Z notation

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An example of a formal specification (in Spanish) using the Z notation.

The Z notation /ˈzɛd/ 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".[1] He used a notation that would later be taught in the University of Grenoble until the end of the 1980s. While at EDF (Électricité de France), Abrial wrote internal notes on Z.[citation needed] The Z notation is used in the 1980 book Méthodes de programmation.[2]

Z was originally proposed by Abrial in 1977 with the help of Steve Schuman and Bertrand Meyer.[3] 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][clarification 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.


ISO completed a Z standardization effort in 2002. This standard[4] and a technical corrigendum[5] are available from ISO for free:

  • the standard is publicly available[4] from the ISO ITTF site free of charge and, separately, available for purchase[4] from the ISO site;
  • the technical corrigendum is available[5] from the ISO site free of charge.


See also


  1. Abrial, Jean-Raymond, "Data Semantics", in Klimbie; Koffeman (eds.), Data Base Management, North-Holland, pp. 1–59<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
  2. Meyer, Bertrand; Baudoin, Claude (1980), Méthodes de programmation (in French), EyrollesCS1 maint: unrecognized language (link)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
  3. Abrial, Jean-Raymond; Schuman, Stephen A; Meyer, Bertrand (1980), "A Specification Language", in Macnaghten, AM; McKeag, RM (eds.), On the Construction of Programs, Cambridge University Press, ISBN 0-521-23090-X<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> (describes early version of the language).
  4. 4.0 4.1 4.2 "ISO/IEC 13568:2002". Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics (Zipped PDF). ISO. 2002-07-01.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> 196 pp.
  5. 5.0 5.1 "ISO/IEC 13568:2002/Cor.1:2007". Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics — Technical corrigendum 1 (PDF). ISO. 2007-07-15.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> 12 pp.

Further reading

External links