World Library  
Flag as Inappropriate
Email this Article

Z notation

Article Id: WHEBN0000034521
Reproduction Date:

Title: Z notation  
Author: World Heritage Encyclopedia
Language: English
Subject: Tie (typography), Specification language, Bracket, ISO 3166, Alloy (specification language)
Publisher: World Heritage Encyclopedia

Z notation

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

The Z notation 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. 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!"

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.


  • Espino, Luis, ERZ: Tool for to transform ER model to Z Notation equivalent .
  • Community Z Tools (CZT) (project), Source forge .
  • Z Word tools (project), Source forge  for developing and checking Z specifications in Microsoft Word.
  • Spivey, Michael ‘Mike’, Fuzz Type-Checker for Z .
  • Z/Eves — A proof checker for the Z notation (German site but all manuals in English)
  • Z/EVES Documentation, papers, and manuals on Z/EVES
  • ZETA open-source system for development software specifications in Z
  • HOL-Z open-source proof environment for Z in Isabelle/HOL
  • CADiZ, a set of free software tools that assist use of Z notation
  • ProofPower, a suite of open-source tools supporting specification and proof in HOL and in the Z notation
  • z-vime z-vimes Alternate source of Vimes.

See also


  1. ^  .
  2. ^  .
  3. ^ Abrial, Jean-Raymond; Schuman, Stephen A; Meyer, Bertrand (1980), "A Specification Language", in Macnaghten, AM; McKeag, RM, On the Construction of Programs, Cambridge University Press,   (describes early version of the language).
  4. ^ a b c "ISO/IEC 13568:2002". Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics (  196 pp.
  5. ^ a b "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.  12 pp.

Further reading

External links

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.