Monadic translation of classical sequent calculus

Detalhes bibliográficos
Autor(a) principal: Espírito Santo, José
Data de Publicação: 2013
Outros Autores: Matthes, Ralph, Nakazawa, Koji, Pinto, Luís F.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/20889
Resumo: Em publicação
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spelling Monadic translation of classical sequent calculusScience & TechnologyEm publicaçãoWe study monadic translations of the call-by-name (cbn) and the call-by-value (cbv) fragments of the classical sequent calculus lambda-mu-mu~ by Curien and Herbelin and give modular and syntactic proofs of strong normalization. The target of the translations is a new meta-language for classical logic, named monadic lambda-mu . It is a monadic reworking of Parigot’s -calculus, where the monadic binding is confined to commands, thus integrating the monad with the classical features. Also its mu -reduction rule is replaced by one expressing the interaction between monadic binding and mu -abstraction. Our monadic translations produce very tight simulations of the respective fragments of lambda-mu-mu~ inside monadic lambda-mu , with reduction steps of lambda-mu-mu~ being translated in 1-1 fashion, except for beta-steps which require two steps. The monad of monadic lambda-mu can be instantiated to the continuations monad so as to ensure strict simulation of monadic lambda-mu inside simply-typed -calculus with beta- and eta -reduction. Through strict simulation, strong normalization of simply-typed -calculus is inherited to monadic lambda-mu and then to cbn and cbv lambda-mu-mu~, thus reproving in an elementary syntactical way strong normalization for these fragments of lambda-mu-mu~ and establishing it for our new calculus. These results extend to second-order logic, with polymorphic -calculus as target, giving new strong normalization results for classical second-order logic in sequent calculus style. CPS translations of cbn and cbv lambda-mu-mu~ with the strict simulation property are obtained by composing our monadic translations with the continuations-monad instantiation. In an appendix to the article we investigate several refinements of the continuations-monad instantiation in order to obtain in a modular way improvements of the CPS translations enjoying extra properties like simulation by cbv beta -reduction or reduction of administrative redexes at compile time.Jose Espirito Santo and Luis Pinto have been financed by FEDER funds through 'Programa Operacional Factores de Competitividade - COMPETE' and by Portuguese funds through FCT - 'Fundacao para a Ciencia e a Tecnologia', within the project PEst-C/MAT/UI0013/2011.Koji Nakazawa has been supported by the Kyoto University Foundation for an extended research visit to Ralph Matthes.Cambridge University PressUniversidade do MinhoEspírito Santo, JoséMatthes, RalphNakazawa, KojiPinto, Luís F.20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/20889eng0960-129510.1017/s0960129512000436info: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:RCAAP2023-07-21T12:24:59Zoai:repositorium.sdum.uminho.pt:1822/20889Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:19:09.204965Repositório 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 Monadic translation of classical sequent calculus
title Monadic translation of classical sequent calculus
spellingShingle Monadic translation of classical sequent calculus
Espírito Santo, José
Science & Technology
title_short Monadic translation of classical sequent calculus
title_full Monadic translation of classical sequent calculus
title_fullStr Monadic translation of classical sequent calculus
title_full_unstemmed Monadic translation of classical sequent calculus
title_sort Monadic translation of classical sequent calculus
author Espírito Santo, José
author_facet Espírito Santo, José
Matthes, Ralph
Nakazawa, Koji
Pinto, Luís F.
author_role author
author2 Matthes, Ralph
Nakazawa, Koji
Pinto, Luís F.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Espírito Santo, José
Matthes, Ralph
Nakazawa, Koji
Pinto, Luís F.
dc.subject.por.fl_str_mv Science & Technology
topic Science & Technology
description Em publicação
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/20889
url http://hdl.handle.net/1822/20889
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0960-1295
10.1017/s0960129512000436
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 Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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
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