An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
A compiled implementation of strong reduction
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
Discrete & Computational Geometry
The theory of multidimensional persistence
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A Mechanized Proof of the Basic Perturbation Lemma
Journal of Automated Reasoning
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Foundations of Computational Mathematics
Effective homology of bicomplexes, formalized in Coq
Theoretical Computer Science
Incidence simplicial matrices formalized in Coq/SSReflect
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Point-free, set-free concrete linear algebra
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Extending coq with imperative features and its application to SAT verification
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Full reduction at full throttle
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Verifying an algorithm computing discrete vector fields for digital imaging
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Towards a certified computation of homology groups for digital images
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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Persistent homology is one of the most active branches of computational algebraic topology with applications in several contexts such as optical character recognition or analysis of point cloud data. In this article, we report on the formal development of certified programs to compute persistent Betti numbers, an instrumental tool of persistent homology, using the Coq proof assistant together with the SSReflect extension. To this aim it has been necessary to formalize the underlying mathematical theory of these algorithms. This is another example showing that interactive theorem provers have reached a point where they are mature enough to tackle the formalization of nontrivial mathematical theories.