Coherent and strongly discrete rings in type theory

Authors:
Thierry Coquand;Anders Mörtberg;Vincent Siles
Affiliations:
Department of Computer Science and Engineering, University of Gothenburg, Sweden;Department of Computer Science and Engineering, University of Gothenburg, Sweden;Department of Computer Science and Engineering, University of Gothenburg, Sweden
Venue:
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Year:
2012

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Abstract

We present a formalization of coherent and strongly discrete rings in type theory. This is a fundamental structure in constructive algebra that represents rings in which it is possible to solve linear systems of equations. These structures have been instantiated with Bézout domains (for instance ℤ and k[x]) and Prüfer domains (generalization of Dedekind domains) so that we get certified algorithms solving systems of equations that are applicable on these general structures. This work can be seen as basis for developing a formalized library of linear algebra over rings.