Refocusing generalised normalisation
Autor(a) principal: | |
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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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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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1817545159526580224 |