Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
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
A verified Common Lisp implementation of Buchberger's algorithm in ACL2
Journal of Symbolic Computation
Triangulations: Structures for Algorithms and Applications
Triangulations: Structures for Algorithms and Applications
Proving with ACL2 the correctness of simplicial sets in the kenzo system
LOPSTR'10 Proceedings of the 20th international conference on Logic-based program synthesis and transformation
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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In this paper we present a complete formalization, using the ACL2 theorem prover, of the Normalization Theorem, a result in Algebraic Simplicial Topology stating that there exists a homotopy equivalence between the chain complex of a simplicial set, and a smaller chain complex for the same simplicial set, called the normalized chain complex. The interest of this work stems from three sources. First, the normalization theorem is the basis for some design decisions in the Kenzo computer algebra system, a program for computing in Algebraic Topology. Second, our proof of the theorem is new and shows the correctness of some formulas found experimentally, giving explicit expressions for the above-mentioned homotopy equivalence. And third, it demonstrates that the ACL2 theorem prover can be effectively used to formalize mathematics, even in areas where higher-order tools could be thought to be more appropriate.