The polarized λ-calculus
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/50672 |
Resumo: | A natural deduction system isomorphic to the focused sequent calculus for polarized intuitionistic logic is proposed. The system comes with a language of proof-terms, named polarized λ-calculus, whose reduction rules express simultaneously a normalization procedure and the isomorphic copy of the cut-elimination procedure pertaining to the focused sequent calculus. Noteworthy features of this natural deduction system are: how the polarity of a connective determines the style of its elimination rule; the existence of a proof-search strategy which is equivalent to focusing in the sequent calculus; the highlydisciplined organization of the syntax - even atoms have introduction, elimination and normalization rules. The polarized λ-calculus is a programming formalism close to call-by-push-value, but justified by its proof-theoretical pedigree. |
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The polarized λ-calculusPolarized logicFocusingBidirectional natural deductionGeneral elimination ruleEta-expansionScience & TechnologyA natural deduction system isomorphic to the focused sequent calculus for polarized intuitionistic logic is proposed. The system comes with a language of proof-terms, named polarized λ-calculus, whose reduction rules express simultaneously a normalization procedure and the isomorphic copy of the cut-elimination procedure pertaining to the focused sequent calculus. Noteworthy features of this natural deduction system are: how the polarity of a connective determines the style of its elimination rule; the existence of a proof-search strategy which is equivalent to focusing in the sequent calculus; the highlydisciplined organization of the syntax - even atoms have introduction, elimination and normalization rules. The polarized λ-calculus is a programming formalism close to call-by-push-value, but justified by its proof-theoretical pedigree.This research was financed by Portuguese Funds through FCT Fundac¸ao para a Ci ˜ encia ˆ e a Tecnologia, within the Project UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersionElsevier EspañaUniversidade do MinhoEspírito Santo, José20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/50672eng1571-066110.1016/j.entcs.2017.04.010info: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:RCAAP2023-07-21T12:44:54Zoai:repositorium.sdum.uminho.pt:1822/50672Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:42:41.703540Repositório 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 |
The polarized λ-calculus |
title |
The polarized λ-calculus |
spellingShingle |
The polarized λ-calculus Espírito Santo, José Polarized logic Focusing Bidirectional natural deduction General elimination rule Eta-expansion Science & Technology |
title_short |
The polarized λ-calculus |
title_full |
The polarized λ-calculus |
title_fullStr |
The polarized λ-calculus |
title_full_unstemmed |
The polarized λ-calculus |
title_sort |
The polarized λ-calculus |
author |
Espírito Santo, José |
author_facet |
Espírito Santo, José |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Espírito Santo, José |
dc.subject.por.fl_str_mv |
Polarized logic Focusing Bidirectional natural deduction General elimination rule Eta-expansion Science & Technology |
topic |
Polarized logic Focusing Bidirectional natural deduction General elimination rule Eta-expansion Science & Technology |
description |
A natural deduction system isomorphic to the focused sequent calculus for polarized intuitionistic logic is proposed. The system comes with a language of proof-terms, named polarized λ-calculus, whose reduction rules express simultaneously a normalization procedure and the isomorphic copy of the cut-elimination procedure pertaining to the focused sequent calculus. Noteworthy features of this natural deduction system are: how the polarity of a connective determines the style of its elimination rule; the existence of a proof-search strategy which is equivalent to focusing in the sequent calculus; the highlydisciplined organization of the syntax - even atoms have introduction, elimination and normalization rules. The polarized λ-calculus is a programming formalism close to call-by-push-value, but justified by its proof-theoretical pedigree. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 2017-01-01T00:00:00Z |
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/1822/50672 |
url |
http://hdl.handle.net/1822/50672 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1571-0661 10.1016/j.entcs.2017.04.010 |
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 |
Elsevier España |
publisher.none.fl_str_mv |
Elsevier España |
dc.source.none.fl_str_mv |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132980855177217 |