Revising Z: Part II – logical development

Henson, Martin C.; Reeves, Steve

doi:10.1007/s001650050039

Cited by 15 publications

(19 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

Section: Related Workmentioning

confidence: 99%

Categorical foundations for structured specifications in Z

et al. 2015

View full text Add to dashboard Cite

show abstract

“…An alternative "Curry-style" approach was described in [38,39]. In that presentation neither terms nor propositions were type-controlled.…”

Section: An Alternative Approachmentioning

confidence: 99%

“…The reader interested in pursuing these issues in more depth, for example for more general operations such as schema-level quantification and generic schemas, should consult [35,38,39] which contain more detail.…”

Section: Schema Preconditionsmentioning

confidence: 99%

See 1 more Smart Citation

Z Logic and Its Applications

Henson

Deutsch

Reeves

2007

Logics of Specification Languages

Self Cite

View full text Add to dashboard Cite

We provide an introduction to the specification language Z from a logical perspective. The possibility of presenting Z in this way is a consequence of a number of joint publications on Z logic that Henson and Reeves have co-written since 1997. We provide an informal as well as a formal introduction to Z logic and show how it may be used, and extended, to investigate issues such as equational logic, the logic of preconditions, operation and data refinement, and monotonicity.

show abstract

“…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%