Computing persistent homology within Coq/SSReflect
Jónathan Heras, Thierry Coquand, Anders Mörtberg, Vincent Siles · ACM Transactions on Computational Logic · 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 article, we report on the formal development of certified programs to compute persistent Betti numbers , an instrumental tool of persistent homology, using the C oq proof assistant together with the SSR eflect 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.