Inhabitation in simply typed lambda-calculus through a lambda-calculus for proof search
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , |
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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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:RCAAP2024-05-11T04:19:00Zoai:repositorium.sdum.uminho.pt:1822/62948Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T04:19Repositório 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 |
repository.mail.fl_str_mv |
mluisa.alvim@gmail.com |
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1817544275116687360 |