The Model-Driven Architecture initiative of the OMG promotes the idea of transformations in the context of mapping from platform independent to platform specific models. Additionally, the popularity of XML and the wide spread use of XSLT has raised the profile of model transformation as an important technique for computing. In fact, computing may well be moving to a new paradigm in which models are considered first class entities and transformations between them are a major function performed on those models. This paper proposes an approach to defining and implementing model transformations which uses metamodelling patterns to capture the essence of mathematical relations. It shows how these patterns can be used to define the relationship between two different metamodels. A goal of the approach is to enable complete specifications from which tools can be generated. The paper describes implementations of the examples, which have been partially generated from the definitions using a tool generation tool. A number of issues emerge which need to be solved in order to achieve the stated goal; these are discussed.
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