Reseña: Implementation of Bourbaki’s Elements of Mathematics in Coq. Part Two: Ordered Sets, Cardinals, Integers

En una entrada anterior comentamos el proyecto de formalización del libro Elements of Mathematics: Theory of Sets de N. Bourbaki en Coq.

En dicha entrada comentamos el primer paso del proyecto consistente en la formalización de la teoría de conjuntos correspondiente al capítulo II del libro de Bourbaki (páginas 65-130).

La formalización del capítulo III (páginas 131-256) constituye el contenido del segundo paso. Dicha formalización ha sido publicada por José Grimm en el artículo Implementation of Bourbaki’s Elements of Mathematics in Coq: Part Two; Ordered Sets, Cardinals, Integers. Su resumen es el siguiente

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 Ordered Sets, Cardinals, Integers”.

Version 3 is based on the Coq ssreflect library. It implements some properties on ordinal numbers. The code (including some exercises) is available on the Web, under http://www-sop.inria.fr/apics/gaia.