Refinement in Z and Object-Z

  title={Refinement in Z and Object-Z},
  author={DPhil John Derrick BSc and PhD Eerke Boiten Ir},
  booktitle={Formal Approaches to Computing and Information Technology},
operation terminates possibly after any internal evolution then the concrete operation terminates after some internal evolution. Finally, in correctness every possible state after the concrete operation must be related by R' to a possible state after the abstract operation, except that now 'after' means an arbitrary number of internal operations may occur before and after the abstract operation. Although we do not have to check conditions for internal operations, the requirements on the… 

Abstract Specification in Object-Z and CSP

It is shown that by adopting a blocking model of preconditions together with an angelic model of outputs one can specify systems at higher levels of abstraction.

An integration of Z and Timed CSP for specifying real time embedded systems

This section defines the implementation relation between abstract and concrete specification units and makes use of the existing refinement techniques of the base formalisms Z and timed CSP to establish that using state-based techniques to refine the Z part should be established.

On using data abstractions for model checking refinements

It is shown how abstract specifications can be systematically constructed and how a standard model checker can be applied to find counter examples in case when refinement is absent, and the applicability of the construction method is discussed.

The behavioural semantics of Event-B refinement

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Atomic Actions , and their Refinements to Isolated and Not-So-Isolated Protocols

The picture is generalised to encompass not-so-isolate atomic actions, exemplified by another motivating example, the lock-free stack, in which arbitrary numbers of agents may collaborate and/or interfere as the protocol runs.

Unifying Theories of Programming That Distinguish Nontermination and Abort

In this paper we focus on the relationship between a number of specification models. The models are formulated in the Unifying Theories of Programming of Hoare and He, but correspond to widely used

Relational concurrent refinement part III: traces, partial relations and automata

The program of deriving simulation conditions for process algebraic refinement by defining further embeddings into the authors' relational model: traces, completed traces, failure traces and extension is continued and extended to include various notions of automata based refinement.

Atomic actions, and their refinements to isolated protocols

This theory relates this theory to serialisations of system runs containing multiple interleaved transactions, showing how the clean picture of the refinement of an isolated atomic action to an isolated protocol becomes obscured by the details of the interleaving.

Relational Concurrent Refinement: Timed Refinement

The program of deriving simulation conditions for process algebraic refinement is continued by considering how notions of time should be embedded into a relational model, and thereby deriving relational notions of timed refinement.

A comparison of refinement orderings and their associated simulation rules




The existence of refinement mappings

  • M. AbadiL. Lamport
  • Computer Science
    [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science
  • 1988

OOZE: An Object Oriented Z Environment

The OOZE system is based on OBJ3, and provides rapid prototyping and theorem proving facilities over a module database, and has a precise and relatively simple semantics based on order sorted, hidden sorted algebra.

Viewpoint specification and Z

Specification and Design of a Transmission Protocol by Successive Refinements Using B1

A formal technique of protocol specification and design by successive refinements is proposed, which states that the protocol is first specified in a time-less fashion by concentrating its intended behavior on one step only, all other steps being just void.

Action refinement in process algebras

A semantic theory based on atomic actions and full abstraction for series-parallel pomsets and on relating concurrency and nondeterminism is presented.

The B-book - assigning programs to meanings

Tribute Foreword Introduction Part I. Mathematics: 1. Mathematical reasoning 2. Set notation 3. Mathematical objects Part II. Abstract Machines: 4. Introduction to abstract machines 5. Formal