022, 141157
National peerreviewed Conferences
 24 inproceedingsDéboîter les constructeurs.Journées Francophones des Langages ApplicatifsSaintMédardd'Excideuil, FranceFebruary 2022
 25 inproceedingsActema : une interface graphique et gestuelle pour preuves formelles (démonstration).Journées Francophones des Langages Applicatifs33èmes Journées Francophones des Langages ApplicatifsSaintMédardd'Excideuil, FranceFebruary 2022, 267268
 26 inproceedingsBacktracking reference stores.Journées Francophones des Langages ApplicatifsJFLA 2023  34èmes Journées Francophones des Langages ApplicatifsPrazsurArly, FranceJanuary 2023, 190210
Conferences without proceedings
 27 inproceedingsA draganddrop proof tactic.CPP 2022: 11th ACM SIGPLAN International Conference on Certified Programs and ProofsPhiladelphia, United StatesACM; ACMJanuary 2022, 197209
 28 inproceedingsParsing as a lifting problem and the ChomskySchützenberger representation theorem.MFPS 2022  38th conference on Mathematical Foundations for Programming SemanticsIthaca, NY, United StatesJuly 2022
 29 inproceedingsBoxroot, fast movable GC roots for a better FFI.ML Family WorkshopLjubljana, SloveniaSeptember 2022
 30 inproceedingsAn OCaml use case for strong callbyneed reduction.ACM SIGPLAN Workshop on ML 2022  ML Family WorkshopLjubljana, SloveniaSeptember 2022
Reports & preprints
 31 miscDistributing and trusting proof checking: a preliminary report.December 2022
 32 miscAn introduction to enriched cofunctors.September 2022
 33 miscComputational logic based on linear logic and fixed points.February 2022
 34 miscA System of Interaction and Structure III: The Complexity of BV and Pomset Logic.2022
 35 reportCoqlex: Generating Formally Verified Lexers.INRIA Saclay  IledeFrance2022
11.3 Cited publications
 36 inproceedingsSubformula Linking as an Interaction Method.4th Conference on Interactive Theorem Proving7998Lecture Notes in Computer ScienceRennes, FranceSpringerJuly 2013, 386401