Concise and Formal Descriptions of Architectures and Patterns

Design patterns describe common features of software systems. Notations intended to describe individual programs are unsuitable for formalizing patterns because they are not sufficiently abstract, expressive, and well-defined. We describe LePUS, a notation that is both formal and sufficiently abstract to represent patterns and provide a framework for reasoning about them. The key features of LePUS are that: it is based on conventional logic; it models meaning as well as structure; and it facilitates reasoning with higher order sets that we have found to occur frequently in design patterns. Although the main focus of this paper is on design patterns, the techniques that we describe can also be applied to architectures.