On the Composability of Design Patterns

In real applications, design patterns are almost always to be found composed with each other. It is crucial that these compositions be validated. This paper examines the notion of validity, and develops a formal method for proving or disproving it, in a context where composition is performed with formally defined operators on formally specified patterns. In particular, for validity, we require that pattern compositions preserve the features, semantics and soundness of the composed patterns. The application of the theory is demonstrated by a formal analysis of overlap-based pattern compositions and a case study of a real pattern-oriented software design.