Abstract. A two-level data transformation consists of a type-level transformation of a data format coupled with value-level transformations of data instances corresponding to that format. Examples of two-level data transformations include XML schema evolution coupled with document migration, and data mappings used for interoperability and persistence. We provide a formal treatment of two-level data transformations that is typesafe in the sense that the well-formedness of the value-level transformations with respect to the type-level transformation is guarded by a strong type system. We rely on various techniques for generic functional programming to implement the formalization in Haskell. The formalization addresses various two-level transformation scenarios, covering fully automated as well as user-driven transformations, and allowing transformations that are information-preserving or not. In each case, two-level transformations are disciplined by one-step transformation rules and type-level transformations induce value-level transformations. We demonstrate an example hierarchicalrelational mapping and subsequent migration of relational data induced by hierarchical format evolution. Keywords: Two-level transformation, Program calculation, Refinement calculus, Strategic term rewriting, Generalized abstract datatypes, Generic programming,

This report describes the development of an industrial strength grammar for the VDM specification language. We present both the development process and its result. The employed methodology can be described as iterative grammar engineering and includes the application of techniques such as grammar metrication, unit testing, and test coverage analysis. The result is a VDM grammar of industrial strength, in the sense that it is well-tested, it can be used for fast parsing of high volumes of VDM specifications, and it allows automatic generation of support for syntax tree representation, traversal, and interchange. 2 Development of an Industrial Strength Grammar for VDM 1

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.