On abstract normalisation beyond neededness

Autores
Bonelli, Eduardo Augusto; Kesner, Delia; Lombardi, Carlos; Rios, Alejandro Norberto
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focusing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form. This is particularly appealing in the setting of non-sequential rewrite systems, in which terms that are not in normal form may not have any needed redex. We first prove a normalisation theorem for abstract rewrite systems (ARS), a general rewriting framework encompassing many rewriting systems developed by P-A. Melliès [20]. The theorem states that multistep strategies reducing so called necessary and never-gripping sets of redexes at a time are normalising in any ARS. Gripping refers to an abstract property reflecting the behaviour of higher-order substitution. We then apply this result to the particular case of PPC, a calculus of patterns and to the lambda-calculus with parallel-or.
Fil: Bonelli, Eduardo Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina
Fil: Kesner, Delia. Université Paris Diderot - Paris 7; Francia. Centre National de la Recherche Scientifique; Francia. Institut de Recherche en Informatique Fondamentale; Francia
Fil: Lombardi, Carlos. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina
Fil: Ríos, Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Materia
NEEDEDNESS
NORMALISATION
PATTERN CALCULI
REWRITING
SEQUENTIALITY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/72890
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On abstract normalisation beyond needednessBonelli, Eduardo AugustoKesner, DeliaLombardi, CarlosRios, Alejandro NorbertoNEEDEDNESSNORMALISATIONPATTERN CALCULIREWRITINGSEQUENTIALITYhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focusing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form. This is particularly appealing in the setting of non-sequential rewrite systems, in which terms that are not in normal form may not have any needed redex. We first prove a normalisation theorem for abstract rewrite systems (ARS), a general rewriting framework encompassing many rewriting systems developed by P-A. Melliès [20]. The theorem states that multistep strategies reducing so called necessary and never-gripping sets of redexes at a time are normalising in any ARS. Gripping refers to an abstract property reflecting the behaviour of higher-order substitution. We then apply this result to the particular case of PPC, a calculus of patterns and to the lambda-calculus with parallel-or.Fil: Bonelli, Eduardo Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; ArgentinaFil: Kesner, Delia. Université Paris Diderot - Paris 7; Francia. Centre National de la Recherche Scientifique; Francia. Institut de Recherche en Informatique Fondamentale; FranciaFil: Lombardi, Carlos. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; ArgentinaFil: Ríos, Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaElsevier Science2017-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/72890Bonelli, Eduardo Augusto; Kesner, Delia; Lombardi, Carlos; Rios, Alejandro Norberto; On abstract normalisation beyond neededness; Elsevier Science; Theoretical Computer Science; 672; 4-2017; 36-630304-3975CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0304397517301019info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2017.01.025info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1412.2118info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:37:27Zoai:ri.conicet.gov.ar:11336/72890instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:37:28.091CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On abstract normalisation beyond neededness
title On abstract normalisation beyond neededness
spellingShingle On abstract normalisation beyond neededness
Bonelli, Eduardo Augusto
NEEDEDNESS
NORMALISATION
PATTERN CALCULI
REWRITING
SEQUENTIALITY
title_short On abstract normalisation beyond neededness
title_full On abstract normalisation beyond neededness
title_fullStr On abstract normalisation beyond neededness
title_full_unstemmed On abstract normalisation beyond neededness
title_sort On abstract normalisation beyond neededness
dc.creator.none.fl_str_mv Bonelli, Eduardo Augusto
Kesner, Delia
Lombardi, Carlos
Rios, Alejandro Norberto
author Bonelli, Eduardo Augusto
author_facet Bonelli, Eduardo Augusto
Kesner, Delia
Lombardi, Carlos
Rios, Alejandro Norberto
author_role author
author2 Kesner, Delia
Lombardi, Carlos
Rios, Alejandro Norberto
author2_role author
author
author
dc.subject.none.fl_str_mv NEEDEDNESS
NORMALISATION
PATTERN CALCULI
REWRITING
SEQUENTIALITY
topic NEEDEDNESS
NORMALISATION
PATTERN CALCULI
REWRITING
SEQUENTIALITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focusing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form. This is particularly appealing in the setting of non-sequential rewrite systems, in which terms that are not in normal form may not have any needed redex. We first prove a normalisation theorem for abstract rewrite systems (ARS), a general rewriting framework encompassing many rewriting systems developed by P-A. Melliès [20]. The theorem states that multistep strategies reducing so called necessary and never-gripping sets of redexes at a time are normalising in any ARS. Gripping refers to an abstract property reflecting the behaviour of higher-order substitution. We then apply this result to the particular case of PPC, a calculus of patterns and to the lambda-calculus with parallel-or.
Fil: Bonelli, Eduardo Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina
Fil: Kesner, Delia. Université Paris Diderot - Paris 7; Francia. Centre National de la Recherche Scientifique; Francia. Institut de Recherche en Informatique Fondamentale; Francia
Fil: Lombardi, Carlos. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina
Fil: Ríos, Alejandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
description We study normalisation of multistep strategies, strategies that reduce a set of redexes at a time, focusing on the notion of necessary sets, those which contain at least one redex that cannot be avoided in order to reach a normal form. This is particularly appealing in the setting of non-sequential rewrite systems, in which terms that are not in normal form may not have any needed redex. We first prove a normalisation theorem for abstract rewrite systems (ARS), a general rewriting framework encompassing many rewriting systems developed by P-A. Melliès [20]. The theorem states that multistep strategies reducing so called necessary and never-gripping sets of redexes at a time are normalising in any ARS. Gripping refers to an abstract property reflecting the behaviour of higher-order substitution. We then apply this result to the particular case of PPC, a calculus of patterns and to the lambda-calculus with parallel-or.
publishDate 2017
dc.date.none.fl_str_mv 2017-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/72890
Bonelli, Eduardo Augusto; Kesner, Delia; Lombardi, Carlos; Rios, Alejandro Norberto; On abstract normalisation beyond neededness; Elsevier Science; Theoretical Computer Science; 672; 4-2017; 36-63
0304-3975
CONICET Digital
CONICET
url http://hdl.handle.net/11336/72890
identifier_str_mv Bonelli, Eduardo Augusto; Kesner, Delia; Lombardi, Carlos; Rios, Alejandro Norberto; On abstract normalisation beyond neededness; Elsevier Science; Theoretical Computer Science; 672; 4-2017; 36-63
0304-3975
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0304397517301019
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2017.01.025
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1412.2118
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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