Towards an Algebraic Semantics for the Object Paradigm

This paper surveys our current state of knowledge (and ignorance) on the use of hidden sorted algebra as a foundation for the object paradigm. Our main goal is to support equational reasoning about properties of concurrent systems of objects, because of its simple and eecient mechanisation. We show how equational speciications can describe objects, inheritance and modules; our treatment of the latter topic emphasises the importance of reuse, and the r^ ole of the so-called Satisfaction Condition. We then consider how to prove things about objects, how to unify the object and logic paradigms by using logical variables that range over objects, and how to connect objects into concurrent systems. We provide a universal characterisation of parallel connection, and more generally, of parallel connection with synchronisation, and show how the former construction gives a class manager that provides unique identiiers for its objects. The paper concludes with some topics for further research.