Object Interaction

Objects are presented as processes endowed with state-dependent slots. Active objects have non-quiescent states. A morphism between two objects expresses that the source object is part-of the target object, in such a way that the possible observations of the part, considered in isolation, are constrained within the whole. Our semantic domain for object-oriented concepts includes a cocomplete category of objects where several kinds of dynamic interaction like event and memory sharing are reflected by colimits. 1 Introduction According to the object-oriented view [10]: (1) an object has an internal state that can be changed by certain actions (events) and observed through slots (attributes); and (2) an object displays behaviour (at any time some actions are possible and some are not). Therefore, an object is, basically, a process endowed with trace-dependent slots. In [4,5] we find contributions to a semantic domain for objects dealing with aggregation of interacting objects as well as object classes and inheritance. A semantic domain for objects must start with the adoption of a semantic domain for processes. In this paper we will work with a trace-based model of processes, called herein the quiescence model. But traces alone do not tell everything about an object. The behaviour of a stack is described satisfactorily if we describe what we can observe, depending on what happened to the stack before. The observations we can make about a stack are the values of its top entry. The top value is determined by the finite sequence of events that happened so far. Formally, if we have a set S of slots and a set obs(S) of observations over S, the observable behaviour of an object is modelled by a slot observation mapping α:E*→obs(S) associating observations with traces. Summing up, our process-oriented model for objects consists of a set E of events, a set S of slots, a set Λ¢E* of quiescent traces, and a slot observation map α:E*→obs(S). This model represents adequately the causal relationship between event traces and attribute observations. The main ideas on categorial fundamentals of object theory could be found in [4,5,7,8]: (a) morphisms express inheritance, ie, an object P inherits the behaviour of an object Q iff there is an object morphism f:Q→P; (b) communities of objects are seen as diagrams in a suitable category; (c) joint behaviour is colimit. In this paper we take the program originally setup in [4] to complete satisfaction within a new …