The vectorial λ-calculus

Autores
Arrighi, Pablo; Díaz Caro, Alejandro; Valiron, Benoît
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus.
Fil: Arrighi, Pablo. Aix-Marseille Université; Francia. Centre National de la Recherche Scientifique; Francia
Fil: Díaz Caro, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina
Fil: Valiron, Benoît. Université Paris Sud; Francia. Centre National de la Recherche Scientifique; Francia. Université Paris-Saclay; Francia
Materia
Lambda calculus
Type theory
Quantum computing
Nivel de accesibilidad
acceso embargado
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:11336/72528
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The vectorial λ-calculusArrighi, PabloDíaz Caro, AlejandroValiron, BenoîtLambda calculusType theoryQuantum computinghttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus.Fil: Arrighi, Pablo. Aix-Marseille Université; Francia. Centre National de la Recherche Scientifique; FranciaFil: Díaz Caro, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; ArgentinaFil: Valiron, Benoît. Université Paris Sud; Francia. Centre National de la Recherche Scientifique; Francia. Université Paris-Saclay; FranciaAcademic Press Inc Elsevier Science2017-06info:eu-repo/date/embargoEnd/2019-07-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/72528Arrighi, Pablo; Díaz Caro, Alejandro; Valiron, Benoît; The vectorial λ-calculus; Academic Press Inc Elsevier Science; Information and Computation; 254; Parte 1; 6-2017; 105-1390890-5401CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0890540117300482info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ic.2017.04.001info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1308.1138info:eu-repo/semantics/embargoedAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:45:59Zoai:ri.conicet.gov.ar:11336/72528instacron: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 09:45:59.975CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The vectorial λ-calculus
title The vectorial λ-calculus
spellingShingle The vectorial λ-calculus
Arrighi, Pablo
Lambda calculus
Type theory
Quantum computing
title_short The vectorial λ-calculus
title_full The vectorial λ-calculus
title_fullStr The vectorial λ-calculus
title_full_unstemmed The vectorial λ-calculus
title_sort The vectorial λ-calculus
dc.creator.none.fl_str_mv Arrighi, Pablo
Díaz Caro, Alejandro
Valiron, Benoît
author Arrighi, Pablo
author_facet Arrighi, Pablo
Díaz Caro, Alejandro
Valiron, Benoît
author_role author
author2 Díaz Caro, Alejandro
Valiron, Benoît
author2_role author
author
dc.subject.none.fl_str_mv Lambda calculus
Type theory
Quantum computing
topic Lambda calculus
Type theory
Quantum computing
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 describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus.
Fil: Arrighi, Pablo. Aix-Marseille Université; Francia. Centre National de la Recherche Scientifique; Francia
Fil: Díaz Caro, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina
Fil: Valiron, Benoît. Université Paris Sud; Francia. Centre National de la Recherche Scientifique; Francia. Université Paris-Saclay; Francia
description We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus.
publishDate 2017
dc.date.none.fl_str_mv 2017-06
info:eu-repo/date/embargoEnd/2019-07-01
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/11336/72528
Arrighi, Pablo; Díaz Caro, Alejandro; Valiron, Benoît; The vectorial λ-calculus; Academic Press Inc Elsevier Science; Information and Computation; 254; Parte 1; 6-2017; 105-139
0890-5401
CONICET Digital
CONICET
url http://hdl.handle.net/11336/72528
identifier_str_mv Arrighi, Pablo; Díaz Caro, Alejandro; Valiron, Benoît; The vectorial λ-calculus; Academic Press Inc Elsevier Science; Information and Computation; 254; Parte 1; 6-2017; 105-139
0890-5401
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/S0890540117300482
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.ic.2017.04.001
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1308.1138
dc.rights.none.fl_str_mv info:eu-repo/semantics/embargoedAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv embargoedAccess
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
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc 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
_version_ 1842268767203098624
score 13.13397

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