2023Activity reportProject-TeamPICUBE

3.1.1 Towards the calculus of constructions

The $\lambda$-calculus, defined by Church  42, is a remarkably succinct model of computation that is defined via only three constructions (abstraction of a program with respect to one of its parameters, reference to such a parameter, application of a program to an argument) and one reduction rule (substitution of the formal parameter of a program by its effective argument). The $\lambda$-calculus, which is Turing-complete, i.e. which has the same expressiveness as a Turing machine (there is for instance an encoding of numbers as functions in $\lambda$-calculus), comes with two possible semantics referred to as call-by-name and call-by-value evaluations. Of these two semantics, the first one, which is the simplest to characterise, has been deeply studied in the last decades  26.

To explain the Curry-Howard correspondence, it is important to distinguish between intuitionistic and classical logic: following Brouwer at the beginning of the 20th century, classical logic is a logic that accepts the use of reasoning by contradiction while intuitionistic logic proscribes it. Then, Howard's observation is that the proofs of the intuitionistic natural deduction formalism exactly coincide with programs in the (simply typed) $\lambda$-calculus.

A major achievement has been accomplished by Martin-Löf who designed in 1971 a formalism, referred to as modern type theory, that was both a logical system and a (typed) programming language  68.

In 1985, Coquand and Huet  45, 43 in the Formel team of INRIA-Rocquencourt explored an alternative approach based on Girard-Reynolds' system $F$  55, 72. This formalism, called the Calculus of Constructions, served as logical foundation of the first implementation of Coq in 1984. Coq was called CoC at this time.

3.1.2 The Calculus of Inductive Constructions

The first public release of CoC dates back to 1989. The same project-team developed the programming language Caml (nowadays called OCaml and coordinated by the Gallium team) that provided the expressive and powerful concept of algebraic data types (a paragon of it being the type of lists). In CoC, it was possible to simulate algebraic data types, but only through a not-so-natural not-so-convenient encoding.

In 1989, Coquand and Paulin  44 designed an extension of the Calculus of Constructions with a generalisation of algebraic types called inductive types, leading to the Calculus of Inductive Constructions (CIC) that started to serve as a new foundation for the Coq system. This new system, which got its current definitive name Coq, was released in 1991.

In practice, the Calculus of Inductive Constructions derives its strength from being both a logic powerful enough to formalise all common mathematics (as set theory is) and an expressive richly-typed functional programming language (like ML but with a richer type system, no effects and no non-terminating functions).

3.6.1 The underlying logic and the verification kernel

The architecture adopts the so-called de Bruijn principle: the well-delimited kernel of Coq ensures the correctness of the proofs validated by the system. The kernel is rather stable with modifications tied to the evolution of the underlying Calculus of Inductive Constructions formalism. The kernel includes an interpreter of the programs expressible in the CIC and this interpreter exists in two flavours: a customisable lazy evaluation machine written in OCaml and a call-by-value bytecode interpreter written in C dedicated to efficient computations. The kernel also provides a module system.

3.6.2 Programming and specification languages

The concrete user language of Coq, called Gallina, is a high-level language built on top of the CIC. It includes a type inference algorithm, definitions by complex pattern-matching, implicit arguments, mathematical notations and various other high-level language features. This high-level language serves both for the development of programs and for the formalisation of mathematical theories. Coq also provides a large set of commands. Gallina and the commands together forms the Vernacular language of Coq.

3.6.3 Standard library

The standard library is written in the vernacular language of Coq. There are libraries for various arithmetical structures and various implementations of numbers (Peano numbers, implementation of $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$ with binary digits, implementation of $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$ using machine words, axiomatisation of $ℝ$). There are libraries for lists, list of a specified length, sorts, and for various implementations of finite maps and finite sets. There are libraries on relations, sets, orders.

3.6.4 Tactics

The tactics are the methods available to conduct proofs. This includes the basic inference rules of the CIC, various advanced higher level inference rules and all the automation tactics. Regarding automation, there are tactics for solving systems of equations, for simplifying ring or field expressions, for arbitrary proof search, for semi-decidability of first-order logic and so on. There is also a powerful and popular untyped scripting language for combining tactics into more complex tactics.

Note that all tactics of Coq produce proof certificates that are checked by the kernel of Coq. As a consequence, possible bugs in proof methods do not hinder the confidence in the correctness of the Coq checker. Note also that the CIC being a programming language, tactics can have their core written (and certified) in the own language of Coq if needed.

3.6.5 Extraction

Extraction is a component of Coq that maps programs (or even computational proofs) of the CIC to functional programs (in OCaml, Scheme or Haskell). Especially, a program certified by Coq can further be extracted to a program of a full-fledged programming language then benefiting of the efficient compilation, linking tools, profiling tools, ... of the target language.

3.6.6 Documentation

Coq is a feature-rich system and requires extensive training in order to be used proficiently; current documentation includes the reference manual, the reference for the standard library, as well as tutorials, and related tooling [sphinx plugins, coqdoc]. The jsCoq tool allows writing interactive web pages were Coq programs can be embedded and executed.

3.6.7 Proof development infrastructure

Coq is used in large-scale proof developments, and provides users miscellaneous tooling to help with them: the coq_makefile and Dune build systems help with incremental proof-checking; the Coq OPAM repository contains a package index for most Coq developments; the CoqIDE, ProofGeneral, jsCoq, and VSCoq user interfaces are environments for proof writing; and the Coq's API does allow users to extend the system in many important ways. Among the current extensions we have QuickChik, a tool for property-based testing; STMCoq and CoqHammer integrating Coq with automated solvers; ParamCoq, providing automatic derivation of parametricity principles; MetaCoq for metaprogramming; Equations for dependently-typed programming; SerAPI, for data-centric applications; etc... This also includes the main open Coq repository living at Github.

3.7.1 Formalisation of mathematics.

We will work for this in a proactive way, in close collaboration with IRIF and IMJ-PRG gathering motivated mathematicians and computer scientists willing to formalise the mathematics they teach at the University, or on which they conduct their research work. Indeed, we aim at formalising classical mathematics curricula, pieces of contemporary mathematics as well as mathematical tools implemented in theoretical computer science. We will draw inspiration from the usually heuristic practice of mathematics, aiming to make the writing and reading of Coq documents altogether more intuitive, more straightforward and more flexible. This software development and mechanisation work will be combined with a study of the linguistic structure of mathematical documents, in collaboration with Philippe de Groote (Sémagramme): we think that there is a need to better understand the linguistic structures at work in the daily life of a mathematician and their formal nature.

More specifically, among the subjects of formalisation of mathematics we plan to carry in the team, three in particular should be mentioned:

• On the mathematical side, formalisation of parts of contemporary mathematics, in connection with members of the IMJ-PRG.
• On the CS side, we plan to formalise and certify algorithms on graphs (Jean-Jacques Lévy), with the aim of establishing links with other IRIF members working on graph algorithms, in particular with Laurent Viennot; we also intend to certify developments in the theory of automata and formal languages ​​or proof theory as used at IRIF, in particular with Thomas Colcombet.
• We also plan to contribute to an ambitious formalisation project aiming at designing a large Coq mathematical library covering undergraduate mathematics. This project is of course of a broader scope and will involve other research teams, within INRIA or elsewhere in France and abroad.

This research topic will therefore be based at the same time on a formalisation activity internal to the team, and on a long-term work of animation and construction of a scientific community involved in formalisation. We plan to contribute to the Coq training of our maths and CS colleagues (from PhD students to post-docs and those holding a permanent position), and not only grad students as it is more commonly the case, in particular through the organisation of regular sessions of working groups dedicated to helping colleagues in their formalisation tasks and by considering the opportunity to set up thematic schools in collaboration with the other teams of the institute contributing to Coq. A medium-term objective could be to achieve that some pure mathematics modules are based directly on formalised content and that some mathematics tutorials take the form of Coq exercise sessions, starting from existing works on Coq  29, 70, 41. This will require to develop close collaborations with the different communities of other proof assistants, especially those designed to be well-adapted to the formalisation of mathematics (Lean, Isabelle and Agda in particular). Understanding linguistic aspects of mathematical proofs will be a key to the success of our project.

3.7.2 Linguistics of proofs.

Formalising inevitably leads to a shift of perspective on what a mathematical proof is. From a mathematical standpoint, it is conventional, even if developments are emerging, to be satisfied of the mere possibility of a formalisation (which is never even sketched out) typically in the set-theoretical formalism, and to focus on the construction of a natural language discourse that is precise enough to convince the reader. From the proof assistant standpoint, the seminal vision which initially aimed only at making effective this virtuality, tends to evolve. New lines of communication and convergence are emerging: a proof is no longer strictly made up of logical inference rules, such as introducing or eliminating a connective, but it is made of more abstract entities such as the use of a lemma, the replacement of equals by equals, reasoning by induction, simplifying a polynomial expression, decomposing a formula in atoms, etc. With the arrival of a new generation of interactive proof engines  77, 27, a proof is no longer seen strictly as a tree derivation, but as a graph whose nodes can be refined with a reasonable degree of freedom; moreover, the order in which these transformations are applied interactively appears in the “incremental” format of the machine maths document. This is in line with the historical evolution of proof methods in order to escape from the “low level” of logic and get closer to more abstract conceptual levels used by humans. Our investigations will follow this line as we plan to analyse the linguistic structure of mathematical texts, with the ambition to develop the levels of abstraction which would eventually allow a direct formal understanding of a mathematical text at the level of mathematical discourse in which it is expressed. Examples of the sorts of linguistic structures we plan to analyse are “reasoning by analogy”, reasoning modulo isomorphism, or even modulo inclusion, and of course reasoning modulo general equational theories in general.

On this natural (mathematical) language processing part, we plan a collaboration with Philippe de Groote of the Sémagramme team (Inria Nancy & Loria), to identify the necessary structures for a flexible formalisation of vernacular mathematical proofs in order to implement this linguistic structure within Coq, procedural and discursive in nature rather than tree-like as described above. One of the objectives will be to be able to formalise in a more transparent and direct way mathematical texts, such Bourbaki's Éléments de mathématiques.

Regarding the design and development of a general mathematical library, it is undoubtedly too early to describe the directions we will take, but we have some ongoing discussions with Assia Mahboubi (Gallinette), Yves Bertot and Cyril Cohen (Scalp) around these essential questions. We also wish to develop the team's scientific interactions with Michael Soegtrop (Apple) and we closely follow his projects on proving algorithms of symbolic computing, around constructive reals and the formal integrator Rubi. We are also in contact with mathematicians from IMJ-PRG, and in particular with Antoine Chambert-Loir, who expressed a keen interest in formalisation.

We want to develop fruitful discussions with the communities of other proof assistants, such as Agda, Isabelle or Lean.

3.8.1 Higher-dimensional algebra

Like ordinary categories, higher-dimensional categorical structures originate in algebraic topology. Indeed, $\infty$-groupoids have been initially considered as a unified point of view for all the information contained in the homotopy groups of a topological space $X$: the fundamental $\infty$-groupoid$\Pi \left(X\right)$ of $X$ contains the elements of $X$ as 0-dimensional cells, continuous paths in $X$ as 1-cells, homotopies between continuous paths as 2-cells, and so on. This point of view translates a topological problem (to determine if two given spaces $X$ and $Y$ are homotopically equivalent) into an algebraic problem (to determine if the fundamental groupoids $\Pi \left(X\right)$ and $\Pi \left(Y\right)$ are equivalent).

In the last decades, the importance of higher-dimensional categories has grown fast, mainly with the new trend of categorification that currently touches algebra and the surrounding fields of mathematics. Categorification is an informal process that consists in the study of higher-dimensional versions of known algebraic objects (such as higher Lie algebras in mathematical physics 24) and/or of “weakened” versions of those objects, where equations hold only up to suitable equivalences (such as weak actions of monoids and groups in representation theory 49).

The categorification process has also reached logic, with the introduction of homotopy type theory. After a preliminary result that had identified categorical structures in type theory 64, it has been observed recently that the so-called “identity types” are naturally equiped with a structure of $\infty$-groupoid: the 1-cells are the proofs of equality, the 2-cells are the proofs of equality between proofs of equality, and so on. The striking resemblance with the fundamental $\infty$-groupoid of a topological space led to the conjecture that homotopy type theory could serve as a replacement of set theory as a foundational language for different fields of mathematics, and homotopical algebra in particular.

3.8.2 Higher-dimensional rewriting

Higher-dimensional categories are algebraic structures that contain, in essence, computational aspects. This has been recognised by Street 78, and independently by Burroni 36, when they have introduced the concept of computad or polygraph as combinatorial descriptions of higher categories. Those are directed presentations of higher-dimensional categories, generalising word and term rewriting systems.

In the recent years, the algebraic structure of polygraph has led to a new theory of rewriting, called higher-dimensional rewriting, as a unifying point of view for usual rewriting paradigms, namely abstract, word and term rewriting 66, 67, 59, 60, and beyond: Petri nets 62 and formal proofs of classical and linear logic have been expressed in this framework 61. Higher-dimensional rewriting has developed its own methods to analyse computational properties of polygraphs, using in particular algebraic tools such as derivations to prove termination, which in turn led to new tools for complexity analysis 32.

8.1.1 Proof-theory of logics with induction and coinduction.

Saurin has completed the line of work aiming at building a full fledge circular proof theory with two new results:

The cut-elimination result for $\mu {\mathrm{𝖬𝖠𝖫𝖫}}^{\infty }$ has been extended to extended to full $\mu {\mathrm{𝖫𝖫}}^{\infty }$ by Saurin 12, by studying the properties of a well-known fixed-point encoding of LL exponentials. This allows, using techniques from infinitary rewriting, to lift $\mu {\mathrm{𝖬𝖠𝖫𝖫}}^{\infty }$ cut-elimination result to $\mu {\mathrm{𝖫𝖫}}^{\infty }$. As a by-product, cut-elimination for non-wellfounded $\mu {\mathrm{𝖫𝖩}}^{\infty }$ and $\mu {\mathrm{𝖫𝖪}}^{\infty }$ was obtained as well. This approach is quite robust w.r.t. modifications of the validity conditions, allowing for instance to be adapted to bouncing validity. This approach also sheds a new light on LL exponentials by providing a natural setting in which non-uniform exponentials do live. This last point was the topics of the LMFI M2 internship of Adrien Shalit jointly supervised by Petrisan and Saurin during the spring and summer 2023.

Together with Bauer, Saurin finally completed the above result providing the first syntactic cut-elimination result for a (circular) proof system containing the full modal $\mu$-calculus: to achieve this, they design a linear version of the modal $\mu$-calculus and prove cut-elimination for a family of linear fixed-point logics with super-exponential, building on previous results by Bauer and Laurent. This result not-only allows to cover the case of the modal $\mu$-calculus but also treat most of the known light logics in the literature, extended with least and greatest fixed-points. A pre-print is available and currently submitted.

8.1.2 Reversible computation with inductive types

Chardonnet, Saurin and Valiron developed a term calculus for a class of type isomorphisms for circular $\mu {\mathrm{𝖬𝖠𝖫𝖫}}^{\infty }$, from which they extract a language for reversible computation with inductive types  9, 39. In the paper published at CSL 2023, they studied the expressiveness of the reversible calculus, its connection with type isomorphisms of circular $\mu {\mathrm{𝖬𝖠𝖫𝖫}}^{\infty }$, providing a first step before moving forward to modelling quantum computations with structured datatypes.

8.1.3 Comparing finitary and infinitary proof systems for $\mu \mathrm{𝖬𝖠𝖫𝖫}$.

Following up on their previous work with Das on the decision problems for various fragments of $\mu \mathrm{𝖬𝖠𝖫𝖫}$  48, they compared in a new work the relative expressivity, at the provability level, of the (finitely-branching) non-wellfounded proofs, $\mu {\mathrm{𝖬𝖠𝖫𝖫}}^{\infty }$, with infinitely branching well-founded proofs built on the language of $\mu \mathrm{𝖬𝖠𝖫𝖫}$. With this aim, they could establish that $\mu {\mathrm{𝖬𝖠𝖫𝖫}}^{\infty }$ is strictly contained in $\mu {\mathrm{𝖬𝖠𝖫𝖫}}_{\omega }$ with, as an immediate consequence, that $\mu {\mathrm{𝖬𝖠𝖫𝖫}}^{\infty }$ does not enjoy a finite model property in any adequate semantics. Those results have been presented and published at FSTTCS 2023  47.

8.1.4 Controlling sequentialization in proof nets.

In a collaboration with Aurore Alcolei and Luc Pellissier, published at MFPS 2023 5, Alexis Saurin internalized the notion of jumps of linear logic proof-nets (which can be used as an alternative to boxes) in a slight extension of MLL (multiplicative linear logic). Jumps, which have been extensively studied by Faggian and di Giamberardino (building on prior work by Curien and Faggian on L-nets), can express intermediate degrees of sequentialization between a sequent calculus proof and a fully desequentialized proof-net. The logical strength of jumps is analyzed by internalizing them in an extension of MLL where axioms on a specific formula introduce constraints on the possible sequentializations. The jumping formula needs to be treated non-linearly, which is done either axiomatically, or by embedding it in a very controlled fragment of multiplicative-exponential linear logic, uncovering the exponential logic of sequentialization.

8.1.5 An operadic account of context-free grammars and languages

Melliès and Zeilberger develop in 10 a categorical framework based on non-symmetric operads (= multicategories) to describe context-free grammars and establish the Chomsky-Schützenberger representation theorem for context-free languages. In this approach, a context-free grammar is defined as a functor from an operad freely generated by a species of production rules, to an operad of spliced words introduced for the first time in this paper. A notion of automaton on a category $𝒞$ generalising the usual notion of automaton on words is formulated there as a functor from $𝒬\to 𝒞$ satisfying a unique-factorisation-lifting as well as a fibrewise finiteness property, where $𝒬$ describes the category of runs over the automaton. One main benefit of the approach is that it provides a more high-level account of traditional aspects of automata-theory. In particular, the fact that the intersection of a context-free language with a regular language is context-free is derived from the fact that pullbacks computed in the category of operads preserves context-free grammars seen as functors. Similarly, the Chomsky-Schützenberger representation theorem is derived from the observation that the functor which turns a category into its spliced arrow operad has a left adjoint functor which turns any operad to its category of contours. In particular, the fact that the unit of the adjunction transports every operad to its spliced operad of contours platys a fundamental role in the argument. This work is part of a long-term project of integrating refinement systems, environment machines and automata theory in a single and unified framework.

8.2.1 Coherent differentiation

Differential Linear Logic (DiLL) has been introduced by Ehrhard and Regnier in the mid 2000's. This extension of linear logic provides a new interpretation of the exponentials, turning them into a modality related to communication rather than to the sole resource replicability and erasing. DiLL also provided a new understanding of resource calculi and of intersection types, allowing to apply to programs and proofs an operation of approximation which is a syntactic version of the standard Taylor expansion of functions. Until 2021, it seemed that DiLL was doomed to feature a strong form of nondeterminism due to the interaction between differentiation and the structural rule of contraction (Leibniz rule), making it incompatible with stable or sequential denotational interpretations of programs. The article 3 presents Coherent Differentiation, a new denotational setting discovered in 2021, featuring differentiation operations while being compatible with stable and sequential interpretations. A syntactic account of this new approach to differentiation has also been proposed by the author in a subsequent paper.

8.2.2 Causality structures in probabilistic rewriting

The question of describing the causal structure of symbolic rewriting systems such as the lambda-calculus is at the heart of an old and vibrant connection established in the 1980s between proof theory and concurrency theory. The idea is that the process of reducing beta-redexes generates causal structures similar to what one finds in Petri nets and process calculi such as CCS or the $\pi$-calculus. Typically, the reduction of one beta-redex $u$ can create a beta-redex $v$ whose reduction can in turn create a third beta-redex $w$, and so on. These causal structures give rise to the notion of family designed by Jean-Jacques Lévy in his theory of optimality. They also appear in term rewriting and graph rewriting and play a fundamental role in the description of the stochastic behaviour of probabilistic rewriting. Together with Nicolas Behr (IRIF) and Noam Zeilberger (LIX), Melliès has developed in 8 a framework where these causality structures can be described in a unified way in the language of double categories. The idea is to compose rewriting rules seen as representable presheaves under the action of context extension. Composition is defined using a generalisation to double categories of the usual Day convolution tensor product of presheaves on a monoidal category. One main novelty of the work is to integrate for the first time unification and rewriting in the same categorical framework.

In joint work with van Gool, Melliès and Moreau introduced in 4 a notion of profinite $\lambda$-calculus which provides a new topological account of $\lambda$-terms, different from the usual Scott domain topology and based on new insights on the connection between typed $\lambda$-calculus and automata theory. The construction provides to every type $A$ a compactification of the set of $\lambda$-terms of type $A$ defined as a profinite limit of the interpretations of the type $A$ in the category of finite sets. The profinite limit may be also understood as providing the Stone dual of the boolean algebra of regular languages of $\lambda$-terms of type $A$ introduced by Salvati 74. The categorical definition of profinite $\lambda$-terms is identified in 4 with a definition based on parametricity. This establishes an important and unexpected connection between polymorphism and automata theory. The profinite completion of the Church encoding of finite words in a given alphabet $\Sigma$ is shown to coincide with the usual notion of profinite monoid. Then, in the continuation of this work, Moreau establishes in joint work with Nguyen 11 that the definition of regular language of simply typed $\lambda$-terms does not depend on the choice of (locally finite) cartesian closed category where the $\lambda$-calculus is interpreted, as long as the category of interpretation has enough points. They also establish the important unifying result that the semantic definition by Salvati  74 of regular languages of simply typed $\lambda$-terms coincides with the purely syntactic definition by Hillebrand and Kanellakis 63.

8.3.1 Survey on the Coq community

The goal of the article 6 is to better understand Coq users and community, and to make informed decisions about the research and development challenges around a system such as Coq. A key point on the paper is the multidisciplinary research team, bringing together researchers from several areas in Computer and Social sciences. Inspired by previous Surveys in Coq, OCaml, and open source world, a survey was designed and ran for the Coq community totaling 109 questions, and obtaining 466 answers, to this date, the largest survey done on users of Interactive Theorem Provers. The data were analyzed using rigorous regression methods common on the social sciences.

10.1.1 Participation in other International Programs

Thomas Ehrhard chairs the french-italian GDRI on Linear Logic which is finishing this year. Paul-André Melliès and Alexis Saurin are also members of the GDRI.

Thomas Ehrhard and Paul-André Melliès are international members of the EPSRC project "Resources in Computation" chaired by Samson Abramsky (UCL) and Anuj Dawar (Cambridge).

Olivier Laurent

• Status
  Senior Researcher
• Institution of origin:
  ENS Lyon, CNRS
• Country:
  France
• Dates:
  25 January 2023
• Context of the visit:
  He participated as an examiner in Farzad Jafarrahmani's PhD thesis defence.

Nicola Gambino

• Status
  Senior Researcher
• Institution of origin:
  University of Leeds
• Country:
  United Kingdom
• Dates:
  from 24 to 26 January 2023
• Context of the visit:
  He participated as an examiner in Farzad Jafarrahmani's PhD thesis defence.

Christine Tasson

• Status
  Senior Researcher
• Institution of origin:
  Sorbonne Université
• Country:
  France
• Dates:
  from 24 to 27 January 2023
• Context of the visit:
  She participated as an examiner in Farzad Jafarrahmani's PhD thesis defence.

Marcelo Fiore

• Status
  Senior Researcher
• Institution of origin:
  University of Cambridge
• Country:
  United Kingdom
• Dates:
  from 24 to 25 January 2023
• Context of the visit:
  He participated as an examiner in Farzad Jafarrahmani's PhD thesis defence.

Ali Caglayan

• Status
  PhD Thesis
• Institution of origin:
  University of Gothenburg
• Country:
  Sweden
• Dates:
  from 30 January to 2 February 2023
• Context of the visit:
  He worked with Emilio Gallego on the Coq proof development.

Nima Rasekh

• Status
  Postdoc student
• Institution of origin:
  Max Planck Institute for Mathematics in Bonn
• Country:
  Germany
• Dates:
  from 17 to 23 February 2023
• Context of the visit:
  He gave a talk at the semantics working group and worked with El Mehdi Cherradi on a joint paper.

Ambroise Lafont

• Status
  Postdoc student
• Institution of origin:
  University of Cambridge
• Country:
  United Kingdom
• Dates:
  from 19 to 24 March 2023
• Context of the visit:
  He worked with the members of the Picube team.

Olivier Laurent

• Status
  Postdoc student
• Institution of origin:
  Max Planck Institute for Mathematics in Bonn
• Country:
  France
• Dates:
  3 April 2023
• Context of the visit:
  He worked with the members of the Picube team.

André Joyal

• Status
  Senior Researcher
• Institution of origin:
  Université de Québec à Montréal
• Country:
  Canada
• Dates:
  from 28 May to 12 June 2023
• Context of the visit:
  He worked with the members of the Picube team on the semantics of homotopy type theory.

Aurore Alcolei

• Status
  Postdoc student
• Institution of origin:
  Universita degli Studi di Bologna,
• Country:
  Italy
• Dates:
  from 30 June to 5 July 2023
• Context of the visit:
  She worked with Alexis Saurin on a joint paper.

11.1.1 Scientific events: organisation

11.1.2 Scientific events: selection

11.1.3 Invited talks

Paul-André Melliès gave an invited lecture in Nice as part of the "Journées Homotopiques" on the occasion of Clemens Berger's 60th birthday.

Paul-André Melliès gave an invited lecture at the "Resources and Co-Resources" workshop at the University of Cambridge from 17 to 19 July 2023.

Alexis Saurin gave an invited tutorial at TLLA 2023, 7th International Workshop on Trends in Linear Logic and Applications, Roma, 1 and 2 July 2023.

11.1.4 Leadership within the scientific community

Alexis Saurin is co-chair of the Scalp working group in GDR-IM (GT Scalp).

11.2.1 Supervision

International journals

• 3 articleT.Thomas Ehrhard. Coherent differentiation.Mathematical Structures in Computer Science334-5April 2023, 259-310HALDOIback to text
• 4 articleS.Sam van Gool, P.-A.Paul-André Melliès and V.Vincent Moreau. Profinite lambda-terms and parametricity.Electronic Notes in Theoretical Informatics and Computer ScienceVolume 3 - Proceedings of MFPS XXXIXNovember 2023HALDOIback to textback to text

International peer-reviewed conferences

• 5 inproceedingsA.Aurore Alcolei, L.Luc Pellissier and A.Alexis Saurin. The exponential logic of sequentialization.EnticsMFPS XXXIX - 39th Conference on the Mathematical Foundations of Programming SemanticsVolume 3 - Proceedings of ENTiCSBloomington (Indiana), United StatesNovember 2023HALDOIback to text
• 6 inproceedingsA.Ana de Almeida Borges, A. C.Annalí Casanueva Artís, J.-R.Jean-Rémy Falleri, E. J.Emilio Jesús Gallego Arias, É.Érik Martin-Dorel, K.Karl Palmskog, A.Alexander Serebrenik and T.Théo Zimmermann. Lessons for Interactive Theorem Proving Researchers from a Survey of Coq Users.Leibniz International Proceedings in Informatics14th International Conference on Interactive Theorem Proving (ITP 2023)268Leibniz International Proceedings in Informatics (LIPIcs)12Białystok, PolandDagstuhl Publishing2023, 1-18HALDOIback to text
• 7 inproceedingsE.Emmanuel Beffara, F.Félix Castro, M.Mauricio Guillermo and É.Étienne Miquey. Concurrent Realizability on Conjunctive Structures.FSCD 2023 - 8th International Conference on Formal Structures for Computation and DeductionRome, Italy2023HAL
• 8 inproceedingsN.Nicolas Behr, P.-A.Paul-André Melliès and N.Noam Zeilberger. Convolution Products on Double Categories and Categorification of Rule Algebras.Leibniz International Proceedings in Informatics (LIPIcs)FSCD 2023 - 8th International Conference on Formal Structures for Computation and Deduction2608th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)Rome, ItalySchloss Dagstuhl - Leibniz-Zentrum für InformatikJune 2023, 17:1-17:20HALDOIback to text
• 9 inproceedingsK.Kostia Chardonnet, A.Alexis Saurin and B.Benoît Valiron. A Curry-Howard Correspondence for Linear, Reversible Computation.31st EACSL Annual Conference on Computer Science Logic (CSL 2023)CSL 2023 - 31st EACSL Annual Conference on Computer Science LogicVarsovie (Warsaw), PolandSchloss Dagstuhl - Leibniz-Zentrum für Informatik2023HALDOIback to text
• 10 inproceedingsP.-A.Paul-André Melliès and N.Noam Zeilberger. Parsing as a lifting problem and the Chomsky-Schützenberger representation theorem.Electronic Notes in Theoretical Informatics and Computer ScienceMFPS 2022 - 38th conference on Mathematical Foundations for Programming SemanticsVolume 1 - Proceedings of...Ithaca, NY, United StatesFebruary 2023HALDOIback to text
• 11 inproceedingsV.Vincent Moreau and L. T.Lê Thành Dũng Nguyễn. Syntactically and Semantically Regular Languages of λ-Terms Coincide Through Logical Relations.32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)288Leibniz International Proceedings in Informatics (LIPIcs)Naples, ItalySchloss Dagstuhl – Leibniz-Zentrum für Informatik2024, 40:1-40:22HALDOIback to text
• 12 inproceedingsA.Alexis Saurin. A Linear Perspective on Cut-Elimination for Non-wellfounded Sequent Calculi with Least and Greatest Fixed-Points.International Conference on Automated Reasoning with Analytic Tableaux and Related MethodsTABLEAUX 2023 - 32nd International Conference on Automated Reasoning with Analytic Tableaux and Related Methods14278LNCS - LNAI - Lecture Notes in Computer Science - Lecture Notes in Artificial IntelligencePrague, Czech RepublicSpringer Nature SwitzerlandSeptember 2023, 203-222HALDOIback to text

Doctoral dissertations and habilitation theses

• 13 thesisA.Antoine Allioux. Higher Structures in Homotopy Type Theory.Université Paris CitéJuly 2023HAL
• 14 thesisA.Alen Ðurić. Quadratic normalisations and coherent presentations of monoids.Université Paris CitéApril 2023HAL

Reports & preprints

• 15 miscE.Esaïe Bauer and A.Alexis Saurin. Cut-elimination for the circular modal mu-calculus: linear logic and super exponentials to the rescue.March 2024HAL
• 16 miscH.Hugo Herbelin and D.Danko Ilik. An analysis of the constructive content of Henkin's proof of Gödel's completeness theorem.January 2024HAL
• 17 miscH.Hugo Herbelin and R.Ramkumar Ramachandra. A parametricity-based formalization of semi-simplicial and semi-cubical sets.January 2023HAL
• 18 miscP.-A.Paul-André Melliès and N.Noam Zeilberger. The categorical contours of the Chomsky-Schützenberger representation theorem.December 2023HAL
• 19 miscA.Alexis Saurin. A linear perspective on cut-elimination for non-wellfounded sequent calculi with least and greatest fixed points (extended version).2023HAL