Proof Nets as Processes
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2012 |
| Tipo de documento: | Relatório |
| Idioma: | eng |
| Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
| Texto Completo: | http://hdl.handle.net/10451/14180 |
Resumo: | This work describes a process algebraic interpretation of Proof-nets, which are the canonical objects of Linear Logic proofs. It therefore offers a logically founded basis for deterministic, implicit parallelism. |
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Proof Nets as ProcessesProgramming languagesProof netsTypesPropositions as typesDeterministic parallelismPi calculusProcess algebraLinear LogicThis work describes a process algebraic interpretation of Proof-nets, which are the canonical objects of Linear Logic proofs. It therefore offers a logically founded basis for deterministic, implicit parallelism.We present delta-calculus, a novel interpretation of Linear Logic, in the form of a typed process algebra that enjoys a Curry-Howard correspondence with Proof Nets. Reduction inherits the qualities of the logical objects: termination, deadlock-freedom, determinism, and very importantly, a high degree of parallelism. We obtain the necessary soundness results and provide a propositions-as-types theorem. The basic system is extended in two directions. First, we adapt it to interpret Affine Logic. Second, we propose extensions for general recursion, and introduce a novel form of recursive linear types. As an application we show a highly parallel type-preserving translation from a linear System F and extend it to the recursive variation. Our interpretation can be seen as a more canonical proof-theoretic alternative to several recent works on pi-calculus interpretations of linear sequent proofs (propositions-as-sessions) which exhibit reduced parallelism.Repositório da Universidade de LisboaMostrous, Dimitris2012-10-31T02:38:34Z2012-10-31T02:38:34Z2012-10-31info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/reportapplication/pdfhttp://hdl.handle.net/10451/14180enginfo: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:RCAAP2023-11-08T15:59:50Zoai:repositorio.ul.pt:10451/14180Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:36:01.020394Repositório 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 |
Proof Nets as Processes |
| title |
Proof Nets as Processes |
| spellingShingle |
Proof Nets as Processes Mostrous, Dimitris Programming languages Proof nets Types Propositions as types Deterministic parallelism Pi calculus Process algebra Linear Logic |
| title_short |
Proof Nets as Processes |
| title_full |
Proof Nets as Processes |
| title_fullStr |
Proof Nets as Processes |
| title_full_unstemmed |
Proof Nets as Processes |
| title_sort |
Proof Nets as Processes |
| author |
Mostrous, Dimitris |
| author_facet |
Mostrous, Dimitris |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
| dc.contributor.author.fl_str_mv |
Mostrous, Dimitris |
| dc.subject.por.fl_str_mv |
Programming languages Proof nets Types Propositions as types Deterministic parallelism Pi calculus Process algebra Linear Logic |
| topic |
Programming languages Proof nets Types Propositions as types Deterministic parallelism Pi calculus Process algebra Linear Logic |
| description |
This work describes a process algebraic interpretation of Proof-nets, which are the canonical objects of Linear Logic proofs. It therefore offers a logically founded basis for deterministic, implicit parallelism. |
| publishDate |
2012 |
| dc.date.none.fl_str_mv |
2012-10-31T02:38:34Z 2012-10-31T02:38:34Z 2012-10-31 |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/report |
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report |
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publishedVersion |
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http://hdl.handle.net/10451/14180 |
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http://hdl.handle.net/10451/14180 |
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eng |
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eng |
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openAccess |
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application/pdf |
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