Object Orientation in Z

Object-ZZ2, 3, 4] is an extension of the formal speciication language ZZ5, 7, 8] to accommodate object orientationn6, 1]. The main reason for this extension is to improve the clarity of large speciications through enhanced structuring. A Z speciication typically deenes a number of state and operation schemas. A state schema groups together variables and deenes the relationship that holds between their values. At any instant, these variables deene the state of that part of the system which they model. An operation schema deenes the relationship between thèbefore' andàfter' states corresponding to one or more state schemas. Therefore, inferring which operation schemas may aaect a particular state schema requires examining the signatures of all operation schemas. In large speciications this is impracticable. Conventions, such as chapters, group states and operations informally, but cannot enforce structure. Object-Z overcomes this problem by connning individual operations to refer to one state schema. The deenition of a state schema with the deenitions of its associated operations (and those of other components to be detailed later) constitute a class. A class is a template for objects of that class: for each such object, its states are instances of the class' state schema and its individual state transitions conform to individual operations of the class. An object is said to be an instance of a class and to evolve according to the deenitions of its class. A class may specify part of a system, so that the potential behaviour of that part may be considered and understood in isolation. Complex classes can be speciied to inherit other classes, or to include references to objects. These structuring mechanisms are called inheritance and instantiation respectively. An Object-Z speciication of a system typically includes a number of class deenitions related by inheritance and instantiation which build towards a class representing the entire system. Section 1.1.2 introduces the syntax of classes and outlines some semantic issues.