| Resumo: | If, as a well-known aphorism states, modelling is for reasoning, this chapter is an attempt to define and apply a formal semantics to interaction patterns captured by UML 2.0 sequence diagrams in order to enable rigourous reasoning about them. Actually, model transformation plays a fundamental role in the process of software development, in general, and in model driven engineering in particular. Being a de facto standard in this area, UML is no exception, even if the number and diversity of diagrams expressing UML models makes it difficult to base its semantics on a single framework. This chapter argues for the use of coalgebra theory, as the mathematics of state-based designs, to give a precise semantics to sequence diagrams with coercions. In particular, it illustrates how an algebra for constructing and reasoning about them can be made explicit and useful for the working software architect.
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