A Coq formalization of finitely presented modules
Paper in proceeding, 2014

This paper presents a formalization of constructive module theory in the intuitionistic type theory of Coq. We build an abstraction layer on top of matrix encodings, in order to represent finitely presented modules, and obtain clean definitions with short proofs justifying that it forms an abelian category. The goal is to use it as a first step to get certified programs for computing topological invariants, like homology groups and Betti numbers.

SSReflect

Homological algebra

Constructive algebra

Formalization of mathematics

Coq

Author

Cyril Cohen

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Anders C O Mörtberg

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 8558 LNCS 193-208
9783319089690 (ISBN)

5th International Conference on Interactive Theorem Proving, ITP 2014 - Held as Part of the Vienna Summer of Logic, VSL 2014
, Austria,

Subject Categories (SSIF 2011)

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/978-3-319-08970-6_13

More information

Latest update

11/23/2022