research-article

Computing persistent homology within Coq/SSReflect

Authors:

Jónathan Heras,

Thierry Coquand,

Anders Mörtberg,

Vincent SilesAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 14, Issue 4

Article No.: 26, Pages 1 - 16

https://doi.org/10.1145/2528929

Published: 28 November 2013 Publication History

Abstract

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.

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Cited By

Lambán LMartín-Mateos FRubio JRuiz-Reina J(2017)Using Abstract Stobjs in ACL2 to Compute Matrix Normal FormsInteractive Theorem Proving10.1007/978-3-319-66107-0_23(354-370)Online publication date: 26-Sep-2017
https://dl.acm.org/doi/10.1007/978-3-319-66107-0_23
Komendantskaya EHeras J(2017)Proof Mining with Dependent TypesIntelligent Computer Mathematics10.1007/978-3-319-62075-6_21(303-318)Online publication date: 28-Jun-2017
https://doi.org/10.1007/978-3-319-62075-6_21
Poza MDomínguez CHeras JRubio J(2014)A Certified Reduction Strategy for Homological Image ProcessingACM Transactions on Computational Logic10.1145/263078915:3(1-23)Online publication date: 17-Jul-2014
https://dl.acm.org/doi/10.1145/2630789
Show More Cited By

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Computing persistent homology within Coq/SSReflect

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 14, Issue 4

November 2013

282 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/2555591

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Copyright © 2013 ACM.

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Publication History

Published: 28 November 2013

Accepted: 01 February 2013

Revised: 01 December 2012

Received: 01 March 2012

Published in TOCL Volume 14, Issue 4

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Ministerio de Educacion y Ciencia, project MTM2009-13842-C02-01
Seventh Framework Programme

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Cited By

Lambán LMartín-Mateos FRubio JRuiz-Reina J(2017)Using Abstract Stobjs in ACL2 to Compute Matrix Normal FormsInteractive Theorem Proving10.1007/978-3-319-66107-0_23(354-370)Online publication date: 26-Sep-2017
https://dl.acm.org/doi/10.1007/978-3-319-66107-0_23
Komendantskaya EHeras J(2017)Proof Mining with Dependent TypesIntelligent Computer Mathematics10.1007/978-3-319-62075-6_21(303-318)Online publication date: 28-Jun-2017
https://doi.org/10.1007/978-3-319-62075-6_21
Poza MDomínguez CHeras JRubio J(2014)A Certified Reduction Strategy for Homological Image ProcessingACM Transactions on Computational Logic10.1145/263078915:3(1-23)Online publication date: 17-Jul-2014
https://dl.acm.org/doi/10.1145/2630789
Aransay JDivasón J(2014)Formalization and Execution of Linear Algebra: From Theorems to AlgorithmsLogic-Based Program Synthesis and Transformation10.1007/978-3-319-14125-1_1(1-18)Online publication date: 11-Dec-2014
https://doi.org/10.1007/978-3-319-14125-1_1
Cohen CMörtberg A(2014)A Coq Formalization of Finitely Presented ModulesInteractive Theorem Proving10.1007/978-3-319-08970-6_13(193-208)Online publication date: 2014
https://doi.org/10.1007/978-3-319-08970-6_13
Heras JMata GRomero ARubio JSáenz R(2013)Verifying a plaftorm for digital imagingProceedings of the 2013 international conference on Intelligent Computer Mathematics10.1007/978-3-642-39320-4_5(66-81)Online publication date: 8-Jul-2013
https://dl.acm.org/doi/10.1007/978-3-642-39320-4_5

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