Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi

Detalhes bibliográficos
Autor(a) principal: Pinto, Luís F.
Data de Publicação: 2000
Outros Autores: Dyckhoff, Roy
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/3833
Resumo: This paper presents two sequent calculi, requiring no clausal form for types, whose typable terms are in 1-1 correspondence with the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma-4calculi. Such sequent calculi allow no permutations in the order in which inference rules occur on derivations of typable terms and are thus appropriate for proof search. In these calculi proof search can be performed in a root-first fashion and type conversions are solely required in axiom formation.
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spelling Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculiDependent typesSequent calculusProof searchThis paper presents two sequent calculi, requiring no clausal form for types, whose typable terms are in 1-1 correspondence with the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma-4calculi. Such sequent calculi allow no permutations in the order in which inference rules occur on derivations of typable terms and are thus appropriate for proof search. In these calculi proof search can be performed in a root-first fashion and type conversions are solely required in axiom formation.Centro de Matemática da Universidade do Minho (CMAT).ElsevierUniversidade do MinhoPinto, Luís F.Dyckhoff, Roy20002000-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/3833eng"Electronic Notes in Theoretical Computer Science". ISSN 1571-0661. 17 (2000) 1-14.1571-0661'The original publication is available at www.sciencedirect.com'info: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:RCAAP2023-07-21T12:13:51Zoai:repositorium.sdum.uminho.pt:1822/3833Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:06:02.652486Repositório 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 Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi
title Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi
spellingShingle Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi
Pinto, Luís F.
Dependent types
Sequent calculus
Proof search
title_short Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi
title_full Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi
title_fullStr Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi
title_full_unstemmed Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi
title_sort Sequent calculi for the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma$-calculi
author Pinto, Luís F.
author_facet Pinto, Luís F.
Dyckhoff, Roy
author_role author
author2 Dyckhoff, Roy
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Pinto, Luís F.
Dyckhoff, Roy
dc.subject.por.fl_str_mv Dependent types
Sequent calculus
Proof search
topic Dependent types
Sequent calculus
Proof search
description This paper presents two sequent calculi, requiring no clausal form for types, whose typable terms are in 1-1 correspondence with the normal terms of the $\lambda\Pi$- and $\lambda\Pi\Sigma-4calculi. Such sequent calculi allow no permutations in the order in which inference rules occur on derivations of typable terms and are thus appropriate for proof search. In these calculi proof search can be performed in a root-first fashion and type conversions are solely required in axiom formation.
publishDate 2000
dc.date.none.fl_str_mv 2000
2000-01-01T00:00:00Z
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/1822/3833
url http://hdl.handle.net/1822/3833
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Electronic Notes in Theoretical Computer Science". ISSN 1571-0661. 17 (2000) 1-14.
1571-0661
'The original publication is available at www.sciencedirect.com'
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
publisher.none.fl_str_mv Elsevier
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
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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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
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