Revising Z: Part I – logic and semantics

Henson, Martin C.; Reeves, Steve

doi:10.1007/s001650050038

Cited by 17 publications

(23 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similarly, in schemas, the observations have values in an implicit state (binding); this point was discussed in section 2.1 (and discussed at length in our other papers e.g. [6], [8]) where we remarked that the states become explicit in derivations which ultimately take place in the underlying logical system Z C . It would be very much more pleasant if we could avoid mention of the state entirely, even in derivations which eventually require calculation in the core logic.…”

Section: Proof-theoretic Simplificationsmentioning

confidence: 78%

See 1 more Smart Citation

A Logic for Schema-Based Program Development

Henson

Reeves

2003

Form. Asp. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Proof-theoretic Simplificationsmentioning

confidence: 78%

“…We will show how it can be constructed as a conservative extension of our existing logic for Z (see [6], [7], [8]) and illustrate the use of the theory in practice with a number of examples. The basis of our approach is to model a specification as a set of legitimate implementations.…”

Section: Introductionmentioning

confidence: 99%

A Logic for Schema-Based Program Development

Henson

Reeves

2003

Form. Asp. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [6], the authors propose a set of rules to manipulate Z schemas; as opposed to our work, these rules are motivated as a means for refactoring specifications. In [16], the authors propose to interpret schemas as types; they build a logical machinery in order to deal with these types. These ideas were adopted in the international ISO standard of Z [17].…”

Section: Related Work and Conclusionmentioning

confidence: 99%

A Categorical Approach to Structuring and Promoting Z Specifications

Castro

Aguirre

Pombo

et al. 2013

Formal Aspects of Component Software

View full text Add to dashboard Cite

Abstract. In this paper, we study a formalisation of specification structuring mechanisms used in Z. These mechanisms are traditionally understood as syntactic transformations. In contrast, we present a characterisation of Z structuring mechanisms which takes into account the semantic counterpart of their typical syntactic descriptions, based on category theory. Our formal foundation for Z employs well established abstract notions of logical systems. This setting has a degree of abstraction that enables us to understand what is the precise semantic relationship between schemas obtained from a schema operator and the schemas it is applied to, in particular with respect to property preservation.Our formalisation is a powerful setting for capturing structuring mechanisms, even enabling us to formalise promotion. Also, its abstract nature provides the rigour and flexibility needed to characterise extensions of Z and related languages, in particular the heterogeneous ones.

show abstract

“…Other work, in particular [HR99a,HR99b], proposes the use of higher-order logic to interpret schemas: this has the clear benefit of interpreting schemas as types in a simple way; however, the semantics of specifications obtained in this way does not reflect the structuring of specifications, flattening a modular Z specification into a typed set theory. In addition, the direct interpretation of schemas as types in a higher-order logic introduces difficulties when dealing with operations; in particular, the authors need to change the Z notation to deal with the constructions S and S .…”

Section: Related Workmentioning

confidence: 99%

Categorical foundations for structured specifications in Z

et al. 2015

View full text Add to dashboard Cite

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.

show abstract

Revising Z: Part I – logic and semantics

Cited by 17 publications

References 4 publications

A Logic for Schema-Based Program Development

A Logic for Schema-Based Program Development

A Categorical Approach to Structuring and Promoting Z Specifications

Categorical foundations for structured specifications in Z

Contact Info

Product

Resources

About