The computational content of atomic polymorphism

Detalhes bibliográficos
Autor(a) principal: Ferreira, Gilda
Data de Publicação: 2019
Outros Autores: Vasconcelos, Vasco T
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/9415
Resumo: We show that the number-theoretic functions de nable in the atomic polymorphic system (Fat) are exactly the extended polynomials. Two proofs of the above result are presented: one reducing the functions' de n- ability problem in Fat to de nability in the simply typed lambda-calculus and other directly adapting Helmut Schwichtenberg's strategy for de nability in the simply typed lambda-calculus to the atomic polymorphic setting. The uniformity granted in the polymorphic system, when compared with the simply typed lambda-calculus, is emphasized.
id RCAP_1f156858090264ce8f3bf89c21dc81cf
oai_identifier_str oai:repositorioaberto.uab.pt:10400.2/9415
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling The computational content of atomic polymorphismPredicative polymorphismRepresentable functionsLambda-calculusNormalizationBeta-equalityExtended polynomialsODS::04:Educação de QualidadeWe show that the number-theoretic functions de nable in the atomic polymorphic system (Fat) are exactly the extended polynomials. Two proofs of the above result are presented: one reducing the functions' de n- ability problem in Fat to de nability in the simply typed lambda-calculus and other directly adapting Helmut Schwichtenberg's strategy for de nability in the simply typed lambda-calculus to the atomic polymorphic setting. The uniformity granted in the polymorphic system, when compared with the simply typed lambda-calculus, is emphasized.This work was supported by Fundação para a Ciência e a Tecnologia [UID/MAT/ 04561/2013, UID/CEC/00408/2013 and grant SFRH/BPD/93278/2013 to G.F.]. The first author is also grateful to Centro de Matemática, Aplicações Fundamentais e Investigação Operacional and to Large-Scale Informatics Systems Laboratory (Universidade de Lisboa).Oxford Academic - Oxford JournalsRepositório AbertoFerreira, GildaVasconcelos, Vasco T2020-03-02T16:17:13Z20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/9415eng1367-075110.1093/jigpal/jzy0761368-9894info: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:RCAAP2023-11-16T15:32:29Zoai:repositorioaberto.uab.pt:10400.2/9415Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:49:13.399981Repositório 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 computational content of atomic polymorphism
title The computational content of atomic polymorphism
spellingShingle The computational content of atomic polymorphism
Ferreira, Gilda
Predicative polymorphism
Representable functions
Lambda-calculus
Normalization
Beta-equality
Extended polynomials
ODS::04:Educação de Qualidade
title_short The computational content of atomic polymorphism
title_full The computational content of atomic polymorphism
title_fullStr The computational content of atomic polymorphism
title_full_unstemmed The computational content of atomic polymorphism
title_sort The computational content of atomic polymorphism
author Ferreira, Gilda
author_facet Ferreira, Gilda
Vasconcelos, Vasco T
author_role author
author2 Vasconcelos, Vasco T
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Ferreira, Gilda
Vasconcelos, Vasco T
dc.subject.por.fl_str_mv Predicative polymorphism
Representable functions
Lambda-calculus
Normalization
Beta-equality
Extended polynomials
ODS::04:Educação de Qualidade
topic Predicative polymorphism
Representable functions
Lambda-calculus
Normalization
Beta-equality
Extended polynomials
ODS::04:Educação de Qualidade
description We show that the number-theoretic functions de nable in the atomic polymorphic system (Fat) are exactly the extended polynomials. Two proofs of the above result are presented: one reducing the functions' de n- ability problem in Fat to de nability in the simply typed lambda-calculus and other directly adapting Helmut Schwichtenberg's strategy for de nability in the simply typed lambda-calculus to the atomic polymorphic setting. The uniformity granted in the polymorphic system, when compared with the simply typed lambda-calculus, is emphasized.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01T00:00:00Z
2020-03-02T16:17:13Z
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/10400.2/9415
url http://hdl.handle.net/10400.2/9415
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1367-0751
10.1093/jigpal/jzy076
1368-9894
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 Oxford Academic - Oxford Journals
publisher.none.fl_str_mv Oxford Academic - Oxford Journals
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
_version_ 1799135075674095616

Registros relacionados