Modal embeddings and calling paradigms
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Outros Autores: | , |
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. |
id |
RCAP_1102ccdbb79e95ea172de0f53f6eacab |
---|---|
oai_identifier_str |
oai:repositorium.sdum.uminho.pt:1822/62978 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
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 |
_version_ |
1817544924251291648 |