. UML static models are expressed using a mixture of class diagrams and OCL expressions. In a well formed static model, the OCL expressions and class diagrams are type consistent. Checking for type consistency of static models involves both inclusion and parametric polymorphism. This paper defines a semantics of type consistency in terms of a type theory for UML static models. The type theory is shown to be correct with respect to a value semantics for OCL. The existence of a consistency checking algorithm for UML static models is established. 1 Introduction The Unified Modeling Language (UML) is a general-purpose visual modelling language that is designed to specify, visualise and construct the artifacts of an object-oriented system [14]. UML supports the OO development process by providing constructs for describing a proposed software system as a collection of data and behavioural models. UML defines system states using static models that freely describe configurations of o...

This paper proposes a new calculus for expressing the behaviour of object-oriented systems. The semantics of the calculus is given in terms of operators from computational category theory. The calculus aims to span the gulf between abstract specification and concrete implementation of object-oriented systems using mathematically verifiable properties and transformations. The calculus is compositional and can be used to express the behaviour of partial system views. The calculus is used to specify, analyse and refine a simple case study. 1