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Atomic polymorphism

Bibliographic Details
Main Author: Ferreira, Fernando
Publication Date: 2013
Other Authors: Ferreira, Gilda
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.2/9417
Summary: It has been known for six years that the restriction of Girard’s polymorphic system F to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait’s method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each β-reduction step of the full intuitionistic propositional calculus translates into one or more βη-reduction steps in the restricted Girard system. As a consequence, we obtain a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to η-conversions.
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spelling Atomic polymorphismPredicative polymorphismStrong normalizationNatural deductionSecond order lambda-calculusIt has been known for six years that the restriction of Girard’s polymorphic system F to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait’s method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each β-reduction step of the full intuitionistic propositional calculus translates into one or more βη-reduction steps in the restricted Girard system. As a consequence, we obtain a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to η-conversions.The Journal of Symbolic LogicRepositório AbertoFerreira, FernandoFerreira, Gilda2020-03-02T16:51:30Z20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/9417eng0022-481210.2178/jsl.7801180info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-26T09:55:00Zoai:repositorioaberto.uab.pt:10400.2/9417Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T21:12:18.600616Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Atomic polymorphism
title Atomic polymorphism
spellingShingle Atomic polymorphism
Ferreira, Fernando
Predicative polymorphism
Strong normalization
Natural deduction
Second order lambda-calculus
title_short Atomic polymorphism
title_full Atomic polymorphism
title_fullStr Atomic polymorphism
title_full_unstemmed Atomic polymorphism
title_sort Atomic polymorphism
author Ferreira, Fernando
author_facet Ferreira, Fernando
Ferreira, Gilda
author_role author
author2 Ferreira, Gilda
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Ferreira, Fernando
Ferreira, Gilda
dc.subject.por.fl_str_mv Predicative polymorphism
Strong normalization
Natural deduction
Second order lambda-calculus
topic Predicative polymorphism
Strong normalization
Natural deduction
Second order lambda-calculus
description It has been known for six years that the restriction of Girard’s polymorphic system F to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait’s method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each β-reduction step of the full intuitionistic propositional calculus translates into one or more βη-reduction steps in the restricted Girard system. As a consequence, we obtain a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to η-conversions.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01T00:00:00Z
2020-03-02T16:51:30Z
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/10400.2/9417
url http://hdl.handle.net/10400.2/9417
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-4812
10.2178/jsl.7801180
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 The Journal of Symbolic Logic
publisher.none.fl_str_mv The Journal of Symbolic Logic
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833599142856753153

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