Gordon A. Rose

Object-Z: a specification language advocated for the description of standards

The importance of formalising the specification of standards has been recognised for a number of years. This paper advocates the use of the formal specification language Object-Z in the definition of standards. Object-Z is an extension to the Z language specifically to facilitate specification in an object-oriented style. First, the syntax and semantics of Object-Z are described informally. Then the use of Object-Z in formalising standards is demonstrated by presenting a case study based on the ODP Trader. Finally, a formal semantics is introduced that suggests an approach to the standardisation of Object-Z itself. Because standards are typically large complex systems, the extra structuring afforded by the Object-Z class construct and operation expressions enables the various hierarchical relationships and the communication between objects in a system to be succinctly specified.

The role of secondary attributes in formal object modelling

When modelling a large and complex system, clarity of the specification becomes an important factor. In object-oriented specification, the states of individual objects are captured by the values of their attributes. Frequently however, there are dependencies between the attributes of an object. An appropriate indication of which attributes are primary (independent) and which are secondary (dependent) can add significantly to clarity. This paper details the notion of secondary attributes, their roles and implications in formal object-oriented specification.

A lower-bound for the number of productions required for a certain class of languages

Abstract W. Bucher, K. Culik II, H. Maurer and D. Wotschke (Theoretical Computer Science 14(1981), pp. 227–246) posed the problem of producing the language Ln = {ab: 1≤a,b≤n and a≠b} with a minimal number of productions. Later, W. Bucher, K. Culik II and H. Maurer showed that 2n + O(n 1 2 ) productions are sufficient. In this note we show that 2n + ⌈2n 1 2 ⌉ productions are necessary for all n≥ 6.

From monolithic to modular formal specification

Formal specification using mathematical text provides a sound basis for developing complex systems, especially safety-critical systems. The paper discusses three formal specification styles for state-based systems from monolithic, through Z to modular each illustrated by the same simple example. In each case, formal text which is left implicit in practice is identified and discussed. The paper includes a denotational semantics for operations within a modular system, including their conjunctive, parallel, choice and sequential composition. The importance of extending the semantics to unwritten formal text implicit in Z and modular style specifications is emphasised because misinterpretation of the implicit can have serious consequences.