Computing persistent homology within Coq/SSReflect
Artikel i vetenskaplig tidskrift, 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.


Persistent Homology

Computational Algebraic Topology

Formalization of Mathematics



J. Heras

University of Dundee

Thierry Coquand

Göteborgs universitet

Anders Mörtberg

Göteborgs universitet

Vincent Siles

Göteborgs universitet

ACM Transactions on Computational Logic

1529-3785 (ISSN)

Vol. 14 26- 26


Annan matematik

Datavetenskap (datalogi)