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A Coq Formalization of Finitely Presented Modules

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Interactive Theorem Proving (ITP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8558))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Chalmers University of Technology and University of Gothenburg, Sweden

    Cyril Cohen & Anders Mörtberg

Authors
  1. Cyril Cohen
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  2. Anders Mörtberg
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Editor information

Editors and Affiliations

  1. NICTA, Sydney, NSW, Australia

    Gerwin Klein

  2. University of Wyoming, Laramie, WY, USA

    Ruben Gamboa

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Cohen, C., Mörtberg, A. (2014). A Coq Formalization of Finitely Presented Modules. In: Klein, G., Gamboa, R. (eds) Interactive Theorem Proving. ITP 2014. Lecture Notes in Computer Science, vol 8558. Springer, Cham. https://doi.org/10.1007/978-3-319-08970-6_13

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  • DOI: https://doi.org/10.1007/978-3-319-08970-6_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08969-0

  • Online ISBN: 978-3-319-08970-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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