Structured systems development methodologies have been recognized as the most popular tools in information systems development. They are widely accepted by practising systems developers because of the top down nature of the methodologies and the graphical nature of the tools. Unfortunately, however, the models are only derived from the experience of the authors. In spite of the popularity of these models, relative little work has been done in providing a theoretical framework to them. In this project, we have tried to solve the problem by defining a unifying theoretical framework behind the popular structured models.

We have defined an initial algebra of structured systems, which can be mapped by unique homomorphisms to a DeMarco algebra of data flow diagrams, a Yourdon algebra of structure charts and a Jackson algebra of structure texts (with equations). As a result, specifications can be transformed from one form to another. Algebraic interpreters may be adapted to validate the specifications.

We have also found that the proposed term algebra as well as the DeMarco, Yourdon and Jackson notations fit nicely into a functorial framework. The framework provides a theoretical basis for manipulating incomplete or unstructured specifications through the concepts of structured tasks and refinement morphisms. Moreover, DeMarco data flow diagrams can be mapped to term algebras through free functors. Conversely, specifications in term algebras can be mapped to other notations such as Yourdon structure charts by means of functors.