Structural proof theory as rewriting

Detalhes bibliográficos
Autor(a) principal: Espírito Santo, José
Data de Publicação: 2006
Outros Autores: Frade, M. J., Pinto, Luís F.
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/6001
Resumo: The multiary version of the $\lambda$-calculus with generalized applications integrates smoothly both a fragment of sequent calculus and the system of natural deduction of von Plato. It is equipped with reduction rules (corresponding to cut-elimination/normalisation rules) and permutation rules, typical of sequent calculus and of natural deduction with generalised elimination rules. We argue that this system is a suitable tool for doing structural proof theory as rewriting. As an illustration, we investigate combinations of reduction and permutation rules and whether these combinations induce rewriting systems which are confluent and terminating. In some cases, the combination allows the simulation of non-terminating reduction sequences known from explicit substitution calculi. In other cases, we succeed in capturing interesting classes of derivations as the normal forms w.r.t. well-behaved combinations of rules. We identify six of these ``combined'' normal forms, among which are two classes, due to Herbelin and Mints, in bijection with normal, ordinary natural deductions. A computational explanation for the variety of ``combined'' normal forms is the existence of three ways of expressing multiple application in the calculus.
id RCAP_f0c84da76b5343e00b8e24e19872d0d7
oai_identifier_str oai:repositorium.sdum.uminho.pt:1822/6001
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Structural proof theory as rewritingLambda-calculusSequent calculusCombined normal formsScience & TechnologyThe multiary version of the $\lambda$-calculus with generalized applications integrates smoothly both a fragment of sequent calculus and the system of natural deduction of von Plato. It is equipped with reduction rules (corresponding to cut-elimination/normalisation rules) and permutation rules, typical of sequent calculus and of natural deduction with generalised elimination rules. We argue that this system is a suitable tool for doing structural proof theory as rewriting. As an illustration, we investigate combinations of reduction and permutation rules and whether these combinations induce rewriting systems which are confluent and terminating. In some cases, the combination allows the simulation of non-terminating reduction sequences known from explicit substitution calculi. In other cases, we succeed in capturing interesting classes of derivations as the normal forms w.r.t. well-behaved combinations of rules. We identify six of these ``combined'' normal forms, among which are two classes, due to Herbelin and Mints, in bijection with normal, ordinary natural deductions. A computational explanation for the variety of ``combined'' normal forms is the existence of three ways of expressing multiple application in the calculus.Fundação para a Ciência e a Tecnologia (FCT)APPSEM II (European Thematic Network)TYPES (European Thematic Network)SpringerUniversidade do MinhoEspírito Santo, JoséFrade, M. J.Pinto, Luís F.20062006-01-01T00:00:00Zconference paperinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/1822/6001engINTERNATIONAL CONFERENCE ON TERM REWRITING AND APPLICATIONS, 17, Seattle, 2006 - “RTA 2006 - International Conference on term Rewriting and applications : proceedings”. [S.l. : s.n. 2006]. ISBN 978-3-540-36834-2.35403683450302-9743info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-05-11T04:47:13Zoai:repositorium.sdum.uminho.pt:1822/6001Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T04:47:13Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Structural proof theory as rewriting
title Structural proof theory as rewriting
spellingShingle Structural proof theory as rewriting
Espírito Santo, José
Lambda-calculus
Sequent calculus
Combined normal forms
Science & Technology
title_short Structural proof theory as rewriting
title_full Structural proof theory as rewriting
title_fullStr Structural proof theory as rewriting
title_full_unstemmed Structural proof theory as rewriting
title_sort Structural proof theory as rewriting
author Espírito Santo, José
author_facet Espírito Santo, José
Frade, M. J.
Pinto, Luís F.
author_role author
author2 Frade, M. J.
Pinto, Luís F.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Espírito Santo, José
Frade, M. J.
Pinto, Luís F.
dc.subject.por.fl_str_mv Lambda-calculus
Sequent calculus
Combined normal forms
Science & Technology
topic Lambda-calculus
Sequent calculus
Combined normal forms
Science & Technology
description The multiary version of the $\lambda$-calculus with generalized applications integrates smoothly both a fragment of sequent calculus and the system of natural deduction of von Plato. It is equipped with reduction rules (corresponding to cut-elimination/normalisation rules) and permutation rules, typical of sequent calculus and of natural deduction with generalised elimination rules. We argue that this system is a suitable tool for doing structural proof theory as rewriting. As an illustration, we investigate combinations of reduction and permutation rules and whether these combinations induce rewriting systems which are confluent and terminating. In some cases, the combination allows the simulation of non-terminating reduction sequences known from explicit substitution calculi. In other cases, we succeed in capturing interesting classes of derivations as the normal forms w.r.t. well-behaved combinations of rules. We identify six of these ``combined'' normal forms, among which are two classes, due to Herbelin and Mints, in bijection with normal, ordinary natural deductions. A computational explanation for the variety of ``combined'' normal forms is the existence of three ways of expressing multiple application in the calculus.
publishDate 2006
dc.date.none.fl_str_mv 2006
2006-01-01T00:00:00Z
dc.type.driver.fl_str_mv conference paper
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/6001
url http://hdl.handle.net/1822/6001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv INTERNATIONAL CONFERENCE ON TERM REWRITING AND APPLICATIONS, 17, Seattle, 2006 - “RTA 2006 - International Conference on term Rewriting and applications : proceedings”. [S.l. : s.n. 2006]. ISBN 978-3-540-36834-2.
3540368345
0302-9743
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv mluisa.alvim@gmail.com
_version_ 1817544418748530688