This thesis investigates the specification, implementation and application of derived data in the context of MADAM, an entity-relationship oriented, map-based data model/programming language for database conceptual schema representation and processing. The data representation and manipulation facilities of MADAM, described in chapter 2; represent a synthesis of ideas from the areas of very high level languages, in particular SETL, and the binary association and entity-relationship approaches to data modeling. Derived data refers to data that appears to exist in its declared form, but is actually derived from related data in the database. Previous approaches to the materialization of derived data have been based on a global recalculation strategy in which derived data is recomputed whenever it is referenced. In this thesis we present an alternative approach in which derived data is explicitly stored and incrementally maintained. In chapter 3, we describe the definition of derived data in MADAM; discuss its importance as a means of fostering logical data independence, providing access control mechanisms, and supporting semantic relativism; and present a unified framework for the automatic maintenance of derived data. This framework is based on the transformational techniques of finite differencing in which repeated costly computations are replaced by more efficient incremental counterparts. In addition to the importance of our incremental maintenance approach for supporting alternative views of the same data, additional applications of our incremental maintenance approach to the implementation of summary data, integrity control, and triggers are discussed in chapter 4.