A verified Common Lisp implementation of Buchberger's algorithm in ACL2

In this article, we present the formal verification of a Common Lisp implementation of Buchberger's algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in ACL2, a system which provides an integrated environment where programming (in a pure functional subset of C...

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Authors: Medina Bulo, Inmaculada, Palomo Lozano, Francisco, Ruiz Reina, José Luis
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2010
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/86196
Online Access:https://hdl.handle.net/11441/86196
https://doi.org/10.1016/j.jsc.2009.07.002
Access Level:Open access
Keyword:Formal verification
ACL2
Computer Algebra
Buchberger's algorithm
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spelling A verified Common Lisp implementation of Buchberger's algorithm in ACL2Medina Bulo, InmaculadaPalomo Lozano, FranciscoRuiz Reina, José LuisFormal verificationACL2Computer AlgebraBuchberger's algorithmIn this article, we present the formal verification of a Common Lisp implementation of Buchberger's algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in ACL2, a system which provides an integrated environment where programming (in a pure functional subset of Common Lisp) and formal verification of programs, with the assistance of a theorem prover, are possible. Our implementation is written in a real programming language and it is directly executable within the ACL2 system or any compliant Common Lisp system. We provide here snippets of real verified code, discuss the formalization details in depth, and present quantitative data about the proof effort.ElsevierCiencias de la Computación e Inteligencia ArtificialTIC137: Lógica, Computación e Ingeniería del Conocimiento2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/86196https://doi.org/10.1016/j.jsc.2009.07.002reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Symbolic Computation, 45 (1), 96-123.https://www.sciencedirect.com/science/article/pii/S0747717109001357info:eu-repo/semantics/openAccessoai:idus.us.es:11441/861962026-06-17T12:51:07Z
dc.title.none.fl_str_mv A verified Common Lisp implementation of Buchberger's algorithm in ACL2
title A verified Common Lisp implementation of Buchberger's algorithm in ACL2
spellingShingle A verified Common Lisp implementation of Buchberger's algorithm in ACL2
Medina Bulo, Inmaculada
Formal verification
ACL2
Computer Algebra
Buchberger's algorithm
title_short A verified Common Lisp implementation of Buchberger's algorithm in ACL2
title_full A verified Common Lisp implementation of Buchberger's algorithm in ACL2
title_fullStr A verified Common Lisp implementation of Buchberger's algorithm in ACL2
title_full_unstemmed A verified Common Lisp implementation of Buchberger's algorithm in ACL2
title_sort A verified Common Lisp implementation of Buchberger's algorithm in ACL2
dc.creator.none.fl_str_mv Medina Bulo, Inmaculada
Palomo Lozano, Francisco
Ruiz Reina, José Luis
author Medina Bulo, Inmaculada
author_facet Medina Bulo, Inmaculada
Palomo Lozano, Francisco
Ruiz Reina, José Luis
author_role author
author2 Palomo Lozano, Francisco
Ruiz Reina, José Luis
author2_role author
author
dc.contributor.none.fl_str_mv Ciencias de la Computación e Inteligencia Artificial
TIC137: Lógica, Computación e Ingeniería del Conocimiento
dc.subject.none.fl_str_mv Formal verification
ACL2
Computer Algebra
Buchberger's algorithm
topic Formal verification
ACL2
Computer Algebra
Buchberger's algorithm
description In this article, we present the formal verification of a Common Lisp implementation of Buchberger's algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in ACL2, a system which provides an integrated environment where programming (in a pure functional subset of Common Lisp) and formal verification of programs, with the assistance of a theorem prover, are possible. Our implementation is written in a real programming language and it is directly executable within the ACL2 system or any compliant Common Lisp system. We provide here snippets of real verified code, discuss the formalization details in depth, and present quantitative data about the proof effort.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/86196
https://doi.org/10.1016/j.jsc.2009.07.002
url https://hdl.handle.net/11441/86196
https://doi.org/10.1016/j.jsc.2009.07.002
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Symbolic Computation, 45 (1), 96-123.
https://www.sciencedirect.com/science/article/pii/S0747717109001357
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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