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.
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. There are also Unicode encodings for all standard Z symbols.
ISO completed a Z standardization effort in 2002. This standard and a technical corrigendum are available from ISO for free:
- Community Z Tools (CZT) (project), Source forge
- Z Word tools (project), Source forge for developing and checking Z specifications in Microsoft Word
- Fuzz, a 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-vimes Z-Vimes: type checker and (eventually) theorem prover for the Z specification language
- ProB is an animator and model checker originally written for the B-Method that provides also support for Z specifications ("ProZ") that conform to the Fuzz type checker
- Z User Group (ZUG)
- Community Z Tools (CZT) project
- Other formal methods (and languages using formal specifications):
- Fastest is a model-based testing tool for the Z notation.
- Abrial, Jean-Raymond (1974), "Data Semantics", in Klimbie, J. W.; Koffeman, K. L., 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), Eyrolles
- Abrial, Jean-Raymond; Schuman, Stephen A; Meyer, Bertrand (1980), "A Specification Language", in Macnaghten, A. M.; McKeag, R. M., 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.
- "ISO/IEC 13568:2002". Information Technology — Z Formal Specification Notation — Syntax, Type System and Semantics (Zipped PDF). ISO. 2002-07-01. 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. 2007-07-15. 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. Archived from the original on 2009-06-27.
- Bowen, Jonathan (1996). Formal Specification and Documentation using Z: A Case Study Approach. International Thomson Computer Press. 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.
- Toyn, Ian, Z Specification proposals, UK: York .
- WSDL 2.0, W3C , a specification containing Z notation assertions and explanation