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##### PI.R2 - 2016

New Software and Platforms
Partnerships and Cooperations
Bibliography

## Section: New Software and Platforms

### Coq

Keywords: Proof - Certification - Formalisation

Functional Description

Coq provides both a dependently-typed functional programming language and a logical formalism, which, altogether, support the formalisation of mathematical theories and the specification and certification of properties of programs. Coq also provides a large and extensible set of automatic or semi-automatic proof methods. Coq's programs are extractible to OCaml, Haskell, Scheme, ...

• Closest participants: Benjamin Grégoire, Enrico Tassi, Bruno Barras, Yves Bertot, Pierre Courtieu, Maxime Dénès, Hugo Herbelin, Matej Košík, Pierre Letouzey, Assia Mahboubi, Cyprien Mangin, Guillaume Melquiond, Jean-Marc Notin, Pierre-Marie Pédrot, Yann Régis-Gianas, Matthieu Sozeau, Arnaud Spiwack, Théo Zimmermann.

• Partners: CNRS - ENS Lyon - Université Paris-Diderot - Université Paris-Sud

• Contact: Matthieu Sozeau

#### Coq 8.6

The 8.6 version of Coq was released in December 2016. It initiates a time-based release cycle and concentrates on a smaller set of features than Coq 8.5 for which compatibility and testing were done more intensively. In the $\pi {r}^{2}$ team, Hugo Herbelin, Cyprien Mangin, Théo Zimmermann and Matthieu Sozeau contributed to the coordination of the development, to the discussion of the roadmap, to the implementation of the features, and to many bugfixes.

Matthieu Sozeau followed up his work on universe polymorphism making the explicit annotation system more accessible and resolving issues in the minimization algorithm used during refinement, resulting in a more predictable system. These improvements were used in the Coq/HoTT library for Homotopy Type Theory, which is described in an upcoming article [26].

Matthieu Sozeau implemented a new variant of the proof-search tactic for typeclasses that is set to replace the existing auto and eauto tactics in the following version. The new variant fully benefits from the features of the underlying proof engine, and allows much more control on proof-search (patterns used consistently, modes for triggering hints, ...). It is at the basis of the work of Théo Zimmermann described below.

#### The Equations plugin

Cyprien Mangin and Matthieu Sozeau continued work on the Equations plugin, modularizing it so that the use of axioms can be minimized, and making it compatible with developments in Homotopy Type Theory. To achieve this, it has moved to a simplification engine in ML based on telescopes and is able to produce axiom-free proofs of the examples that were previously implicitly using them. This work will be presented at the POPL workshop Type-Theoretic Tools (TTT), next January 2017.

#### Maintenance

Among other contributions, Hugo Herbelin, Pierre Letouzey, Matej Košík and Matthieu Sozeau worked at the maintenance of the system.

In particular, Pierre Letouzey vastly reworked the build mechanism of Coq, taking advantage of code evolutions driven by Pierre-Marie Pédrot. Pierre Letouzey also administrated (and improved) several machines or systems that are critical for the Coq community (web server, build test server, git repositories ...), in coordination with Inria's SIC support team.

Matej Košík developed a new benchmarking infrastructure based on Jenkins and continuous integration (http://ci.inria.fr). It allows easily testing any developer branch on the benchmark suite prior to integration to the main archive.

#### Coordination and animation

After 10 years coordinating the Coq development team, Hugo Herbelin handed over the coordination to Matthieu Sozeau.

A Coq working group is organised every two months (5 times a year). Discussions about the development happen, in particular, on coq-dev@inria.fr , Coq's GitHub http://github.com/coq and http://coq.inria.fr/bugs. This year, a week-long working group organized in Sophia-Antipolis was devoted to the 8.6 roadmap discussion.

#### Documentation and stabilization of Coq's programming interface

Matej Košík worked on the programming interfaces of Coq, starting to isolate a subset of key functions to be used by Coq plugin developers.