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.

Klappentext

The mathematical concepts and notational conventions known as Z were first proposed around 1981. The objective was to establish a mathematical basis for programming concepts, and to verify the work by case studies with industry. Since 1986 there has been a steady growth in the number of Z users, and a corresponding increase in the publication of technical papers and reports of work with Z. The annual Z user meetings offer an excellent focal point for work published on Z, and provide a forum for the discussion of new developments. BZ User Workshop, York 1991/B, provides an important overview of new developments in theoretical and practical aspects of Z. It will be of interest to academic and industrial researchers, as well as teachers of formal methods, and industrial software engineers.

Inhalt
Theoretical Foundations.- On Recursive Free Types in Z.- On Free Type Definitions in Z.- Z and Hoare Logics.- W: A Logic for Z.- Scope of Use.- The Use of Z.- Extending the Useful Application Domain for Formal Methods.- Domains of Application for Formal Methods.- Z, an Executable Subset of Z.- Special Applications.- Engineering Human-Error Tolerant Software.- Techniques for Partial Specification and Specification of Switching Systems.- Tools.- Z and Eves.- zedB: A Proof Tool for Z Built on B.- Structured Methods and Object-Oriented Approaches.- A Method for the Specification of Relational Database Applications.- Structured Analysis' A Draft Method for Writing Z Specifications.- Enhancing the Structure of Z Specifications.- ZOOM Workshop Report.- Bibliography etc.- Select Z Bibliography and Frequently Asked Questions.- Author Index.