The Geometry of Object

In object-oriented systems, it is often the case that an object will have an attribute whose value identiies (points or refers to) some other object in the system so that the identiied object can be sent messages. In general, there is no assumed geometric notion of relative location associated with such object references, e.g. when a bank customer references a bank account for the purposes of depositing money, the two objects involved may be anywhere inside the system. However, it sometimes happens that the object referenced is geometrically related to the referencing object, e.g. when a car references its wheels, each wheel is envisaged as being contained within the car. The aim of this paper is to investigate this geometric notion of object containment ; to capture it within a formal framework; and then to incorporate the containment notion into the Object-Z speciication notation. This view of object containment is then compared with related ideas found in object-oriented programming languages. The distinction between object containment and the notion of object ownership (control) is also discussed. Finally, a generalised notion of object containment is investigated.