Inheritance and OMT: a CSP Approach

Abstract:Much research has been conducted on the formulation of inheritance in object-orientedness. Most proposals retain the semantic relationship between the superclass and subclass, but deliberately ignore the issues of overriding, which plays an important role in object-oriented modelling. Others use class inheritance and module inheritance to distinguish between the cases of inheritance with and without overriding, but, as a result, one fundamental concept is partitioned into two. Some research supports overriding, but not transitivity. This thesis addresses the issue of overriding in object-orientedness, illustrates how a single inheritance concept can be formalized using Communicating Sequential Processes (CSP), proposes a refined concept of conformance which is transitive, and demonstrates the practical application of our theory. This project compares favourably with other related work.
In this thesis, we identify that reflexivity, anti-symmetry, transitivity, overriding, behavioural compatibility, formality, incrementality and multiple inheritance are the desirable features of a theory of inheritance. We formalize the concept of behavioural inheritance as a special kind of conformance relation that links a subclass to its superclass by the Fidge’s priority choice operator. Using the priority choice operator, we integrate naturally the concept of overriding into our formalization and provide a support for an incremental development. Transitivity is realized by the introduction of strong conformance which can be used as a unification of extension and reduction. It also provides a framework of reflexivity and anti-symmetry for the inheritance relation. Through strong conformance, behaviour compatibilities between the superclasses and subclasses can be ensured. We also refine our theory to support multiple inheritance and propose a method to resolve ambiguity raised by multiple inheritance. Finally, a criteria for generating an optimal incremental change will be presented.
Citation:W.K. Chan, Inheritance and OMT: a CSP Approach, M.Phil. Thesis, The University of Hong Kong (1995).
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