A Coq Formalization of Finitely Presented Modules

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 c...

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Bibliographic Details
Published inInteractive Theorem Proving Vol. 8558; pp. 193 - 208
Main Authors Cohen, Cyril, Mörtberg, Anders
Format Book Chapter Conference Proceeding
LanguageEnglish
Published Cham Springer International Publishing 2014
SeriesLecture Notes in Computer Science
Subjects
Computer Science
Constructive algebra
Coq
Datavetenskap (datalogi)
Formalization of mathematics
Homological algebra
SSReflect
Homological algebra
Coq
SSReflect
Formalization of mathematics
Constructive algebra
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Summary: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.
ISBN:9783319089690
3319089692
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-08970-6_13