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 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.