Object-Oriented Refinement and Proof using Behaviour Functions

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.