Modal embeddings and calling paradigms

Detalhes bibliográficos
Autor(a) principal: Espírito Santo, José
Data de Publicação: 2019
Outros Autores: Pinto, Luís F., Uustalu, Tarmo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/62978
Resumo: We study the computational interpretation of the two standard modal embeddings, usually named after Girard and Gödel, of intuitionistic logic into IS4. As source system we take either the call-byname (cbn) or the call-by-value (cbv) lambda-calculus with simple types. The target system can be taken to be the, arguably, simplest fragment of IS4, here recast as a very simple lambda-calculus equipped with an indeterminate lax monoidal comonad. A slight refinement of the target and of the embeddings shows that: the target is a calculus indifferent to the calling paradigms cbn/cbv, obeying a new paradigm that we baptize call-by-box (cbb), and enjoying standardization; and that Girard’s (resp. Gödel’s) embbedding is a translation of cbn (resp. cbv) lambda-calculus into this calculus, using a compilation technique we call protecting-by-a-box, enjoying the preservation and reflection properties known for cps translations - but in a stronger form that allows the extraction of standardization for cbn or cbv as consequence of standardization for cbb. The modal target and embeddings achieve thus an unification of call-by-name and call-by-value as call-by-box.
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spelling Modal embeddings and calling paradigmsIntuitionistic S4Call-by-nameCall-by-valueComonadic lambda-calculusStandardizationIndifference propertyCiências Naturais::MatemáticasCiências Naturais::Ciências da Computação e da InformaçãoWe study the computational interpretation of the two standard modal embeddings, usually named after Girard and Gödel, of intuitionistic logic into IS4. As source system we take either the call-byname (cbn) or the call-by-value (cbv) lambda-calculus with simple types. The target system can be taken to be the, arguably, simplest fragment of IS4, here recast as a very simple lambda-calculus equipped with an indeterminate lax monoidal comonad. A slight refinement of the target and of the embeddings shows that: the target is a calculus indifferent to the calling paradigms cbn/cbv, obeying a new paradigm that we baptize call-by-box (cbb), and enjoying standardization; and that Girard’s (resp. Gödel’s) embbedding is a translation of cbn (resp. cbv) lambda-calculus into this calculus, using a compilation technique we call protecting-by-a-box, enjoying the preservation and reflection properties known for cps translations - but in a stronger form that allows the extraction of standardization for cbn or cbv as consequence of standardization for cbb. The modal target and embeddings achieve thus an unification of call-by-name and call-by-value as call-by-box.J.E.S. and L.P. were supported by Fundação para a Ciência e a Tecnologia (FCT) throughproject UID/MAT/00013/2013. T.U. was supported by the Estonian Ministry of Education and Research through institutional research grant IUT33-13. All three authors received support fromthe COST action CA15123 EUTYPES.Schloss Dagstuhl - Leibniz-Zentrum für InformatikUniversidade do MinhoEspírito Santo, JoséPinto, Luís F.Uustalu, Tarmo20192019-01-01T00:00:00Zconference paperinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/1822/62978engEspírito Santo, J., Pinto, L., & Uustalu, T. (2019). Modal Embeddings and Calling Paradigms. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.978-3-95977-107-81868-896910.4230/LIPIcs.FSCD.2019.18https://drops.dagstuhl.de/opus/volltexte/2019/10525/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:RCAAP2024-05-11T06:18:03Zoai:repositorium.sdum.uminho.pt:1822/62978Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T06:18:03Repositório 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 Modal embeddings and calling paradigms
title Modal embeddings and calling paradigms
spellingShingle Modal embeddings and calling paradigms
Espírito Santo, José
Intuitionistic S4
Call-by-name
Call-by-value
Comonadic lambda-calculus
Standardization
Indifference property
Ciências Naturais::Matemáticas
Ciências Naturais::Ciências da Computação e da Informação
title_short Modal embeddings and calling paradigms
title_full Modal embeddings and calling paradigms
title_fullStr Modal embeddings and calling paradigms
title_full_unstemmed Modal embeddings and calling paradigms
title_sort Modal embeddings and calling paradigms
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 Intuitionistic S4
Call-by-name
Call-by-value
Comonadic lambda-calculus
Standardization
Indifference property
Ciências Naturais::Matemáticas
Ciências Naturais::Ciências da Computação e da Informação
topic Intuitionistic S4
Call-by-name
Call-by-value
Comonadic lambda-calculus
Standardization
Indifference property
Ciências Naturais::Matemáticas
Ciências Naturais::Ciências da Computação e da Informação
description We study the computational interpretation of the two standard modal embeddings, usually named after Girard and Gödel, of intuitionistic logic into IS4. As source system we take either the call-byname (cbn) or the call-by-value (cbv) lambda-calculus with simple types. The target system can be taken to be the, arguably, simplest fragment of IS4, here recast as a very simple lambda-calculus equipped with an indeterminate lax monoidal comonad. A slight refinement of the target and of the embeddings shows that: the target is a calculus indifferent to the calling paradigms cbn/cbv, obeying a new paradigm that we baptize call-by-box (cbb), and enjoying standardization; and that Girard’s (resp. Gödel’s) embbedding is a translation of cbn (resp. cbv) lambda-calculus into this calculus, using a compilation technique we call protecting-by-a-box, enjoying the preservation and reflection properties known for cps translations - but in a stronger form that allows the extraction of standardization for cbn or cbv as consequence of standardization for cbb. The modal target and embeddings achieve thus an unification of call-by-name and call-by-value as call-by-box.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01T00:00:00Z
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/1822/62978
url http://hdl.handle.net/1822/62978
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Espírito Santo, J., Pinto, L., & Uustalu, T. (2019). Modal Embeddings and Calling Paradigms. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.
978-3-95977-107-8
1868-8969
10.4230/LIPIcs.FSCD.2019.18
https://drops.dagstuhl.de/opus/volltexte/2019/10525/
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 Schloss Dagstuhl - Leibniz-Zentrum für Informatik
publisher.none.fl_str_mv Schloss Dagstuhl - Leibniz-Zentrum für Informatik
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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