Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/89543
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Campo DC | Valor | Idioma |
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dc.contributor.author | Dahlqvist, Fredrik | por |
dc.contributor.author | Neves, Renato Jorge Araújo | por |
dc.date.accessioned | 2024-03-14T16:27:55Z | - |
dc.date.available | 2024-03-14T16:27:55Z | - |
dc.date.issued | 2023 | - |
dc.identifier.citation | Dahlqvist, F., & Neves, R. (2023, December 18). The syntactic side of autonomous categories enriched over generalised metric spaces. Logical Methods in Computer Science. Logical Methods in Computer Science. http://doi.org/10.46298/lmcs-19(4:31)2023 | por |
dc.identifier.issn | 1860-5974 | - |
dc.identifier.uri | https://hdl.handle.net/1822/89543 | - |
dc.description.abstract | Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the idea of equivalence taking values in a quantale V, which covers the cases of (in)equations and (ultra)metric equations among others. Our main result is the introduction of a V-equational deductive system for linear λ-calculus together with a proof that it is sound and complete. In fact we go further than this, by showing that linear λ-theories based on this V-equational system form a category equivalent to a category of autonomous categories enriched over ‘generalised metric spaces’. If we instantiate this result to inequations, we get an equivalence with autonomous categories enriched over partial orders. In the case of (ultra)metric equations, we get an equivalence with autonomous categories enriched over (ultra)metric spaces. Additionally, we show that this syntax-semantics correspondence extends to the affine setting. We use our results to develop examples of inequational and metric equational systems for higher-order programming in the setting of real-time, probabilistic, and quantum computing. | por |
dc.description.sponsorship | This work is financed by National Funds through FCT - Fundação para a Ciência e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) within project IBEX, with reference PTDC/CCI-COM/4280/2021. We are also thankful for the reviewers’ helpful feedback. | por |
dc.language.iso | eng | por |
dc.publisher | Logical Methods in Computer Science | por |
dc.relation | info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FCCI-COM%2F4280%2F2021/PT | por |
dc.rights | openAccess | por |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | por |
dc.subject | categorical logic | por |
dc.subject | enriched category theory | por |
dc.subject | quantale | por |
dc.subject | λ-calculus | por |
dc.title | The syntactic side of autonomous categories enriched over generalised metric spaces | por |
dc.type | article | por |
dc.peerreviewed | yes | por |
dc.relation.publisherversion | https://lmcs.episciences.org/12719 | por |
oaire.citationStartPage | 31:1 | por |
oaire.citationEndPage | 31:42 | por |
oaire.citationIssue | 4 | por |
oaire.citationVolume | 19 | por |
dc.date.updated | 2024-03-14T08:09:26Z | - |
dc.identifier.doi | 10.46298/lmcs-19(4:31)2023 | por |
dc.subject.fos | Ciências Naturais::Ciências da Computação e da Informação | por |
dc.subject.fos | Engenharia e Tecnologia::Engenharia Eletrotécnica, Eletrónica e Informática | por |
sdum.export.identifier | 13433 | - |
sdum.journal | Logical Methods in Computer Science | por |
oaire.version | VoR | por |
Aparece nas coleções: | HASLab - Artigos em revistas internacionais |
Este trabalho está licenciado sob uma Licença Creative Commons