Computing Persistent Homology within Coq/SSReflect [article]

Jónathan Heras and Thierry Coquand and Anders Mörtberg and Vincent Siles
2012 arXiv   pre-print
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
more » ... heory 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.
arXiv:1209.1905v1 fatcat:nkgtdzs26berfbbwfso7doph3m