Refocusing generalised normalisation

Detalhes bibliográficos
Autor(a) principal: Espírito Santo, José
Data de Publicação: 2007
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/8423
Resumo: When defined with general elimination/application rules, natural deduction and $\lambda$-calculus become closer to sequent calculus. In order to get real isomorphism, normalisation has to be defined in a ``multiary'' variant, in which reduction rules are necessarily non-local (reason: nomalisation, like cut-elimination, acts at the \emph{head} of applicative terms, but natural deduction focuses at the \emph{tail} of such terms). Non-local rules are bad, for instance, for the mechanization of the system. A solution is to extend natural deduction even further to a \emph{unified calculus} based on the unification of cut and general elimination. In the unified calculus, a sequent term behaves like in the sequent calculus, whereas the reduction steps of a natural deduction term are interleaved with explicit steps for bringing heads to focus. A variant of the calculus has the symmetric role of improving sequent calculus in dealing with tail-active permutative conversions.
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spelling Refocusing generalised normalisationnormalisationgeneralised elimination rulesmultiarityScience & TechnologyWhen defined with general elimination/application rules, natural deduction and $\lambda$-calculus become closer to sequent calculus. In order to get real isomorphism, normalisation has to be defined in a ``multiary'' variant, in which reduction rules are necessarily non-local (reason: nomalisation, like cut-elimination, acts at the \emph{head} of applicative terms, but natural deduction focuses at the \emph{tail} of such terms). Non-local rules are bad, for instance, for the mechanization of the system. A solution is to extend natural deduction even further to a \emph{unified calculus} based on the unification of cut and general elimination. In the unified calculus, a sequent term behaves like in the sequent calculus, whereas the reduction steps of a natural deduction term are interleaved with explicit steps for bringing heads to focus. A variant of the calculus has the symmetric role of improving sequent calculus in dealing with tail-active permutative conversions.Springer VerlagUniversidade do MinhoEspírito Santo, José20072007-01-01T00:00:00Zconference paperinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/1822/8423engCONFERENCE ON COMPUTABILITY IN EUROPE, (CiE2007) 3, Sienna, 2007 – “Conference on Computability in Europe, CiE 2007: Proceedings”. [S.l. : s. n.,] 2007.97835407300020302-974310.1007/978-3-540-73001-9_27www.springerlink.cominfo: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:RCAAP2024-05-11T06:58:52Zoai:repositorium.sdum.uminho.pt:1822/8423Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T06:58:52Repositório 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 Refocusing generalised normalisation
title Refocusing generalised normalisation
spellingShingle Refocusing generalised normalisation
Espírito Santo, José
normalisation
generalised elimination rules
multiarity
Science & Technology
title_short Refocusing generalised normalisation
title_full Refocusing generalised normalisation
title_fullStr Refocusing generalised normalisation
title_full_unstemmed Refocusing generalised normalisation
title_sort Refocusing generalised normalisation
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 normalisation
generalised elimination rules
multiarity
Science & Technology
topic normalisation
generalised elimination rules
multiarity
Science & Technology
description When defined with general elimination/application rules, natural deduction and $\lambda$-calculus become closer to sequent calculus. In order to get real isomorphism, normalisation has to be defined in a ``multiary'' variant, in which reduction rules are necessarily non-local (reason: nomalisation, like cut-elimination, acts at the \emph{head} of applicative terms, but natural deduction focuses at the \emph{tail} of such terms). Non-local rules are bad, for instance, for the mechanization of the system. A solution is to extend natural deduction even further to a \emph{unified calculus} based on the unification of cut and general elimination. In the unified calculus, a sequent term behaves like in the sequent calculus, whereas the reduction steps of a natural deduction term are interleaved with explicit steps for bringing heads to focus. A variant of the calculus has the symmetric role of improving sequent calculus in dealing with tail-active permutative conversions.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-01-01T00:00:00Z
dc.type.driver.fl_str_mv conference paper
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/8423
url http://hdl.handle.net/1822/8423
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv CONFERENCE ON COMPUTABILITY IN EUROPE, (CiE2007) 3, Sienna, 2007 – “Conference on Computability in Europe, CiE 2007: Proceedings”. [S.l. : s. n.,] 2007.
9783540730002
0302-9743
10.1007/978-3-540-73001-9_27
www.springerlink.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 Springer Verlag
publisher.none.fl_str_mv Springer Verlag
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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