Verifying the bridge between simplicial topology and algebra: the Eilenberg–Zilber algorithm

The Eilenberg–Zilber algorithm is one of the central components of the computer algebra system called Kenzo, devoted to computing in Algebraic Topology. In this article we report on a complete formal proof of the underlying Eilenberg–Zilber theorem, using the ACL2 theorem prover. As our formalizatio...

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Detalhes bibliográficos
Autores: Lambán Pardo, Laureano, Rubio, Julio, Martín Mateos, Francisco Jesús, Ruiz Reina, José Luis
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2013
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/86519
Acesso em linha:https://hdl.handle.net/11441/86519
https://doi.org/10.1093/jigpal/jzt034
Access Level:acceso abierto
Palavra-chave:Formalisation of mathematics
Computational algebraic topology
Program verification
Descrição
Resumo:The Eilenberg–Zilber algorithm is one of the central components of the computer algebra system called Kenzo, devoted to computing in Algebraic Topology. In this article we report on a complete formal proof of the underlying Eilenberg–Zilber theorem, using the ACL2 theorem prover. As our formalization is executable, we are able to compare the results of the certified programme with those of Kenzo on some universal examples. Since the results coincide, the reliability of Kenzo is reinforced. This is a new step in our long-term project towards certified programming for Algebraic Topology.