A Coq Formalization of Finitely Presented Modules

Cyril Cohen (1) , Anders Mörtberg (1)

1 CSE - Department of Computer Science and Engineering [Göteborg]

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.

Mots clés: Formalization of mathematics; Homological algebra; Constructive algebra; Coq; SSReflect

Domaines: Théorie et langage formel [cs.FL]; Anneaux et algèbres [math.RA]

Cyril Cohen, Anders Mörtberg. A Coq Formalization of Finitely Presented Modules. 5th International Conference, ITP 2014, Jul 2014, Vienna, Austria. pp.193 - 208, ⟨10.1007/978-3-319-08970-6_13⟩. ⟨hal-01378905⟩