Section: New Results

Developments of systems

Translation of HOL-light proofs into Coq

Participants : Chantal Keller, Benjamin Werner.

Chantal Keller and Benjamin Werner have designed a new way to translate HOL-proofs and import them into Coq. This translation has been implemented by Chantal Keller and is operational. It is based on ideas coming from a previous implementation of normalization-by-evaluation in Coq, by Benjamin Werner and François Garillot. The results of the implementation are encouraging; a pleasing particularity of this translation is that the theorems are translated into Coq in an intelligible and reusable form.

Interfacing Coq with SMT solvers

Participants : Germain Faure, Chantal Keller, Benjamin Werner, Assia Mahboubi.

The starting point of this work is to note that SMT solvers, deciding the Satisfiability Modulo Theories, are in constant evolution to take into account new decision procedures as well as theories. These systems are rather complex and it is now clearly established that they all contain bugs. The standard approach is to ask the SMT solver to append to the decision result a certificate that can be checked by another tool.

In this context, we are using formal systems like Coq to check the certificate. The first experiments we have done in close collaboration with the Marelle team (INRIA Sophia Antipolis) are clearly promising.

A new engine to interpret Coq tactics

Participant : Arnaud Spiwack.

Arnaud Spiwack implemented a new engine to interpret Coq tactics. It gives new functionalities (structured proofs based on bullets, true refinement, non-determinism in tactics...) and the overall development will be part of the 2010 release of Coq.

Implementation of the lambda Pi-modulo calculus

Participant : Mathieu Boespflug.

Mathieu Boespflug wrote a full implementation of a type checker for proofs written in the -modulo calculus, called Dedukti . Version 1.0 of Dedukti was released in September.

Translator of Coq proofs into lambda Pi-modulo proofs

Participants : Mathieu Boespflug, Denis Cousineau.

Denis Cousineau has written a prototype called Coqine for a translator from Coq proofs to proofs in the -calculus modulo. This translator was further developed by Guillaume Burel and Mathieu Boespflug. Coqine has not yet seen a formal released and is under active development. Dependant pattern-matching has yet to be supported, as well as other advanced Coq features such as modules.

Prototyping programming languages

Participants : Gilles Dowek, César Muñoz, Camilo Rocha.

Gilles Dowek, César Muñoz and Camilo Rocha have proposed an environment to prototype parallel languages [13] , including an evaluator based on the Maude system and a proof environment based on the PVS theorem prover. They have used this environment to compare several variants of the PLEXIL language.

Air Traffic Control

Participants : Gilles Dowek, Jeff Maddalon, Rick Butler, César Muñoz.

Gilles Dowek, Jeff Maddalon, Rick Butler, and César Muñoz have designed a prevention band algorithm and proved it correct [11] .

Release, maintenance and documentation of the ssreflect extension

Participant : Assia Mahboubi.

In the context of her participation to the Mathematical Components project, Assia Mahboubi has pursued her contribution to the development, maintenance, documentation and distribution of the ssreflect extension. Version 1.2 of the ssreflect extension has been released in August 2009. The documentation has been adequately updated [17] .