MARELLE - 2017 - Annual activity report

MARELLE

MARELLE - 2017

Project-Team Marelle

Personnel

Overall Objectives

Research Program

Type theory and formalization of mathematics
Verification of scientific algorithms
Programming language semantics

Highlights of the Year

New Software and Platforms

Coq
Easycrypt
ELPI
Math-Components
Semantics
Ssreflect
AutoGnP

New Results

Implementing Theorem Proving in Higher Order Logic Programming
Coqoon: An IDE for interactive proof development in Coq
Proofs of transcendence
Cubical type theory and univalent foundations
Formal study of double-word arithmetic algorithms
Formal study of comparisons between numbers in different formats
A formal study of the towers of Hanoi
Formaly study of algorithms to compute $π$
Formal foundations of 3D geometry for robot manipulators
Formalization of Analysis concepts
Formalization of proofs in control theory
Formalization of graph algorithms
Extension of the CoqEAL library
Formalizing Exterior Algebras
Formalizing Cylindrical Algebraic Decomposition
Formal study of probabilistic programs
Generating Efficient Resistant Code
Formal Security Proof in EasyCrypt: case studies and extensions
Formalizing Bourbaki-style mathematics

Partnerships and Cooperations

National Initiatives
European Initiatives
International Initiatives

Dissemination

Promoting Scientific Activities
Teaching - Supervision - Juries
Popularization

Bibliography

Major publications
Publications of the year
References in notes

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Section: New Results

Formalizing Exterior Algebras

Participants : Maxime Bombar, Cyril Cohen.

We formalized exterior algebras as vector spaces with dimension $2^{n}$ . This provides an alternative representation to that constructed earlier by Laurent Théry and Laurent Fuchs. The new representation is closer to the objects found in the mathematical components library.

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