The vectorial Lambda calculus revisited
- Autores
- Noriega, Francisco José
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- tesis de grado
- Estado
- versión publicada
- Colaborador/a o director/a de tesis
- Díaz-Caro, Alejandro
- Descripción
- We revisit the Vectorial λ-Calculus [3], a system that provides a way to model a vector space of terms by extending the classic terms of the λ-calculus with linear combinations of them; and by introducing a type system on top. The system can be summarized by the slogan If Γ ⊢ : T and Γ ⊢ r : R then Γ ⊢ α · t + β · r : α · T + β · R. However, the type system in Vectorial only provides a weakened version of the Subject Reduction property. We prove that our revised Vectorial λ-Calculus supports the standard version of said property as well as many others in the original system, such as Progress. We also introduce the concept of weight of types and terms, and a new property relating the weight of a term with the weight of its type.
Fil: Noriega, Francisco José. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar
- Repositorio
.jpg)
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- seminario:seminario_nCOM000587_Noriega
Ver los metadatos del registro completo
| id |
BDUBAFCEN_e44c91100effe00ce89bd3ae89c09e38 |
|---|---|
| oai_identifier_str |
seminario:seminario_nCOM000587_Noriega |
| network_acronym_str |
BDUBAFCEN |
| repository_id_str |
1896 |
| network_name_str |
Biblioteca Digital (UBA-FCEN) |
| spelling |
The vectorial Lambda calculus revisitedNoriega, Francisco JoséWe revisit the Vectorial λ-Calculus [3], a system that provides a way to model a vector space of terms by extending the classic terms of the λ-calculus with linear combinations of them; and by introducing a type system on top. The system can be summarized by the slogan If Γ ⊢ : T and Γ ⊢ r : R then Γ ⊢ α · t + β · r : α · T + β · R. However, the type system in Vectorial only provides a weakened version of the Subject Reduction property. We prove that our revised Vectorial λ-Calculus supports the standard version of said property as well as many others in the original system, such as Progress. We also introduce the concept of weight of types and terms, and a new property relating the weight of a term with the weight of its type.Fil: Noriega, Francisco José. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Universidad de Buenos Aires. Facultad de Ciencias Exactas y NaturalesDíaz-Caro, Alejandro2020info:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_7a1finfo:ar-repo/semantics/tesisDeGradoapplication/pdfhttps://hdl.handle.net/20.500.12110/seminario_nCOM000587_Noriegaenginfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/arreponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCEN2025-09-29T13:43:33Zseminario:seminario_nCOM000587_NoriegaInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:43:33.935Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
| dc.title.none.fl_str_mv |
The vectorial Lambda calculus revisited |
| title |
The vectorial Lambda calculus revisited |
| spellingShingle |
The vectorial Lambda calculus revisited Noriega, Francisco José |
| title_short |
The vectorial Lambda calculus revisited |
| title_full |
The vectorial Lambda calculus revisited |
| title_fullStr |
The vectorial Lambda calculus revisited |
| title_full_unstemmed |
The vectorial Lambda calculus revisited |
| title_sort |
The vectorial Lambda calculus revisited |
| dc.creator.none.fl_str_mv |
Noriega, Francisco José |
| author |
Noriega, Francisco José |
| author_facet |
Noriega, Francisco José |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Díaz-Caro, Alejandro |
| dc.description.none.fl_txt_mv |
We revisit the Vectorial λ-Calculus [3], a system that provides a way to model a vector space of terms by extending the classic terms of the λ-calculus with linear combinations of them; and by introducing a type system on top. The system can be summarized by the slogan If Γ ⊢ : T and Γ ⊢ r : R then Γ ⊢ α · t + β · r : α · T + β · R. However, the type system in Vectorial only provides a weakened version of the Subject Reduction property. We prove that our revised Vectorial λ-Calculus supports the standard version of said property as well as many others in the original system, such as Progress. We also introduce the concept of weight of types and terms, and a new property relating the weight of a term with the weight of its type. Fil: Noriega, Francisco José. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. |
| description |
We revisit the Vectorial λ-Calculus [3], a system that provides a way to model a vector space of terms by extending the classic terms of the λ-calculus with linear combinations of them; and by introducing a type system on top. The system can be summarized by the slogan If Γ ⊢ : T and Γ ⊢ r : R then Γ ⊢ α · t + β · r : α · T + β · R. However, the type system in Vectorial only provides a weakened version of the Subject Reduction property. We prove that our revised Vectorial λ-Calculus supports the standard version of said property as well as many others in the original system, such as Progress. We also introduce the concept of weight of types and terms, and a new property relating the weight of a term with the weight of its type. |
| publishDate |
2020 |
| dc.date.none.fl_str_mv |
2020 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/bachelorThesis info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_7a1f info:ar-repo/semantics/tesisDeGrado |
| format |
bachelorThesis |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/20.500.12110/seminario_nCOM000587_Noriega |
| url |
https://hdl.handle.net/20.500.12110/seminario_nCOM000587_Noriega |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar |
| eu_rights_str_mv |
openAccess |
| rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| publisher.none.fl_str_mv |
Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| dc.source.none.fl_str_mv |
reponame:Biblioteca Digital (UBA-FCEN) instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales instacron:UBA-FCEN |
| reponame_str |
Biblioteca Digital (UBA-FCEN) |
| collection |
Biblioteca Digital (UBA-FCEN) |
| instname_str |
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| instacron_str |
UBA-FCEN |
| institution |
UBA-FCEN |
| repository.name.fl_str_mv |
Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| repository.mail.fl_str_mv |
ana@bl.fcen.uba.ar |
| _version_ |
1844618753361313792 |
| score |
13.070432 |