Notes on logic and set theory
The foundation of a generic theorem prover
Journal of Automated Reasoning
A formulation of the simple theory of types (for Isabelle)
COLOG-88 Proceedings of the international conference on Computer logic
Type theory and functional programming
Type theory and functional programming
A Formal Proof of Sylow‘s Theorem
Journal of Automated Reasoning
Object-Oriented Verification Based on Record Subtyping in Higher-Order Logic
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
A logical approach to abstract algebra
Mathematical Structures in Computer Science
Mechanized reasoning in homological algebra
Mechanized reasoning in homological algebra
A formally verified proof of the prime number theorem
ACM Transactions on Computational Logic (TOCL)
A Mechanized Proof of the Basic Perturbation Lemma
Journal of Automated Reasoning
Towards Constructive Homological Algebra in Type Theory
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Program extraction in simply-typed higher order logic
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Interpretation of locales in isabelle: theories and proof contexts
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
A Mechanized Proof of the Basic Perturbation Lemma
Journal of Automated Reasoning
Formalizing in Coq Hidden Algebras to Specify Symbolic Computation Systems
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Mechanized reasoning in Homological Algebra
AI Communications
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
Computing in coq with infinite algebraic data structures
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Effective homology of bicomplexes, formalized in Coq
Theoretical Computer Science
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
Incidence simplicial matrices formalized in Coq/SSReflect
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
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
Certified symbolic manipulation: bivariate simplicial polynomials
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Computing persistent homology within Coq/SSReflect
ACM Transactions on Computational Logic (TOCL)
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We present a complete mechanized proof of the result in homological algebra known as basic perturbation lemma. The proof has been carried out in the proof assistant Isabelle, more concretely, in the implementation of higher-order logic (HOL) available in the system. We report on the difficulties found when dealing with abstract algebra in HOL, and also on the ongoing stages of our project to give a certified version of some of the algorithms present in the Kenzo symbolic computation system.