Categorical foundations for structured specifications in Z

Autores
Castro, Pablo Francisco; Aguirre, Nazareno Matias; Lopez Pombo, Carlos Gustavo; T.S.E. Maibaum
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we present a formalization of the Z notation and its structuring mechanisms. One of the main features of our formal framework, based on category theory and the theory of institutions, is that it enables us to provide an abstract view of Z and its related concepts. We show that the main structuring mechanisms of Z are captured smoothly by categorical constructions. In particular, we provide a straightforward and clear semantics for promotion, a powerful structuring technique that is often not presented as part of the schema calculus. Here we show that promotion is already an operation over schemas (and more generally over specifications), that allows one to promote schemas that operate on a local notion of state to operate on a subsuming global state, and in particular can be used to conveniently define large specifications from collections of simpler ones. Moreover, our proposed formalization facilitates the combination of Z with other notations in order to produce heterogeneous specifications, i.e., specifications that are obtained by using various different mathematical formalisms. Thus, our abstract and precise formulation of Z is useful for relating this notation with other formal languages used by the formal methods community. We illustrate this by means of a known combination of formal languages, namely the combination of Z with CSP.
Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; Argentina
Fil: Aguirre, Nazareno Matias. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; Argentina
Fil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: T.S.E. Maibaum. Mc Master University; Canadá
Materia
Category Theory
Heterogeneous Specifications
System Specification
System Verification
Z Notation
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/70265
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Categorical foundations for structured specifications in ZCastro, Pablo FranciscoAguirre, Nazareno MatiasLopez Pombo, Carlos GustavoT.S.E. MaibaumCategory TheoryHeterogeneous SpecificationsSystem SpecificationSystem VerificationZ Notationhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1In this paper we present a formalization of the Z notation and its structuring mechanisms. One of the main features of our formal framework, based on category theory and the theory of institutions, is that it enables us to provide an abstract view of Z and its related concepts. We show that the main structuring mechanisms of Z are captured smoothly by categorical constructions. In particular, we provide a straightforward and clear semantics for promotion, a powerful structuring technique that is often not presented as part of the schema calculus. Here we show that promotion is already an operation over schemas (and more generally over specifications), that allows one to promote schemas that operate on a local notion of state to operate on a subsuming global state, and in particular can be used to conveniently define large specifications from collections of simpler ones. Moreover, our proposed formalization facilitates the combination of Z with other notations in order to produce heterogeneous specifications, i.e., specifications that are obtained by using various different mathematical formalisms. Thus, our abstract and precise formulation of Z is useful for relating this notation with other formal languages used by the formal methods community. We illustrate this by means of a known combination of formal languages, namely the combination of Z with CSP.Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; ArgentinaFil: Aguirre, Nazareno Matias. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; ArgentinaFil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: T.S.E. Maibaum. Mc Master University; CanadáSpringer2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/70265Castro, Pablo Francisco; Aguirre, Nazareno Matias; Lopez Pombo, Carlos Gustavo; T.S.E. Maibaum; Categorical foundations for structured specifications in Z; Springer; Formal Aspects Of Computing; 27; 5-6; 11-2015; 831-8650934-5043CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00165-015-0336-0info:eu-repo/semantics/altIdentifier/doi/10.1007/s00165-015-0336-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:17:22Zoai:ri.conicet.gov.ar:11336/70265instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:17:22.53CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Categorical foundations for structured specifications in Z
title Categorical foundations for structured specifications in Z
spellingShingle Categorical foundations for structured specifications in Z
Castro, Pablo Francisco
Category Theory
Heterogeneous Specifications
System Specification
System Verification
Z Notation
title_short Categorical foundations for structured specifications in Z
title_full Categorical foundations for structured specifications in Z
title_fullStr Categorical foundations for structured specifications in Z
title_full_unstemmed Categorical foundations for structured specifications in Z
title_sort Categorical foundations for structured specifications in Z
dc.creator.none.fl_str_mv Castro, Pablo Francisco
Aguirre, Nazareno Matias
Lopez Pombo, Carlos Gustavo
T.S.E. Maibaum
author Castro, Pablo Francisco
author_facet Castro, Pablo Francisco
Aguirre, Nazareno Matias
Lopez Pombo, Carlos Gustavo
T.S.E. Maibaum
author_role author
author2 Aguirre, Nazareno Matias
Lopez Pombo, Carlos Gustavo
T.S.E. Maibaum
author2_role author
author
author
dc.subject.none.fl_str_mv Category Theory
Heterogeneous Specifications
System Specification
System Verification
Z Notation
topic Category Theory
Heterogeneous Specifications
System Specification
System Verification
Z Notation
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we present a formalization of the Z notation and its structuring mechanisms. One of the main features of our formal framework, based on category theory and the theory of institutions, is that it enables us to provide an abstract view of Z and its related concepts. We show that the main structuring mechanisms of Z are captured smoothly by categorical constructions. In particular, we provide a straightforward and clear semantics for promotion, a powerful structuring technique that is often not presented as part of the schema calculus. Here we show that promotion is already an operation over schemas (and more generally over specifications), that allows one to promote schemas that operate on a local notion of state to operate on a subsuming global state, and in particular can be used to conveniently define large specifications from collections of simpler ones. Moreover, our proposed formalization facilitates the combination of Z with other notations in order to produce heterogeneous specifications, i.e., specifications that are obtained by using various different mathematical formalisms. Thus, our abstract and precise formulation of Z is useful for relating this notation with other formal languages used by the formal methods community. We illustrate this by means of a known combination of formal languages, namely the combination of Z with CSP.
Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; Argentina
Fil: Aguirre, Nazareno Matias. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Computación; Argentina
Fil: Lopez Pombo, Carlos Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: T.S.E. Maibaum. Mc Master University; Canadá
description In this paper we present a formalization of the Z notation and its structuring mechanisms. One of the main features of our formal framework, based on category theory and the theory of institutions, is that it enables us to provide an abstract view of Z and its related concepts. We show that the main structuring mechanisms of Z are captured smoothly by categorical constructions. In particular, we provide a straightforward and clear semantics for promotion, a powerful structuring technique that is often not presented as part of the schema calculus. Here we show that promotion is already an operation over schemas (and more generally over specifications), that allows one to promote schemas that operate on a local notion of state to operate on a subsuming global state, and in particular can be used to conveniently define large specifications from collections of simpler ones. Moreover, our proposed formalization facilitates the combination of Z with other notations in order to produce heterogeneous specifications, i.e., specifications that are obtained by using various different mathematical formalisms. Thus, our abstract and precise formulation of Z is useful for relating this notation with other formal languages used by the formal methods community. We illustrate this by means of a known combination of formal languages, namely the combination of Z with CSP.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/70265
Castro, Pablo Francisco; Aguirre, Nazareno Matias; Lopez Pombo, Carlos Gustavo; T.S.E. Maibaum; Categorical foundations for structured specifications in Z; Springer; Formal Aspects Of Computing; 27; 5-6; 11-2015; 831-865
0934-5043
CONICET Digital
CONICET
url http://hdl.handle.net/11336/70265
identifier_str_mv Castro, Pablo Francisco; Aguirre, Nazareno Matias; Lopez Pombo, Carlos Gustavo; T.S.E. Maibaum; Categorical foundations for structured specifications in Z; Springer; Formal Aspects Of Computing; 27; 5-6; 11-2015; 831-865
0934-5043
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00165-015-0336-0
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00165-015-0336-0
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.069144

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