Structural proof theory as rewriting
Autor(a) principal: | |
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Data de Publicação: | 2006 |
Outros Autores: | , |
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. |
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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 |
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1817544418748530688 |