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". 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.
Z was originally proposed by Abrial in 1977 with the help of Steve Schuman and Bertrand Meyer. 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.
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 catalogue (called the mathematical toolkit) of commonly used mathematical functions and predicates, defined using Z itself.
Because 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. There are also Unicode encodings for all standard Z symbols.
- the standard is publicly available from the ISO ITTF site free of charge and, separately, available for purchase from the ISO site;
- the technical corrigendum is available from the ISO site free of charge.
- Z User Group (ZUG)
- Community Z Tools (CZT) project
- Other formal methods (and languages using formal specifications):
- FDM (Formal Development Methodology), revolving around the Ina Jo and Ina Flo specification sub-languages, quite popular in the 1980s and 1990s
- VDM-SL, the main alternative to Z
- B-Method, developed by Jean-Raymond Abrial (creator of Z notation)
- Z++ and Object-Z : object extensions for the Z notation
- Alloy, a specification language inspired by Z notation and implementing the principles of Object Constraint Language (OCL).
- Verus, a proprietary tool built by Compion, Champaign, Illinois (later purchased by Motorola), for use in the multi-level secure UNIX project pioneered by its Addamax division.
- Fastest is a model-based testing tool for the Z notation.
- Abrial, Jean-Raymond (1974), "Data Semantics", in Klimbie, J. W.; Koffeman, K. L. (eds.), Proceedings of the IFIP Working Conference on Data Base Management, North-Holland, pp. 1–59
- Meyer, Bertrand; Baudoin, Claude (1980), Méthodes de programmation (in French),
- Abrial, Jean-Raymond; Schuman, Stephen A; Meyer, Bertrand (1980), "A Specification Language", in Macnaghten, A. M.; McKeag, R. M. (eds.), On the Construction of Programs, Cambridge University Press, ISBN 0-521-23090-X (describes early version of the language).
- Hoogeboom, Hendrik Jan. "Formal Methods in Software Engineering" (PDF). The Netherland: University of Leiden. Retrieved 14 April 2017.
- Korpela, Jukka K. "Unicode Explained: Internationalize Documents, Programs, and Web Sites". unicode-search.net. Retrieved 24 March 2020.
- "ISO/IEC 13568:2002". Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics (Zipped PDF). ISO. 1 July 2002. 196 pp.
- "ISO/IEC 13568:2002/Cor.1:2007". Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics — Technical corrigendum 1 (PDF). ISO. 15 July 2007. 12 pp.
- Spivey, John Michael (1992). The Z Notation: A reference manual. International Series in Computer Science (2nd ed.). Prentice Hall.
- Davies, Jim; Woodcock, Jim (1996). Using Z: Specification, Refinement and Proof. International Series in Computer Science. Prentice Hall. ISBN 0-13-948472-8.
- Bowen, Jonathan (1996). Formal Specification and Documentation using Z: A Case Study Approach. International Thomson Computer Press, International Thomson Publishing. ISBN 1-85032-230-9.
- Jacky, Jonathan (1997). The Way of Z: Practical Programming with Formal Methods. Cambridge University Press. ISBN 0-521-55976-6.