## Section: Partnerships and Cooperations

### National Initiatives

Alexis Saurin (coordinator) and Yann Régis-Gianas are members of the four-year RAPIDO ANR project accepted in 2014 and starting in January 2015.
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 fixed points 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 PPS, David Baelde from LSV,
ENS-Cachan, and Pierre Clairambault, Damien Pous and Colin Riba from LIP, ENS-Lyon.

Pierre-Louis Curien (coordinator), Yves Guiraud and Philippe Malbos are members of the three-year Focal project of the IDEX Sorbonne Paris Cité, started in June 2013. This project, giving the support for the PhD grant of Cyrille Chenavier, concerns the interactions between higher-dimensional rewriting and combinatorial algebra. This project is joint with members of the LAGA (Laboratory of Mathematics, Univ. Paris 13).

Pierre-Louis Curien (coordinator), Yves Guiraud and Philippe Malbos are members of the four-year Cathre ANR project, started in January 2014. This project, giving the support for the PhD grant of Maxime Lucas, investigates the general theory of higher-dimensional rewriting, the development of a general-purpose library for higher-dimensional rewriting, and applications in the fields of combinatorial algebra, combinatorial group theory and theoretical computer science. This project is joint with members of the LAGA (Univ. Paris 13), the LIX (École Polytechnique), the ICJ (Univ. Lyon 1 and Univ. Saint-Étienne), the I2M (Univ. Aix-Marseille) and the IMT (Univ. Toulouse 3).

Pierre-Louis Curien, Yves Guiraud (local coordinator) and Matthieu Sozeau are members of the Groupement de Recherche 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, motivic homotopy, string theory.

Matthieu Sozeau, Hugo Herbelin, Lourdes del Carmen González Huesca and Yann Régis-Gianas were members of the ANR Paral-ITP, which started in November 2011 and ended in June 2015, and aimed at preparing the Coq and Isabelle interactive theorem provers to a new generation of user interfaces thanks to massive parallelism and incremental type-checking.

Hugo Herbelin is the coordinator of the PPS site for the ANR Récré accepted in 2011, which started in January 2012 and will end mid 2016. Récré is about realisability and rewriting, with applications to proving with side-effects and concurrency.

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 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).

Matthieu Sozeau is a member of the CoqHoTT project led by Nicolas Tabareau (Ascola team, École des Mines de Nantes), funded by an ERC Starting Grant. The PhD grant of Gabriel Lewertowski is funded by the CoqHoTT ERC.