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Implementation of Bourbaki's Elements of Mathematics in Coq: Part One, Theory of Sets

José Grimm 1
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We believe that it is possible to put the whole work of Bourbaki into a computer. One of the objectives of the Gaia project concerns homological algebra (theory as well as algorithms); in a first step we want to implement all nine chapters of the book Algebra. But this requires a theory of sets (with axiom of choice etc.) more powerful than what is provided by Ensembles; we have chosen the work of Carlos Simpson as basis. This reports lists and comments all definitions and theorems of the Chapter ''Theory of Sets''. The code (including almost all exercises) is available on the Web, under . Version one was released in July 2009, version 2 in December 2009, version 3 in March 2010. Version 4 is based on the Coq ssreflect library. In version 5, released in December 2011, the ''iff_eq'' axiom has been withdraw, and the axiom of choice modified. Version 6 was released in October 2013
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Submitted on : Thursday, October 31, 2013 - 4:36:13 PM
Last modification on : Thursday, January 7, 2021 - 3:40:07 PM
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  • HAL Id : inria-00408143, version 6


José Grimm. Implementation of Bourbaki's Elements of Mathematics in Coq: Part One, Theory of Sets. [Research Report] RR-6999, INRIA. 2013, pp.205. ⟨inria-00408143v6⟩



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