A Mechanized Proof of the Basic Perturbation Lemma
Journal of Automated Reasoning
ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Using Open Mathematical Documents to Interface Computer Algebra and Proof Assistant Systems
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Generating certified code from formal proofs: a case study in homological algebra
Formal Aspects of Computing
Applying ACL2 to the formalization of algebraic topology: simplicial polynomials
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
A certified module to study digital images with the kenzo system
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Formalization of a normalization theorem in simplicial topology
Annals of Mathematics and Artificial Intelligence
Verifying an algorithm computing discrete vector fields for digital imaging
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
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Kenzo is a Common Lisp system devoted to Algebraic Topology. Although Kenzo uses higher-order functional programming intensively, we show in this paper how the theorem prover ACL2 can be used to prove the correctness of first order fragments of Kenzo. More concretely, we report on the verification in ACL2 of the implementation of simplicial sets. By means of a generic instantiation mechanism, we achieve the reduction of the proving effort for each family of simplicial sets, letting ACL2 automate the routine parts of the proofs.