Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search

Detalhes bibliográficos
Autor(a) principal: Espírito Santo, José
Data de Publicação: 2019
Outros Autores: Matthes, Ralph, Pinto, Luís F.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/62948
Resumo: A new approach to inhabitation problems in simply typed lambda-calculus is shown, dealing with both decision and counting problems. This approach works by exploiting a representation of the search space generated by a given inhabitation problem, which is in terms of a lambda-calculus for proof search that the authors developed recently. The representation may be seen as extending the Curry-Howard representation of proofs by lambda terms. Our methodology reveals inductive descriptions of the decision problems, driven by the syntax of the proof-search expressions, and produces simple, recursive decision procedures and counting functions. These allow to predict the number of inhabitants by testing the given type for syntactic criteria. This new approach is comprehensive and robust: based on the same syntactic representation, we also derive the state-of-the-art coherence theorems ensuring uniqueness of inhabitants.
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spelling Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof searchCiências Naturais::MatemáticasScience & TechnologyA new approach to inhabitation problems in simply typed lambda-calculus is shown, dealing with both decision and counting problems. This approach works by exploiting a representation of the search space generated by a given inhabitation problem, which is in terms of a lambda-calculus for proof search that the authors developed recently. The representation may be seen as extending the Curry-Howard representation of proofs by lambda terms. Our methodology reveals inductive descriptions of the decision problems, driven by the syntax of the proof-search expressions, and produces simple, recursive decision procedures and counting functions. These allow to predict the number of inhabitants by testing the given type for syntactic criteria. This new approach is comprehensive and robust: based on the same syntactic representation, we also derive the state-of-the-art coherence theorems ensuring uniqueness of inhabitants.We would like to thank our anonymous referees for their detailed and thoughtful reviews. The first and the last author were partially financed by Fundacao para a Ciencia e a Tecnologia (FCT) through project UID/MAT/00013/2013. The second author was partially financed by the project Climt, ANR-11-BS02-016, of the French Agence Nationale de la Recherche. All authors got financial support by the COST action CA15123 EUTYPES.Cambridge University PressUniversidade do MinhoEspírito Santo, JoséMatthes, RalphPinto, Luís F.20192019-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/62948eng0960-12951469-807210.1017/S0960129518000099info: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:RCAAP2023-07-21T11:56:36Zoai:repositorium.sdum.uminho.pt:1822/62948Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:46:13.537145Repositório 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 Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
title Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
spellingShingle Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
Espírito Santo, José
Ciências Naturais::Matemáticas
Science & Technology
title_short Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
title_full Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
title_fullStr Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
title_full_unstemmed Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
title_sort Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
author Espírito Santo, José
author_facet Espírito Santo, José
Matthes, Ralph
Pinto, Luís F.
author_role author
author2 Matthes, Ralph
Pinto, Luís F.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Espírito Santo, José
Matthes, Ralph
Pinto, Luís F.
dc.subject.por.fl_str_mv Ciências Naturais::Matemáticas
Science & Technology
topic Ciências Naturais::Matemáticas
Science & Technology
description A new approach to inhabitation problems in simply typed lambda-calculus is shown, dealing with both decision and counting problems. This approach works by exploiting a representation of the search space generated by a given inhabitation problem, which is in terms of a lambda-calculus for proof search that the authors developed recently. The representation may be seen as extending the Curry-Howard representation of proofs by lambda terms. Our methodology reveals inductive descriptions of the decision problems, driven by the syntax of the proof-search expressions, and produces simple, recursive decision procedures and counting functions. These allow to predict the number of inhabitants by testing the given type for syntactic criteria. This new approach is comprehensive and robust: based on the same syntactic representation, we also derive the state-of-the-art coherence theorems ensuring uniqueness of inhabitants.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/62948
url http://hdl.handle.net/1822/62948
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0960-1295
1469-8072
10.1017/S0960129518000099
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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