## Section: Partnerships and Cooperations

### National Initiatives

Pierre-Louis Curien, Emilio J. Gallego Arias, Yves Guiraud, Hugo Herbelin, and Alexis Saurin are members of the GDR Informatique Mathématique, in the LHC (Logique, Homotopie, Catégories) and Scalp (Structures formelles pour le calcul et les preuves) working groups. Alexis Saurin is coordinator of the Scalp working group.

Pierre-Louis Curien, Yves Guiraud (local coordinator until Sept. 2019) and Matthieu Sozeau are members of the GDR Topologie Algébrique, federating French researchers working on classical topics of algebraic topology and homological algebra, such as homotopy theory, group homology, K-theory, deformation theory, and on more recent interactions of topology with other themes, such as higher categories and theoretical computer science.

Yves Guiraud is member of the GDR Tresses, federating French researchers working on algebraic, algorithmic and topological aspects of braid groups, low-dimensional topology, and connected subjects.

Yves Guiraud will coordinate the four-year Action Exploratoire Inria Réal (Réécriture Algébrique), starting in January 2020. Its aim is to continue the unification of rewriting-like methods in abtract and higher algebra, with a view toward applications in homological and higher algebra, and group and representation theory. This investigation is pursued in immersion at IMJ-PRG, the fundamental maths common laboratory of Sorbonne Université and Université Paris Diderot.

Emilio J. Gallego Arias is a member of the GDR Génie de la Programation et du Logiciel, in the LTP (Langages, Types et Preuves) group.

Yann Régis-Gianas collaborates with Mitsubishi Rennes on the topic of differential semantics. This collaboration led to the CIFRE grant for the PhD of Thibaut Girka.

Yann Régis-Gianas collaborates with ANSSI on the topic of certified ful programming in Coq.

Yann Régis-Gianas collaborates with Nomadic Labs on the topic of certified smart contract compilation.

Yann Régis-Gianas is a member of the ANR COLIS dedicated to the verification of Linux Distribution installation scripts. This project is joint with members of VALS (Univ Paris Sud) and LIFL (Univ Lille).

Yann Régis-Gianas and Alexis Saurin (coordinator) are members of the four-year RAPIDO ANR project, started in January 2015 and ended in September 2019.
RAPIDO aims at investigating the use of proof-theoretical methods
to reason and program on infinite data objects. The goal of the project
is to develop logical
systems capturing infinite proofs (proof systems with least and
greatest fixpoints as well as infinitary proof systems), to design
and to study programming languages for manipulating infinite data such
as streams both from a syntactical and semantical point of
view. Moreover, the ambition of the project is to apply the
fundamental results obtained from the proof-theoretical investigations
(i) to the development of software tools dedicated to the reasoning
about programs computing on infinite data, *e.g.* stream programs
(more generally coinductive programs), and (ii) to the study of
properties of automata on infinite words and trees from a proof-theoretical
perspective with an eye towards model-checking problems.
Other permanent members of the project are Christine Tasson from IRIF (PPS team), David Baelde from LSV,
ENS-Cachan, and Pierre Clairambault, Damien Pous and Colin Riba from LIP, ENS-Lyon.

Matthieu Sozeau is a member of the CoqHoTT project led by Nicolas Tabareau (Gallinette team, Inria Nantes & École des Mines de Nantes), funded by an ERC Starting Grant, ending in 2020. The PhD grant of Antoine Allioux is funded by the CoqHoTT ERC.