UML Metamodel Formalization with Object-Z: the State Machine Package

This paper presents a formalization using Object-Z of the State Machine package in the UML metamodel. In the specification, the abstract syntax and the static and dynamic semantics for each individual model construct in the package are grouped together and encapsulated within a single Object-Z class. For formalizing the dynamic semantics, a denotational semantics of the construct is first given ignoring detailed operational sequences. Based on this denotational semantics, an operational semantics is then defined in terms of (Object-Z) class operations and invariants constraining the operation sequences. The timed refinement calculus is used to define the operation sequences within Object-Z. With this approach, we provide not only a denotational semantics of the UML state machine but also an operational semantics consistent with the denotational semantics. This should enhance the precision of the UML state machine and also overcome the lack of modularity, extensibility and reusability of the current UML semantic representation.