Abstract. This paper addresses the foundations of data-model transformation. A catalog of data mappings is presented which includes abstraction and representation relations and associated constraints. These are justified in an algebraic style via the pointfree-transform, a technique whereby predicates are lifted to binary relation terms (of the algebra of programming) in a two-level style encompassing both data and operations. This approach to data calculation, which also includes transformation of recursive data models into “flat ” database schemes, is offered as alternative to standard database design from abstract models. The calculus is also used to establish a link between the proposed transformational style and bidirectional lenses developed in the context of the classical view-update problem.

Abstract—Although increasingly popular, Model Driven Architecture (MDA) still lacks suitable formal foundations on top of which rigorous methodologies for the description, analysis and transformation of models could be built. This paper aims to contribute in this direction: building on previous work by the authors on coalgebraic refinement for software components and architectures, it discusses refactoring of models within a coalgebraic semantic framework. Architectures are defined through aggregation based on a coalgebraic semantics for (subsets of) UML. On the other hand, such aggregations, no matter how large and complex they are, can always be dealt with as coalgebras themselves. This paves the way to a discipline of models’ transformations which, being invariant under either behavioural equivalence or refinement, are able to formally capture a large number of refactoring patterns. The main ideas underlying this research are presented through a detailed example in the context of refactoring of UML class diagrams. I.