A mathematical approach to object oriented design patterns

Although design patterns are reusable design elements, existing pattern descriptions focus on specific solutions that are not easily reusable in new designs. This paper introduces a new pattern description method for object oriented design patterns. The description method aims at providing a more general description of patterns so that patterns can be readily reusable. This method also helps a programmer to analyze, compare patterns, and detect patterns from existing software programmes. This method differs from the existing pattern description methods in that it captures both static and dynamic properties of patterns. It describes them in terms of mathematical entities rather than natural language narratives, incomplete graphical notations or programme fragments. It also helps users to understand the patterns and relationships between them; and select appropriate patterns to the problem at hand. We also present a case study to demonstrate the methods' suitability for specifying object oriented design patterns.