Publicação
Modal embeddings and calling paradigms
| 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. |
|---|---|
| Autores principais: | Espírito Santo, José |
| Outros Autores: | Pinto, Luís F.; Uustalu, Tarmo |
| Assunto: | Intuitionistic S4 Call-by-name Call-by-value Comonadic lambda-calculus Standardization Indifference property |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | comunicação em conferência |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1866877153700741120 |
|---|---|
| author | Espírito Santo, José |
| author2 | Pinto, Luís F. Uustalu, Tarmo |
| author2_role | author author |
| author_facet | Espírito Santo, José Pinto, Luís F. Uustalu, Tarmo |
| author_role | author |
| contributor_name_str_mv | Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Espírito Santo, José\"},{\"Person.name\":\"Pinto, Luís F.\"},{\"Person.name\":\"Uustalu, Tarmo\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Espírito Santo, José Pinto, Luís F. Uustalu, Tarmo |
| datacite.date.Accepted.fl_str_mv | 2019-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2020-01-07T11:13:25Z |
| datacite.date.embargoed.fl_str_mv | 2020-01-07T11:13:25Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Intuitionistic S4 Call-by-name Call-by-value Comonadic lambda-calculus Standardization Indifference property |
| datacite.titles.title.fl_str_mv | Modal embeddings and calling paradigms |
| dc.contributor.none.fl_str_mv | Universidade do Minho |
| dc.creator.none.fl_str_mv | Espírito Santo, José Pinto, Luís F. Uustalu, Tarmo |
| dc.date.Accepted.fl_str_mv | 2019-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2020-01-07T11:13:25Z |
| dc.date.embargoed.fl_str_mv | 2020-01-07T11:13:25Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/62978 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
| dc.rights.cclincense.fl_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.rights.rights.copyright.fl_str_mv | openAccess |
| dc.subject.none.fl_str_mv | Intuitionistic S4 Call-by-name Call-by-value Comonadic lambda-calculus Standardization Indifference property |
| dc.title.fl_str_mv | Modal embeddings and calling paradigms |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_5794 |
| 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. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | conferencePaper |
| fulltext.url.fl_str_mv | https://prod-dspace.uminho.pt/bitstreams/b82da79b-2266-427f-957b-0228ab024cbd/download |
| id | rum_e8d16cf486b855fc7f0d8a39a6917c0e |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/62978 |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/62978 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Espírito Santo, José Pinto, Luís F. Uustalu, Tarmo |
| publishDate | 2019 |
| publisher.none.fl_str_mv | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engSchloss Dagstuhl - Leibniz-Zentrum für InformatikporWe 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.application/pdfporModal embeddings and calling paradigmsEspírito Santo, JoséPinto, Luís F.Uustalu, TarmoHostingInstitutionOrganizationalUniversidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptISBNIsPartOf978-3-95977-107-8ISSNIsPartOf1868-8969DOIIsPartOf10.4230/LIPIcs.FSCD.2019.182020-01-07T11:13:25Z20192019-01-01T00:00:00ZHandlehttps://hdl.handle.net/1822/62978http://purl.org/coar/access_right/c_abf2open accessIntuitionistic S4Call-by-nameCall-by-valueComonadic lambda-calculusStandardizationIndifference property577583 bytesother research producthttp://purl.org/coar/resource_type/c_5794conference paper2019http://creativecommons.org/licenses/by/4.0/openAccesshttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://prod-dspace.uminho.pt/bitstreams/b82da79b-2266-427f-957b-0228ab024cbd/download |
| spellingShingle | Modal embeddings and calling paradigms Espírito Santo, José Intuitionistic S4 Call-by-name Call-by-value Comonadic lambda-calculus Standardization Indifference property |
| status | SINGLETON |
| subject.fl_str_mv | Intuitionistic S4 Call-by-name Call-by-value Comonadic lambda-calculus Standardization Indifference property |
| title | 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_short | Modal embeddings and calling paradigms |
| title_sort | Modal embeddings and calling paradigms |
| topic | Intuitionistic S4 Call-by-name Call-by-value Comonadic lambda-calculus Standardization Indifference property |
| topic_facet | Intuitionistic S4 Call-by-name Call-by-value Comonadic lambda-calculus Standardization Indifference property |
| url | https://hdl.handle.net/1822/62978 |
| visible | 1 |