A Relational Approach to Defining Transformations in a Metamodel

Metamodelling is becoming a standard way of defining languages such as the UML. A language definition distinguishes between concrete syntax, abstract syntax and semantics domain. It is possible to define all three using a metamodelling approach, but it is less clear how to define the transformations between them. This paper proposes an approach which uses metamodelling patterns that capture the essence of mathematical relations. It shows how these patterns can be used to define both the relationship between concrete syntax and abstract syntax, and between abstract syntax and semantics domain, for a fragment of UML. A goal of the approach is to provide a complete specification of a language from which intelligent tools can be generated. The extent to which the approach meets this goal is discussed in the paper.