Frameworks in Catalysis: pictorial notation and formal semantics

In OO Design, it is widely recognised that the distribution of tasks between objects and the contracts between them are key to effective design. In composing designs from reusable parts, the parts are therefore frameworks, namely descriptions of the interactive relationships between objects which participate in the interactions. Designs are then built by composing these frameworks, and any object in the final design will play (various) roles from several frameworks. Practitioners of OO Design use pictorial notations for design. However, in order to reason formally about design, we need a sound (formal) semantics for the diagrams. In this paper, we show that frameworks can be formalised as many-sorted theories, and then present a pictorial representation of such theories, developed in the Catalysis project.