Transformation rules for Z

  • Authors:
  • Mark Utting;Petra Malik;Ian Toyn

  • Affiliations:
  • The University of Waikato, Hamilton, New Zealand;Victoria University, Wellington, New Zealand;Victoria University, Wellington, New Zealand

  • Venue:
  • CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
  • Year:
  • 2009

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Abstract

Z is a formal specification language combining typed set theory, predicate calculus, and a schema calculus. This paper describes an extension of Z that allows transformation and reasoning rules to be written in a Z-like notation. This gives a high-level, declarative, way of specifying transformations of Z terms, which makes it easier to build new Z manipulation tools. We describe the syntax and semantics of these rules, plus some example reasoning engines that use sets of rules to manipulate Z terms. The utility of these rules is demonstrated by discussing two sets of rules. One set defines expansion of Z schema expressions. The other set is used by the ZLive animator to preprocess Z expressions into a form more suitable for animation.