Z notation

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The Z notation (formally pronounced /ˈzɛd/ notation), named after Zermelo–Fraenkel 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 computer-based systems in general.



In 1974, Jean-Raymond Abrial published "Data Semantics" in Data Base Management (Klimbie, Koffeman, eds), North-Holland, pp 1–59. He used a notation that would later be taught in the Université de Grenoble until the end of the eighties. While at EDF (Électricité de France), Abrial wrote internal notes on Z. The Z notation is used in the book of Bertrand Meyer and Claude Baudoin, Méthodes de programmation, published by Eyrolles in 1980.

Z was originally proposed by 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 1980s, having arrived at Oxford in September 1979.

Abrial answers the question "Why Z?" with "Because it is the ultimate language!"[citation needed]

Usage and notation

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 (just like the APL language, long before it) uses many non-ASCII symbols, the specification includes suggestions for rendering the Z notation symbols in ASCII and in LaTeX.


The ISO completed a Z standardization effort in 2002. This standard can be obtained directly from ISO.[2]

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