Z User Workshop Oxford 1990

Z User Workshop, Oxford 1990

Z User Workshop, London 1992

The Z notation has been developed at the Programming Research Group at the Oxford University Computing Laboratory and elsewhere for over a decade. It is now used by industry as part of the software (and hardware) development process in both Europe and the USA. It is currently undergoing BSI standardisation in the UK, and has been proposed for ISO standardisation internationally. In recent years researchers have begun to focus increasingly on the development of techniques and tools to encourage the wider application of Z and other formal methods and notations. This volume contains papers from the Seventh Annual Z User Meeting, held in London in December 1992. In contrast to previous years the meeting concentrated specifically on industrial applications of Z, and a high proportion of the participants came from an industrial background. The theme is well represented by the four invited papers. Three of these discuss ways in which formal methods are being introduced, and the fourth presents an international survey of industrial applications. It also provides a reminder of the improvements which are needed to make these methods an accepted part of software development. In addition the volume contains several submitted papers on the industrial use of Z, two of which discuss the key area of safety-critical applications. There are also a number of papers related to the recently-completed ZIP project. The papers cover all the main areas of the project including methods, tools, and the development of a Z Standard, the first publicly-available version of which was made available at the meeting. Finally the volume contains a select Z bibliography, and section on how to access information on Z through comp.specification.z, the international, computer-based USENET newsgroup. Z User Workshop, London 1992 provides an important overview of current research into industrial applications of Z, and will provide invaluable reading for researchers, postgraduate students andalso potential industrial users of Z.

Z User Workshop, York 1991

In ordinary mathematics, an equation can be written down which is syntactically correct, but for which no solution exists. For example, consider the equation x = x + 1 defined over the real numbers; there is no value of x which satisfies it. Similarly it is possible to specify objects using the formal specification language Z [3,4], which can not possibly exist. Such specifications are called inconsistent and can arise in a number of ways. Example 1 The following Z specification of a functionf, from integers to integers "f x : ~ 1 x ~ O· fx = x + 1 (i) "f x : ~ 1 x ~ O· fx = x + 2 (ii) is inconsistent, because axiom (i) gives f 0 = 1, while axiom (ii) gives f 0 = 2. This contradicts the fact that f was declared as a function, that is, f must have a unique result when applied to an argument. Hence no suchfexists. Furthermore, iff 0 = 1 andfO = 2 then 1 = 2 can be deduced! From 1 = 2 anything can be deduced, thus showing the danger of an inconsistent specification. Note that all examples and proofs start with the word Example or Proof and end with the symbol.1.