The object of this project is to demonstrate that formalized mathematical theories can, like modern software, be built out of components. By components we mean modules that comprise both the static (objects and facts) and dynamic (proof and computation methods) contents of theories. We propose to develop a general platform for mathematical components, based on the Coq “Ssreflect” extension that was used to carry out the formalization of the Four Colour Theorem. We would validate the platform on two significant developments: a theory of efficient arithmetic, and the proof of the Odd Order theorem. The former could be used in the resolution of several outstanding computer proof challenges, among them the Kepler Conjecture, and the latter could become the first step in a new major challenge: the classification of finite simple groups.
Current state of the project
The formal proof of the Odd Order theorem has been completed on September 20th, 2012. Read more here.
Resources
Download sources, browse documentation, subscribe to the users’ mailing list here.
The Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Jul 2014, Vienna, Austria. ⟨10.1145/2603088.2603090⟩
Peter Aczel, Benedikt Ahrens, Thorsten Altenkirch, Steve Awodey, Bruno Barras, Andrej Bauer, Yves Bertot, Marc Bezem, Thierry Coquand, Eric Finster, Daniel Grayson, Hugo Herbelin, André Joyal, Dan Licata, Peter Lumsdaine, Assia Mahboubi, Per Martin-Löf, Sergey Melikhov, Alvaro Pelayo, Andrew Polonsky, Michael Shulman, Matthieu Sozeau, Bas Spitters, Benno van den Berg, Vladimir Voevodsky, Michael Warren, Carlo Angiuli, Anthony Bordg, Guillaume Brunerie, Chris Kapulkin, Egbert Rijke, Kristina Sojakova, Jeremy Avigad, Cyril Cohen, Robert Constable, Pierre-Louis Curien, Peter Dybjer, Martín Escardó, Kuen-Bang Hou, Nicola Gambino, Richard Garner, Georges Gonthier, Thomas Hales, Robert Harper, Martin Hofmann, Pieter Hofstra, Joachim Koch, Nicolai Kraus, Nuo Li, Zhaohui Luo, Michael Nahas, Erik Palmgren, Emily Riehl, Dana Scott, Philip Scott, Sergei Soloviev
Symposium on the Integration of Symbolic Computation and Mechanised Reasoning, Calculemus, Jul 2010, Paris, France. pp.189-203, ⟨10.1007/978-3-642-14128-7_17⟩
Ran Chen, Cyril Cohen, Jean-Jacques Levy, Stephan Merz, Laurent Théry
article
ITP 2019 - 10th International Conference on Interactive Theorem Proving, Sep 2019, Portland, United States. pp.13:1 - 13:19, ⟨10.4230/LIPIcs.ITP.2019.13⟩
The Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Jul 2014, Vienna, Austria. ⟨10.1145/2603088.2603090⟩
Pierre Boutillier, Stephane Glondu, Benjamin Grégoire, Hugo Herbelin, Pierre Letouzey, Pierre-Marie Pédrot, Yann Régis-Gianas, Matthieu Sozeau, Arnaud Spiwack, Enrico Tassi
Peter Aczel, Benedikt Ahrens, Thorsten Altenkirch, Steve Awodey, Bruno Barras, Andrej Bauer, Yves Bertot, Marc Bezem, Thierry Coquand, Eric Finster, Daniel Grayson, Hugo Herbelin, André Joyal, Dan Licata, Peter Lumsdaine, Assia Mahboubi, Per Martin-Löf, Sergey Melikhov, Alvaro Pelayo, Andrew Polonsky, Michael Shulman, Matthieu Sozeau, Bas Spitters, Benno van den Berg, Vladimir Voevodsky, Michael Warren, Carlo Angiuli, Anthony Bordg, Guillaume Brunerie, Chris Kapulkin, Egbert Rijke, Kristina Sojakova, Jeremy Avigad, Cyril Cohen, Robert Constable, Pierre-Louis Curien, Peter Dybjer, Martín Escardó, Kuen-Bang Hou, Nicola Gambino, Richard Garner, Georges Gonthier, Thomas Hales, Robert Harper, Martin Hofmann, Pieter Hofstra, Joachim Koch, Nicolai Kraus, Nuo Li, Zhaohui Luo, Michael Nahas, Erik Palmgren, Emily Riehl, Dana Scott, Philip Scott, Sergei Soloviev
Symposium on the Integration of Symbolic Computation and Mechanised Reasoning, Calculemus, Jul 2010, Paris, France. pp.189-203, ⟨10.1007/978-3-642-14128-7_17⟩
