Z Formal Specification Language

  • Gerard O’Regan
Part of the Undergraduate Topics in Computer Science book series (UTICS)


Z is a formal specification language based on Zermelo set theory. It was developed at the Programming Research Group at Oxford University in the early 1980s and became an ISO standard in 2002. Z specifications are mathematical and employ a classical two-valued logic. The use of mathematics ensures precision, and allows inconsistencies and gaps in the specification to be identified. Theorem provers may be employed to demonstrate the correctness of the refinement steps, and that the software implementation meets its specification.

Z is a ‘model oriented’ approach with an explicit model of the state of an abstract machine given, and operations are defined in terms of this state. Its mathematical notation is used for formal specification, and the schema calculus is used to structure the specifications. The latter is visually striking, and consists essentially of boxes, with these boxes or schemas used to describe operations and states. The schema calculus enables schemas to be used as building blocks and combined with other schemas.


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    Diller A (1990) Z. An introduction to formal methods. Wiley, EnglandGoogle Scholar
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    O’Regan G (2013) Mathematics in computing. Springer, LondonGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Gerard O’Regan
    • 1
  1. 1.SQC ConsultingMallowIreland

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