From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap

Autores
Baum, Gabriel Alfredo; Frias, Marcelo F.; Haeberer, Armando Martin; Martínez López, Pablo E.
Año de publicación
1996
Idioma
español castellano
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
The development of programs from first-order specifications has as its main difficulty that of dealing with universal quantifiers. This work is focused in that point, i.e., in the construction of programs whose specifications involve universal quantifiers. This task is performed within a relational calculus based on fork algebras. The fact that first-order theories can be translated into equational theories in abstract fork algebras suggests that such work can be accomplished in a satisfactory way. Furthermore, the fact that these abstract algebras are representable guarantees that all properties valid in the standard models are captured by the axiomatization given for them, allowing the reasoning formalism to be shifted back and forth between any model and the abstract algebra. In order to cope with universal quantifiers, a new algebraic operation — relational implication — is introduced. This operation is shown to have deep significance in the relational statement of first-order expressions involving universal quantifiers. Several algebraic properties of the relational implication are stated showing its usefulness in program calculation. Finally, a non-trivial example of derivation is given to asses the merits of the relational implication as an specification tool, and also in calculation steps, where its algebraic properties are clearly appropriate as transformation rules.
Laboratorio de Investigación y Formación en Informática Avanzada
Materia
Informática
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/137421

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spelling From Specifications to Programs: A Fork-Algebraic Approach to Bridge the GapBaum, Gabriel AlfredoFrias, Marcelo F.Haeberer, Armando MartinMartínez López, Pablo E.InformáticaThe development of programs from first-order specifications has as its main difficulty that of dealing with universal quantifiers. This work is focused in that point, i.e., in the construction of programs whose specifications involve universal quantifiers. This task is performed within a relational calculus based on fork algebras. The fact that first-order theories can be translated into equational theories in abstract fork algebras suggests that such work can be accomplished in a satisfactory way. Furthermore, the fact that these abstract algebras are representable guarantees that all properties valid in the standard models are captured by the axiomatization given for them, allowing the reasoning formalism to be shifted back and forth between any model and the abstract algebra. In order to cope with universal quantifiers, a new algebraic operation — relational implication — is introduced. This operation is shown to have deep significance in the relational statement of first-order expressions involving universal quantifiers. Several algebraic properties of the relational implication are stated showing its usefulness in program calculation. Finally, a non-trivial example of derivation is given to asses the merits of the relational implication as an specification tool, and also in calculation steps, where its algebraic properties are clearly appropriate as transformation rules.Laboratorio de Investigación y Formación en Informática Avanzada1996info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionObjeto de conferenciahttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdf180-191http://sedici.unlp.edu.ar/handle/10915/137421spainfo:eu-repo/semantics/altIdentifier/issn/0302-9743info:eu-repo/semantics/altIdentifier/issn/1611-3349info:eu-repo/semantics/altIdentifier/doi/10.1007/3-540-61550-4_147info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T11:03:59Zoai:sedici.unlp.edu.ar:10915/137421Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 11:03:59.675SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap
title From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap
spellingShingle From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap
Baum, Gabriel Alfredo
Informática
title_short From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap
title_full From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap
title_fullStr From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap
title_full_unstemmed From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap
title_sort From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap
dc.creator.none.fl_str_mv Baum, Gabriel Alfredo
Frias, Marcelo F.
Haeberer, Armando Martin
Martínez López, Pablo E.
author Baum, Gabriel Alfredo
author_facet Baum, Gabriel Alfredo
Frias, Marcelo F.
Haeberer, Armando Martin
Martínez López, Pablo E.
author_role author
author2 Frias, Marcelo F.
Haeberer, Armando Martin
Martínez López, Pablo E.
author2_role author
author
author
dc.subject.none.fl_str_mv Informática
topic Informática
dc.description.none.fl_txt_mv The development of programs from first-order specifications has as its main difficulty that of dealing with universal quantifiers. This work is focused in that point, i.e., in the construction of programs whose specifications involve universal quantifiers. This task is performed within a relational calculus based on fork algebras. The fact that first-order theories can be translated into equational theories in abstract fork algebras suggests that such work can be accomplished in a satisfactory way. Furthermore, the fact that these abstract algebras are representable guarantees that all properties valid in the standard models are captured by the axiomatization given for them, allowing the reasoning formalism to be shifted back and forth between any model and the abstract algebra. In order to cope with universal quantifiers, a new algebraic operation — relational implication — is introduced. This operation is shown to have deep significance in the relational statement of first-order expressions involving universal quantifiers. Several algebraic properties of the relational implication are stated showing its usefulness in program calculation. Finally, a non-trivial example of derivation is given to asses the merits of the relational implication as an specification tool, and also in calculation steps, where its algebraic properties are clearly appropriate as transformation rules.
Laboratorio de Investigación y Formación en Informática Avanzada
description The development of programs from first-order specifications has as its main difficulty that of dealing with universal quantifiers. This work is focused in that point, i.e., in the construction of programs whose specifications involve universal quantifiers. This task is performed within a relational calculus based on fork algebras. The fact that first-order theories can be translated into equational theories in abstract fork algebras suggests that such work can be accomplished in a satisfactory way. Furthermore, the fact that these abstract algebras are representable guarantees that all properties valid in the standard models are captured by the axiomatization given for them, allowing the reasoning formalism to be shifted back and forth between any model and the abstract algebra. In order to cope with universal quantifiers, a new algebraic operation — relational implication — is introduced. This operation is shown to have deep significance in the relational statement of first-order expressions involving universal quantifiers. Several algebraic properties of the relational implication are stated showing its usefulness in program calculation. Finally, a non-trivial example of derivation is given to asses the merits of the relational implication as an specification tool, and also in calculation steps, where its algebraic properties are clearly appropriate as transformation rules.
publishDate 1996
dc.date.none.fl_str_mv 1996
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