Mechanized reasoning in homological algebra
Mechanized reasoning in homological algebra
A Mechanized Proof of the Basic Perturbation Lemma
Journal of Automated Reasoning
Generating certified code from formal proofs: a case study in homological algebra
Formal Aspects of Computing
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Extracting computer algebra programs from statements
EUROCAST'05 Proceedings of the 10th international conference on Computer Aided Systems Theory
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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.