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Refinement in Z and Object-Z

Foundations and Advanced Applications

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  • © 2014
  • Latest edition


  • The most comprehensive text on refinement in state based systems
  • Includes detailed explanations and a wide range of illustrative examples, perfect for use as an advanced Under-Graduate or Masters textbook
  • With extensive bibliographical notes, now updated to 2013 state of the art
  • Includes supplementary material:

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Table of contents (20 chapters)

  1. Refining Z Specifications

  2. Interfaces and Operations: ADTs Viewed in an Environment

  3. Object-Oriented Refinement


About this book

Refinement is one of the cornerstones of the formal approach to software engineering, and its use in various domains has led to research on new applications and generalisation. This book brings together this important research in one volume, with the addition of examples drawn from different application areas. It covers four main themes:

  • Data refinement and its application to Z
  • Generalisations of refinement that change the interface and atomicity of operations
  • Refinement in Object-Z
  • Modelling state and behaviour by combining Object-Z with CSP

Refinement in Z and Object-Z: Foundations and Advanced Applications provides an invaluable overview of recent research for academic and industrial researchers, lecturers teaching formal specification and development, industrial practitioners using formal methods in their work, and postgraduate and advanced undergraduate students.

This second edition is a comprehensive update to the first and includes the following new material:

  • Early chapters have been extended to also include trace refinement, based directly on partial relations rather than through totalisation
  • Provides an updated discussion on divergence, non-atomic refinements and approximate refinement
  • Includes a discussion of the differing semantics of operations and outputs and how they affect the abstraction of models written using Object-Z and CSP
  • Presents a fuller account of the relationship between relational refinement and various models of refinement in CSP
  • Bibliographic notes at the end of each chapter have been extended with the most up to date citations and research


From the reviews of the second edition:

“This is a slightly revised edition of a monograph that was published in 2001 … . It contains a mixture of original text and revised material from research papers published by the authors in various venues. … suitable for researchers in this same field who are already competent in Z.” (B. Belkhouche, Computing Reviews, January, 2014)

Authors and Affiliations

  • University of Sheffield Department of Computer Science, Sheffield, United Kingdom

    John Derrick

  • University of Kent School of Computing, Canterbury, United Kingdom

    Eerke A. Boiten

Bibliographic Information

  • Book Title: Refinement in Z and Object-Z

  • Book Subtitle: Foundations and Advanced Applications

  • Authors: John Derrick, Eerke A. Boiten

  • DOI:

  • Publisher: Springer London

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer-Verlag London 2014

  • Hardcover ISBN: 978-1-4471-5354-2Published: 12 September 2013

  • Softcover ISBN: 978-1-4471-6167-7Published: 23 August 2015

  • eBook ISBN: 978-1-4471-5355-9Published: 30 August 2013

  • Edition Number: 2

  • Number of Pages: XVIII, 492

  • Topics: Mathematical Logic and Formal Languages, Software Engineering

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