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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/70265
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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 Técnicas2025-09-03T10:02:08Zoai: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:34982025-09-03 10:02:09.032CONICET 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 |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.13397 |