Mechanized reasoning in Homological Algebra

Article type: Research Article

Authors: Aransay, Jesús

Affiliations: Departamento de Matemáticas y Computación Universidad de La Rioja, Edificio Luis Vives c/Luis de Ulloa, Logroño E26004, Spain. E-mail: jesus-maria.aransay@unirioja.es

Abstract: In this work we face the problem of obtaining a certified version of a crucial algorithm in Homological Algebra, known as Perturbation Lemma. This lemma is intensively used in the software system Kenzo, devoted to symbolic computation in Homological Algebra. To this end we use the proof assistant Isabelle. Our motivations are to increase the knowledge in the algorithmic nature of this mathematical result and to test different possibilities offered by Isabelle to formally prove theorems in Homological Algebra. A detailed mathematical proof of the Perturbation Lemma, a methodology to obtain certified software in Homological Algebra, a suitable infrastructure to formalize the proof, a complete Isabelle formal proof, and a discussion on the constructiveness of the mathematical results introduced are presented.

Keywords: Formalized mathematics, Homological Algebra, Isabelle/HOL, certified software

DOI: 10.3233/AIC-2008-0427

Journal: AI Communications, vol. 21, no. 4, pp. 265-267, 2008