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.
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.
In 1992, “Her Majesty the Queen [was] graciously pleased to approve the Prime Minister’s recommendation that The Queen’s Award for Technological Achievement should be conferred this year upon Oxford University Computing Laboratory. Oxford University Computing Laboratory [gained] the Award jointly with IBM United Kingdom Laboratories Limited for the development of a programming method based on elementary set theory and logic known as the Z notation, and its application in the IBM Customer Information Control System (CICS) product.”