A -model with ∞-groupoid structure based in the Scott’s -model D∞

Detalhes bibliográficos
Ano de defesa: 2020
Autor(a) principal: MARTÍNEZ RIVILLAS, Daniel Orlando
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: eng
Instituição de defesa: Universidade Federal de Pernambuco
UFPE
Brasil
Programa de Pos Graduacao em Ciencia da Computacao
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Teoria da computação
Cálculo lambda
Link de acesso: https://repositorio.ufpe.br/handle/123456789/38554
Resumo: The lambda calculus is a universal programming language that represents the functions computable from the point of view of the functions as a rule, that allow the evaluation of a function on any other function. This language can be seen as a theory, with certain pre-established axioms and inference rules, which can be represented by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, known as ∞, in order to represent the -terms as the typical functions of set theory, where it is not allowed to evaluate a function about itself. This thesis propose a construction of an ∞-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case ∞ and we observe that the Scott topology does not provide relevant information about of the relation between higher equivalences. This motivates the search for a new line of research focused on the exploration of -models with the structure of a non-trivial ∞-groupoid to generalize the proofs of term conversion (e.g., -equality, -equality) to higher proof in -calculus.
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spelling A -model with ∞-groupoid structure based in the Scott’s -model D∞Teoria da computaçãoCálculo lambdaThe lambda calculus is a universal programming language that represents the functions computable from the point of view of the functions as a rule, that allow the evaluation of a function on any other function. This language can be seen as a theory, with certain pre-established axioms and inference rules, which can be represented by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, known as ∞, in order to represent the -terms as the typical functions of set theory, where it is not allowed to evaluate a function about itself. This thesis propose a construction of an ∞-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case ∞ and we observe that the Scott topology does not provide relevant information about of the relation between higher equivalences. This motivates the search for a new line of research focused on the exploration of -models with the structure of a non-trivial ∞-groupoid to generalize the proofs of term conversion (e.g., -equality, -equality) to higher proof in -calculus.O cálculo lambda é uma linguagem de programação universal que representa as funções computáveis do ponto de vista das funções como regra, que permitem a avaliação de uma função em qualquer outra função. Essa linguagem pode ser vista como uma teoria, com certos axiomas e regras de inferência pré-estabelecidos, que podem ser representados por modelos. Dana Scott propôs o primeiro modelo não-trivial do cálculo lambda extensional, conhecido como ∞, para representar os -termos como as funções típicas da teoria dos conjuntos, onde não é permitido avaliar uma função sobre si mesmo. Esta tese propõe a construção de um ∞-groupoid a partir de qualquer modelo lambda dotado de uma topologia. Aplicamos esta construção para o caso particular ∞ e observamos que a topologia Scott não fornece informações relevantes sobre a relação entre equivalências superiores. Isso motiva uma nova linha de pesquisa focada na exploração de -modelos com a estrutura de um ∞-groupoide não trivial para generalizar as provas de conversão de termos (e.g., -igualdade, -equalidade) à provas do ordem superior em -calculus.Universidade Federal de PernambucoUFPEBrasilPrograma de Pos Graduacao em Ciencia da ComputacaoQUEIROZ, José Guerra Barretto dehttp://lattes.cnpq.br/1825502153580661MARTÍNEZ RIVILLAS, Daniel Orlando2020-11-09T21:32:03Z2020-11-09T21:32:03Z2020-02-28info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfMARTÍNEZ RIVILLAS, Daniel Orlando. A -model with ∞-groupoid structure based in the Scott’s -model D∞. 2020. Dissertação (Mestrado em Ciência da Computação) – Universidade Federal de Pernambuco, Recife, 2020.https://repositorio.ufpe.br/handle/123456789/38554engAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPE2020-11-10T05:16:17Zoai:repositorio.ufpe.br:123456789/38554Repositório InstitucionalPUBhttps://repositorio.ufpe.br/oai/requestattena@ufpe.bropendoar:22212020-11-10T05:16:17Repositório Institucional da UFPE - Universidade Federal de Pernambuco (UFPE)false
dc.title.none.fl_str_mv A -model with ∞-groupoid structure based in the Scott’s -model D∞
title A -model with ∞-groupoid structure based in the Scott’s -model D∞
spellingShingle A -model with ∞-groupoid structure based in the Scott’s -model D∞
MARTÍNEZ RIVILLAS, Daniel Orlando
Teoria da computação
Cálculo lambda
title_short A -model with ∞-groupoid structure based in the Scott’s -model D∞
title_full A -model with ∞-groupoid structure based in the Scott’s -model D∞
title_fullStr A -model with ∞-groupoid structure based in the Scott’s -model D∞
title_full_unstemmed A -model with ∞-groupoid structure based in the Scott’s -model D∞
title_sort A -model with ∞-groupoid structure based in the Scott’s -model D∞
author MARTÍNEZ RIVILLAS, Daniel Orlando
author_facet MARTÍNEZ RIVILLAS, Daniel Orlando
author_role author
dc.contributor.none.fl_str_mv QUEIROZ, José Guerra Barretto de
http://lattes.cnpq.br/1825502153580661
dc.contributor.author.fl_str_mv MARTÍNEZ RIVILLAS, Daniel Orlando
dc.subject.por.fl_str_mv Teoria da computação
Cálculo lambda
topic Teoria da computação
Cálculo lambda
description The lambda calculus is a universal programming language that represents the functions computable from the point of view of the functions as a rule, that allow the evaluation of a function on any other function. This language can be seen as a theory, with certain pre-established axioms and inference rules, which can be represented by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, known as ∞, in order to represent the -terms as the typical functions of set theory, where it is not allowed to evaluate a function about itself. This thesis propose a construction of an ∞-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case ∞ and we observe that the Scott topology does not provide relevant information about of the relation between higher equivalences. This motivates the search for a new line of research focused on the exploration of -models with the structure of a non-trivial ∞-groupoid to generalize the proofs of term conversion (e.g., -equality, -equality) to higher proof in -calculus.
publishDate 2020
dc.date.none.fl_str_mv 2020-11-09T21:32:03Z
2020-11-09T21:32:03Z
2020-02-28
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv MARTÍNEZ RIVILLAS, Daniel Orlando. A -model with ∞-groupoid structure based in the Scott’s -model D∞. 2020. Dissertação (Mestrado em Ciência da Computação) – Universidade Federal de Pernambuco, Recife, 2020.
https://repositorio.ufpe.br/handle/123456789/38554
identifier_str_mv MARTÍNEZ RIVILLAS, Daniel Orlando. A -model with ∞-groupoid structure based in the Scott’s -model D∞. 2020. Dissertação (Mestrado em Ciência da Computação) – Universidade Federal de Pernambuco, Recife, 2020.
url https://repositorio.ufpe.br/handle/123456789/38554
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Pernambuco
UFPE
Brasil
Programa de Pos Graduacao em Ciencia da Computacao
publisher.none.fl_str_mv Universidade Federal de Pernambuco
UFPE
Brasil
Programa de Pos Graduacao em Ciencia da Computacao
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFPE
instname:Universidade Federal de Pernambuco (UFPE)
instacron:UFPE
instname_str Universidade Federal de Pernambuco (UFPE)
instacron_str UFPE
institution UFPE
reponame_str Repositório Institucional da UFPE
collection Repositório Institucional da UFPE
repository.name.fl_str_mv Repositório Institucional da UFPE - Universidade Federal de Pernambuco (UFPE)
repository.mail.fl_str_mv attena@ufpe.br
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