Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2019 |
| Tipo de documento: | Tese |
| Idioma: | eng |
| Título da fonte: | Repositório Institucional do IBICT - RIDI |
| Texto Completo: | http://ridi.ibict.br/handle/123456789/1012 |
Resumo: | A sintaxe nominal tem sido utilizada em vários contextos por quase duas décadas. Ela é uma ferramenta poderosa para se lidar com ligação de variáveis de uma forma concreta, que pode ser aplicada a qualquer especificação na qual parâmetros são utilizados para se abstrair variáveis, tal como em predicados e funções. Na sintaxe nominal, objetos que são sintaticamente diferentes podem ter a mesma semântica módulo alfa-conversão, tal como acontece no Cálculo Lambda. O tratamento de igualdades, em especial a alphaequivalêcia, é algo essencial em linguagens formais e implementações. Este trabalho investiga a alpha-equivalência nominal com símbolos de função associativos (A), comutativos (C) e associativos-comutativos (AC). Verificação de equivalência, casamento e unificação módulo A, C e AC são investigados. Em relação a verificação de igualdade, as alphaequivalências nominais módulo A, C e AC foram especificadas em Coq e provadas ser corretas. Um algoritmo implementado em OCaml para verificação de igualdade módulo A, C e AC é automaticamente extraído da especificação e experimentos são executados utilizando-se também um algoritmo aperfeiçoado. Limites superiores para o tempo de execução na solução de problemas nominais de verificação equacional são fornecidos. Um algoritmo de unificação módulo C baseado em regras de redução é especificado em Coq e provado ser correto e completo. Por meio do uso de variáveis protegidas, este algoritmo de unificação resolve problemas de casamento nominal módulo C, o que foi também formalizado ser correto e completo. O algoritmo de unificação baseado em regras de redução fornece uma família finita de conjuntos de equações nominais de ponto fixo. Cada uma destas equações pode ter um conjunto infinito de soluções independentes. Portanto, demonstra-se que problemas de unificação nominal módulo C e AC podem gerar um conjunto infinito de soluções independentes. Este fato contrasta com unificação sintática módulo C ou AC, que são conhecidas por estar na classe finitária de problemas. Uma implementação em OCaml do algoritmo de unificação nominal é fornecida e utilizado para se construir exemplos. |
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2019-05-06T16:04:02Z2019-03-192019-05-06T16:04:02Z2019http://ridi.ibict.br/handle/123456789/1012A sintaxe nominal tem sido utilizada em vários contextos por quase duas décadas. Ela é uma ferramenta poderosa para se lidar com ligação de variáveis de uma forma concreta, que pode ser aplicada a qualquer especificação na qual parâmetros são utilizados para se abstrair variáveis, tal como em predicados e funções. Na sintaxe nominal, objetos que são sintaticamente diferentes podem ter a mesma semântica módulo alfa-conversão, tal como acontece no Cálculo Lambda. O tratamento de igualdades, em especial a alphaequivalêcia, é algo essencial em linguagens formais e implementações. Este trabalho investiga a alpha-equivalência nominal com símbolos de função associativos (A), comutativos (C) e associativos-comutativos (AC). Verificação de equivalência, casamento e unificação módulo A, C e AC são investigados. Em relação a verificação de igualdade, as alphaequivalências nominais módulo A, C e AC foram especificadas em Coq e provadas ser corretas. Um algoritmo implementado em OCaml para verificação de igualdade módulo A, C e AC é automaticamente extraído da especificação e experimentos são executados utilizando-se também um algoritmo aperfeiçoado. Limites superiores para o tempo de execução na solução de problemas nominais de verificação equacional são fornecidos. Um algoritmo de unificação módulo C baseado em regras de redução é especificado em Coq e provado ser correto e completo. Por meio do uso de variáveis protegidas, este algoritmo de unificação resolve problemas de casamento nominal módulo C, o que foi também formalizado ser correto e completo. O algoritmo de unificação baseado em regras de redução fornece uma família finita de conjuntos de equações nominais de ponto fixo. Cada uma destas equações pode ter um conjunto infinito de soluções independentes. Portanto, demonstra-se que problemas de unificação nominal módulo C e AC podem gerar um conjunto infinito de soluções independentes. Este fato contrasta com unificação sintática módulo C ou AC, que são conhecidas por estar na classe finitária de problemas. Uma implementação em OCaml do algoritmo de unificação nominal é fornecida e utilizado para se construir exemplos.The nominal syntax has been used in many application contexts for almost two decades. It is a powerful tool for dealing with variable binding in a concrete manner that can be applied to any specification in which parameters are used to abstract variables, such as in predicates and functions. In the nominal syntax, syntactically different objects can have the same semantics modulo alpha-conversion, as happens in the lambda calculus. Dealing with equality, and in special with alpha-equivalence, is essential in formal languages and implementations. This work investigates the nominal alpha-equivalence with associative (A), commutative (C) and associative-comutative (AC) function symbols. Equalitychecking, matching and unification modulo A, C and AC are investigated. Regarding equality-checking, nominal alpha-equivalence modulo A, C and AC are specified in Coq and proved sound. An algorithm implemented in OCaml for equality-checking modulo A, C and AC is automatically extracted from the specification and experiments are performed using also an improved algorithm. Upper bounds for solving nominal equality-checking problems are given. A rule-based nominal unification modulo C algorithm is specified in Coq and proved sound and complete. By using protected variables, this unification algorithm solves nominal matching problems modulo C, which is formalised to be sound and complete. The rule-based nominal unification algorithm outputs a finite family of sets of fixed point nominal equations. Each of which might have an infinite set of independent solutions. Therefore, nominal unification modulo C or AC are proved to potentially generate infinite independent solutions. This contrasts with syntactic unification modulo C or AC that are known to be in the finitary class. An OCaml implementation of the nominal unification algorithm is provided and used to build examples.Submitted by Washington Segundo (washingtonsegundo@ibict.br) on 2019-05-06T16:02:20Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) thesis20190319.pdf: 2460573 bytes, checksum: a110e47747c4883105433dc23db4d6b6 (MD5)Approved for entry into archive by Washington Segundo (washingtonsegundo@ibict.br) on 2019-05-06T16:04:02Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) thesis20190319.pdf: 2460573 bytes, checksum: a110e47747c4883105433dc23db4d6b6 (MD5)Made available in DSpace on 2019-05-06T16:04:02Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) thesis20190319.pdf: 2460573 bytes, checksum: a110e47747c4883105433dc23db4d6b6 (MD5) Previous issue date: 2019-02-20Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorengUniversidade de BrasíliaPrograma de Pós-Graduação em Informática - UnBUnBBrasilCiência da Computaçãohttp://dx.doi.org/10.5281/zenodo.2582109[1] T. Aoto and K. Kikuchi. Nominal Confluence Tool. In Proc. of the 8th Int. Joint Conf.: Automated Reasoning (IJCAR), volume 9706 of LNCS, pages 173–182. Springer, 2016. 4 [2] A. B. Avelar, A. L. Galdino, F. L. C. de Moura, and M. Ayala-Rincón. First-order unification in the PVS proof assistant. Logic Journal of the IGPL, 22(5):758–789, 2014. 5 [3] M. Ayala-Rincón, W. Carvalho-Segundo, M. Fernández, and D. Nantes-Sobrinho. Nominal C-Unification. In Proc. of the 27th Int. Symp. Logic-Based Program Synthesis and Transformation (LOPSTR), volume 10855 of LNCS, pages 235–251. 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Theory and Practice of Software Development, pages 391–405, 1993. 4CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::COMPUTABILIDADE E MODELOS DE COMPUTACAOCNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::ANALISE DE ALGORITMOS E COMPLEXIDADE DE COMPUTACAOCNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAOLógica nominalAlpha-equivalênciaUnificação de primeira-ordemUnificação nominalUnificação módulo teorias equacionaisEquações de ponto fixoNominal logicAlpha-equivalenceFirst-order unificationNominal unificationUnification modulo equational theoriesFixed point equationsNominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativityinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisAyala-Rincón, Mauriciohttp://lattes.cnpq.br/8466420403941522Fernández, MaribelNalon, Cláudiahttp://lattes.cnpq.br/7793795625581127Díaz-Caro, AlejandroKutsia, TemurVentura, Daniel L.http://lattes.cnpq.br/4443822193261575SIAPE:2002064http://lattes.cnpq.br/9453481318889500de Carvalho-Segundo, Washington L. 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| dc.title.pt_BR.fl_str_mv |
Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity |
| title |
Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity |
| spellingShingle |
Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity de Carvalho-Segundo, Washington L. R. CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::COMPUTABILIDADE E MODELOS DE COMPUTACAO CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::ANALISE DE ALGORITMOS E COMPLEXIDADE DE COMPUTACAO CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO Lógica nominal Alpha-equivalência Unificação de primeira-ordem Unificação nominal Unificação módulo teorias equacionais Equações de ponto fixo Nominal logic Alpha-equivalence First-order unification Nominal unification Unification modulo equational theories Fixed point equations |
| title_short |
Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity |
| title_full |
Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity |
| title_fullStr |
Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity |
| title_full_unstemmed |
Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity |
| title_sort |
Nominal Equational Problems Modulo Associativity, Commutativity and Associativity-Commutativity |
| author |
de Carvalho-Segundo, Washington L. R. |
| author_facet |
de Carvalho-Segundo, Washington L. R. |
| author_role |
author |
| dc.contributor.advisor1.fl_str_mv |
Ayala-Rincón, Mauricio |
| dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8466420403941522 |
| dc.contributor.advisor-co1.fl_str_mv |
Fernández, Maribel |
| dc.contributor.referee1.fl_str_mv |
Nalon, Cláudia |
| dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/7793795625581127 |
| dc.contributor.referee2.fl_str_mv |
Díaz-Caro, Alejandro |
| dc.contributor.referee3.fl_str_mv |
Kutsia, Temur |
| dc.contributor.referee4.fl_str_mv |
Ventura, Daniel L. |
| dc.contributor.referee4Lattes.fl_str_mv |
http://lattes.cnpq.br/4443822193261575 |
| dc.contributor.authorID.fl_str_mv |
SIAPE:2002064 |
| dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/9453481318889500 |
| dc.contributor.author.fl_str_mv |
de Carvalho-Segundo, Washington L. R. |
| contributor_str_mv |
Ayala-Rincón, Mauricio Fernández, Maribel Nalon, Cláudia Díaz-Caro, Alejandro Kutsia, Temur Ventura, Daniel L. |
| dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::COMPUTABILIDADE E MODELOS DE COMPUTACAO CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::ANALISE DE ALGORITMOS E COMPLEXIDADE DE COMPUTACAO CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO |
| topic |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::COMPUTABILIDADE E MODELOS DE COMPUTACAO CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO::ANALISE DE ALGORITMOS E COMPLEXIDADE DE COMPUTACAO CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO Lógica nominal Alpha-equivalência Unificação de primeira-ordem Unificação nominal Unificação módulo teorias equacionais Equações de ponto fixo Nominal logic Alpha-equivalence First-order unification Nominal unification Unification modulo equational theories Fixed point equations |
| dc.subject.por.fl_str_mv |
Lógica nominal Alpha-equivalência Unificação de primeira-ordem Unificação nominal Unificação módulo teorias equacionais Equações de ponto fixo Nominal logic Alpha-equivalence First-order unification Nominal unification Unification modulo equational theories Fixed point equations |
| description |
A sintaxe nominal tem sido utilizada em vários contextos por quase duas décadas. Ela é uma ferramenta poderosa para se lidar com ligação de variáveis de uma forma concreta, que pode ser aplicada a qualquer especificação na qual parâmetros são utilizados para se abstrair variáveis, tal como em predicados e funções. Na sintaxe nominal, objetos que são sintaticamente diferentes podem ter a mesma semântica módulo alfa-conversão, tal como acontece no Cálculo Lambda. O tratamento de igualdades, em especial a alphaequivalêcia, é algo essencial em linguagens formais e implementações. Este trabalho investiga a alpha-equivalência nominal com símbolos de função associativos (A), comutativos (C) e associativos-comutativos (AC). Verificação de equivalência, casamento e unificação módulo A, C e AC são investigados. Em relação a verificação de igualdade, as alphaequivalências nominais módulo A, C e AC foram especificadas em Coq e provadas ser corretas. Um algoritmo implementado em OCaml para verificação de igualdade módulo A, C e AC é automaticamente extraído da especificação e experimentos são executados utilizando-se também um algoritmo aperfeiçoado. Limites superiores para o tempo de execução na solução de problemas nominais de verificação equacional são fornecidos. Um algoritmo de unificação módulo C baseado em regras de redução é especificado em Coq e provado ser correto e completo. Por meio do uso de variáveis protegidas, este algoritmo de unificação resolve problemas de casamento nominal módulo C, o que foi também formalizado ser correto e completo. O algoritmo de unificação baseado em regras de redução fornece uma família finita de conjuntos de equações nominais de ponto fixo. Cada uma destas equações pode ter um conjunto infinito de soluções independentes. Portanto, demonstra-se que problemas de unificação nominal módulo C e AC podem gerar um conjunto infinito de soluções independentes. Este fato contrasta com unificação sintática módulo C ou AC, que são conhecidas por estar na classe finitária de problemas. Uma implementação em OCaml do algoritmo de unificação nominal é fornecida e utilizado para se construir exemplos. |
| publishDate |
2019 |
| dc.date.accessioned.fl_str_mv |
2019-05-06T16:04:02Z |
| dc.date.available.fl_str_mv |
2019-03-19 2019-05-06T16:04:02Z |
| dc.date.issued.fl_str_mv |
2019 |
| dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
| format |
doctoralThesis |
| status_str |
publishedVersion |
| dc.identifier.uri.fl_str_mv |
http://ridi.ibict.br/handle/123456789/1012 |
| url |
http://ridi.ibict.br/handle/123456789/1012 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.relation.pt_BR.fl_str_mv |
http://dx.doi.org/10.5281/zenodo.2582109 |
| dc.relation.references.pt_BR.fl_str_mv |
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