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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/72890
Ver los metadatos del registro completo
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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 Técnicas2025-09-03T10:08:33Zoai: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:34982025-09-03 10:08:33.803CONICET 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/ |
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openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
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application/pdf application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Science |
publisher.none.fl_str_mv |
Elsevier Science |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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