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...
| Autores: | , , , |
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| 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 |
| 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. |
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