Monadic translation of classical sequent calculus
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , , |
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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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:RCAAP2024-05-11T05:56:36Zoai:repositorium.sdum.uminho.pt:1822/20889Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T05:56:36Repositório 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 |
mluisa.alvim@gmail.com |
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1817544794904199168 |