La formalisation en Coq de la preuve du théorème de Feit-Thompson (ou théorème de l'ordre impair) est maintenant terminée ( 20 septembre 2012). Plus de détails sur la preuve ici et sur les bibliothèques Coq ici.
V. Lefèvre, N. Louvet, J.-M. Muller, J. Picot and L. Rideau Accurate calculation of Euclidean Norms using Double-word arithmetic ACM Transactions on Mathematical Software, Vol. 49, issue 1, March 2023, https://doi.org/10.1145/3568672.
J.-M. Muller and Laurence Rideau Formalization of double-word arithmetic, and comments on "Tight and rigorous error bounds for basic building blocks of double-word arithmetic" ACM Transactions on Mathematical Software, Vol. 48 No 1, DOI 10.1145/3484514, March 2022.
Yves Bertot, Laurence Rideau, Laurent Théry Distant decimals of π : Formal proofs of some algorithms computing them and guarantees of exact computation. Journal of Automated Reasoning, December 2017 (open archive version)
Georges Gonthier & al.
A Machine-Checked Proof of the Odd Order Theorem
In Sandrine Blazy and Christine Paulin and David Pichardie. ITP 2013, 4th Conference on Interactive Theorem Proving,2013, Rennes, France. Springer, 7998, pp. 163-179, LNCS
Laurence Rideau, Bernard P. Serpette, and Xavier Leroy.
Tilting at windmills with Coq: formal verification of a compilation algorithm for parallel moves. Journal of Automated Reasoning, 2008.Volume 40, number 4, p.307--326.
(open archive version)
V. Lefèvre, N. Louvet, J.-M. Muller, J. Picot and L. Rideau Accurate calculation of Euclidean Norms using Double-word arithmetic to appear in ACM Transactions on Mathematical Software.
J.-M. Muller and Laurence Rideau Formalization of double-word arithmetic, and comments on "Tight and rigorous error bounds for basic building blocks of double-word arithmetic" ACM Transactions on Mathematical Software, Vol. 48 No 1, DOI 10.1145/3484514, March 2022.
Yves Bertot, Laurence Rideau, Laurent Théry Distant decimals of π : Formal proofs of some algorithms computing them and guarantees of exact computation. Journal of Automated Reasoning, December 2017 (open archive version)
Sophie Bernard, Yves Bertot, Laurence Rideau, Pierre-Yves Strub
Formal Proofs of Transcendence for e and pi as an Application of Multivariate and Symmetric Polynomials Certified Programs and Proofs (CPP'16) (2016), ACM.
(open archive version)
Georges Gonthier & al.
A Machine-Checked Proof of the Odd Order Theorem
In Sandrine Blazy and Christine Paulin and David Pichardie. ITP 2013, 4th Conference on Interactive Theorem Proving,2013, Rennes, France. Springer, 7998, pp. 163-179, LNCS
J. Heras, M. Poza, M. Dénès and L. Rideau
Incidence simplicial matrices formalized in Coq/SSReflect.
in CICM'11. Lecture Notes in Computer Science, 6824, pages 30--44, 2011
François Garillot, Georges Gonthier, Assia Mahboubi, Laurence Rideau
`Packaging mathematical structures' Proceedings of TPHOLs'2009, LNCS, 2009.
Rapport de Recherche .
Laurence Rideau, Bernard P. Serpette, and Xavier Leroy.
Tilting at windmills with Coq: formal verification of a compilation algorithm for parallel moves. Journal of Automated Reasoning, 2008.Volume 40, number 4, p.307--326.
(open archive version)
Georges Gonthier, Assia Mahboubi, Laurence Rideau, Enrico Tassi, Laurent Théry
`A Modular Formalisation of Finite Group Theory' Proceedings of TPHOLs'2007, LNCS 4732, 2007.
Rapport de Recherche 6156.
Laurence Rideau et Laurent Théry,
`Formalising Sylow's theorems
in Coq',
Rapport Technique 327 .
L.Rideau, B.P. Serpette
Coq
à la conquête des moulins,
JFLA'2005, Obernai, France, 9-10 Mars 2005
Ph. Audebaud, L.Rideau
TeXmacs
as Authoring Tool for Publication and Dissemination of Formal
Developments,
UITP'2003, Roma, Italy, 8 Sep 2003, aussi ENTCS volume
103, 2004
H.Naciri, L.Rideau.
Affichage
et diffusion sur Internet d'explications en langue arabe de preuves
mathématiques,
CARI'2002 6ème Colloque Africain sur la Recherche en
Informatique,
Yaoundé, Cameroun,14-17 Oct, 2002
H.Naciri, L.Rideau.
Formal
Mathematical Proof Explanations in Natural Language Using MathML: An
Application
to Proofs in Arabic,
MathML International Conference 2002, Chicago,USA, June
28-30,
2002
H.Naciri, L.Rideau.
FIGUE:
Mathematical Formula Layout with Interaction and MathML Support.,
The Fifth Asian Symposium on Computer Mathematics ASCM'2001,
Matsuyama, Japan, September 26-28, 2001.
ASCM'2001 Page Web
Marc Daumas, Laurence Rideau, and Laurent Théry,
``
A Generic Library for Floating-Point Numbers and Its Application to
exact
Computing.'', Proceedings of TPHOLs'2001, LNCS 2152, 2001.
H.Naciri, L.Rideau.
The
Mariage of MathML and Theorem Proving.
IAMC'2001 Workshop,London Ontario, Canada, Juillet 2001.
IAMC'2001
Proceedings
Ahmed Amerkad, Yves Bertot, Laurence Rideau, and Loïc
Pottier.
Mathematics
and proof presentation in Pcoq.
PTP'01 Workshop, Siena, Italy, June 2001.
H.Naciri, L.Rideau.
Affichage
et manipulation interactive de formules mathématiques dans les
documents
structurés.
Rapport de recherche INRIA RR-4140, Janvier 2001
(accepté
pour publication dans la revue ARIMA, Décembre 2002)
Hanane Naciri et Laurence Rideau,
``Affichage
interactif, bidimensionnel et incrémental de formules
mathématiques.'',
Actes du 5ème Colloque Africain sur la Recherche en
Informatique,
p. 473-481, CARI'2000, ANTANANARIVO (Madagascar), 16-19
octobre
2000.
Olivier Pons, Yves bertot and Laurence Rideau,
"Notions of dependency in proof assistants",
In User Interfaces for Theorem Provers 1998, Eindhoven University of
Technology.
Laurence Rideau and Laurent Théry,
``Interactive
Programming
Environment for ML'',
Rapport de Recherche INRIA 3139, Mars 1997.
P. Asar, (generic name for the Project ASAR, including L.
Rideau),
``Framework
and Multi-Formalism: The ASAR Project'',
The Fourth International IFIP 10.5 Working Conference on Electronic
Design Automation Frameworks, Gramado (Brazil), November 1994.
A.-M. Déry and L. Rideau,
``Distributed
programming
environments: an example of a message protocol'',
Inria Technical Report no. 165, August 1994.
I. Jacobs and L. Rideau,
``A Centaur
Tutorial'',
Inria Technical Report no. 140, July 1992.
T. Bouguerba, J. Benzakki, M. Israel and L. Rideau,
"A
front-end VHDL editor for synthesis tools",
proceedings VIUF'95 San-Diego - April 1995.
T. Bouguerba, J. Benzakki,M. Israel and L. Rideau,
"VHDL
subsets in the SDEV environment. A Case Study : The Synopsys Subset.",
proceedings VIUF'95 Boston - pages 2.11-2.16 - October 1995
P. Asar, (generic name for the Project ASAR, including L.
Rideau),
"Vers un Atelier d'accueil générique pour la
Synthèse
ARchitecturale bâti autour de CENTAUR : ASAR"
Symposium Architectures Nouvelles de Machines - Rennes -
Décember
2-3, 1995.
Quelques preuves
Les décimales de Π en Coq en utilisant la formule de Plouffe
Une preuve simple que Π est irrationnel en utilisant Coquelicot
Une preuve que Π et e sont transcendants avec Coquelicot
Une Preuve Formelle du théorème de Feit-Thompson (terminé le 20 Septembre 2012).