Z notation

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The Z notation (formally pronounced /zɛd/), named after Zermelo-Fränkel set theory, is a formal specification language used for describing and modelling computing systems. It is targeted at the clear specification of computer programs and the formulation of proofs about the intended program behavior.

Z was originally proposed by Jean-Raymond Abrial in 1977 with the help of Steve Schuman and Bertrand Meyer [1]. It was developed further at the Programming Research Group at Oxford University, where Abrial worked in the early eighties.

Z is based on the standard mathematical notation used in axiomatic set theory, lambda calculus, and first-order predicate logic. All expressions in Z notation are typed, thereby avoiding some of the paradoxes of naive set theory. Z contains a standardized catalog (called the mathematical toolkit) of commonly used mathematical functions and predicates.

Although Z notation uses many non-ASCII symbols, the specification includes suggestions for rendering the Z notation symbols in ASCII and in LaTeX.

A valuable resource for newcomers interested in learning Z is The Z Notation: a reference manual.

Z notation was used in the IBM CICS project.

Contents

The ISO completed a Z standardization effort in 2002. This standard, entitled Information Technology – Z Formal Specification Notation – Syntax, Type System and Semantics, ISO/IEC 13568:2002, can be obtained directly from ISO.

13568_2002.zip, 1 MB PDF, 196 pages

  1. ^ Jean-Raymond Abrial, Stephen A. Schuman and Bertrand Meyer: A Specification Language, in On the Construction of Programs, Cambridge University Press, eds. A. M. Macnaghten and R. M. McKeag, 1980 (describes early version of the language). ISBN 0-521-23090-X

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