Plotkin's call-by-value λ-calculus as a modal calculus

Detalhes bibliográficos
Autor(a) principal: Espírito Santo, José
Data de Publicação: 2022
Outros Autores: Pinto, Luís F., Uustalu, Tarmo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/87619
Resumo: In the authors' previous analysis of the calling paradigms call-by-name and call-by-value through Girard's and Gödel's embeddings into the S4 modal logic, an asymmetry remains: the two paradigms are unified by the call-by-box paradigm of the modal target, but only for call-by-name can one say that the paradigm exists, up to isomorphism, inside the modal target. In this paper, we show that, by pushing further the modal analysis, a symmetric situation is revealed, in that ordinary and Plotkin's λ-calculi are shown to truly co-exist inside a simple modal calculus.
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spelling Plotkin's call-by-value λ-calculus as a modal calculusCall-by-nameCall-by-valueGirard's embeddingGödel's embeddingS4 modal logicλ-calculuslambda-calculusGodel's embeddingScience & TechnologyIn the authors' previous analysis of the calling paradigms call-by-name and call-by-value through Girard's and Gödel's embeddings into the S4 modal logic, an asymmetry remains: the two paradigms are unified by the call-by-box paradigm of the modal target, but only for call-by-name can one say that the paradigm exists, up to isomorphism, inside the modal target. In this paper, we show that, by pushing further the modal analysis, a symmetric situation is revealed, in that ordinary and Plotkin's λ-calculi are shown to truly co-exist inside a simple modal calculus.The first and second authors were partially financed by Portuguese Funds through FCT (Fundação para a Ciência e Tecnologia) within the projects UIDB/00013/2020 and UIDP/00013/2020. The third author was supported by the Estonian Ministry of Education and Research institutional research grant IUT33-13. All the three authors were supported by the EU COST action CA15123 EUTYPESElsevierUniversidade do MinhoEspírito Santo, JoséPinto, Luís F.Uustalu, Tarmo2022-012022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/87619engEspírito Santo, J., Pinto, L., & Uustalu, T. (2022, June). Plotkin's call-by-value λ-calculus as a modal calculus. Journal of Logical and Algebraic Methods in Programming. Elsevier BV. http://doi.org/10.1016/j.jlamp.2022.1007752352-22082352-221610.1016/j.jlamp.2022.100775https://www.sciencedirect.com/science/article/pii/S2352220822000281info: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:RCAAP2024-02-10T01:19:25Zoai:repositorium.sdum.uminho.pt:1822/87619Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:55:39.948728Repositório 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 Plotkin's call-by-value λ-calculus as a modal calculus
title Plotkin's call-by-value λ-calculus as a modal calculus
spellingShingle Plotkin's call-by-value λ-calculus as a modal calculus
Espírito Santo, José
Call-by-name
Call-by-value
Girard's embedding
Gödel's embedding
S4 modal logic
λ-calculus
lambda-calculus
Godel's embedding
Science & Technology
title_short Plotkin's call-by-value λ-calculus as a modal calculus
title_full Plotkin's call-by-value λ-calculus as a modal calculus
title_fullStr Plotkin's call-by-value λ-calculus as a modal calculus
title_full_unstemmed Plotkin's call-by-value λ-calculus as a modal calculus
title_sort Plotkin's call-by-value λ-calculus as a modal calculus
author Espírito Santo, José
author_facet Espírito Santo, José
Pinto, Luís F.
Uustalu, Tarmo
author_role author
author2 Pinto, Luís F.
Uustalu, Tarmo
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Espírito Santo, José
Pinto, Luís F.
Uustalu, Tarmo
dc.subject.por.fl_str_mv Call-by-name
Call-by-value
Girard's embedding
Gödel's embedding
S4 modal logic
λ-calculus
lambda-calculus
Godel's embedding
Science & Technology
topic Call-by-name
Call-by-value
Girard's embedding
Gödel's embedding
S4 modal logic
λ-calculus
lambda-calculus
Godel's embedding
Science & Technology
description In the authors' previous analysis of the calling paradigms call-by-name and call-by-value through Girard's and Gödel's embeddings into the S4 modal logic, an asymmetry remains: the two paradigms are unified by the call-by-box paradigm of the modal target, but only for call-by-name can one say that the paradigm exists, up to isomorphism, inside the modal target. In this paper, we show that, by pushing further the modal analysis, a symmetric situation is revealed, in that ordinary and Plotkin's λ-calculi are shown to truly co-exist inside a simple modal calculus.
publishDate 2022
dc.date.none.fl_str_mv 2022-01
2022-01-01T00:00:00Z
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 https://hdl.handle.net/1822/87619
url https://hdl.handle.net/1822/87619
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Espírito Santo, J., Pinto, L., & Uustalu, T. (2022, June). Plotkin's call-by-value λ-calculus as a modal calculus. Journal of Logical and Algebraic Methods in Programming. Elsevier BV. http://doi.org/10.1016/j.jlamp.2022.100775
2352-2208
2352-2216
10.1016/j.jlamp.2022.100775
https://www.sciencedirect.com/science/article/pii/S2352220822000281
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
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
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