Computing persistent homology within Coq/SSReflect
Journal article, 2013

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 paper, 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.

Coq

SSReflect

Persistent Homology

Formalization of Mathematics

Computational Algebraic Topology

Author

J. Heras

University of Dundee

Thierry Coquand

University of Gothenburg

Anders Mörtberg

University of Gothenburg

Vincent Siles

University of Gothenburg

ACM Transactions on Computational Logic

1529-3785 (ISSN) 1557945x (eISSN)

Vol. 14 4 26- 26

Subject Categories

Other Mathematics

Computer Science

DOI

10.1145/2528929

More information

Latest update

8/23/2019