Transformational Design of Digital Systems based on Graph Rewriting

Transformational design integrates design and verification. It combines “correctness by construction” and design creativity by the use of preproven behaviour preserving transformations as design steps. Transformational design is a formal design methodology in which formal aspects are hidden for the designer. Formal aspects of transformational design as a methodology for high-level synthesis, are discussed in this paper. Moreover graph rewriting theory is shown to be useful as a formal framework for transformational design. Transformations are defined as graph rewritings. Graph rewriting theory does not cover semantic aspects of graphs, which are useful as design representations because they visualise design information. A compositional formal semantics of design representations is essential in transformational design in order to prove the correctness of the transformations. This paper presents an extension of graph rewriting to attributed graphs as a suitable way to include semantical aspects. The used attribute algebra, table algebra, is a relation algebra derived from database theory. The combination of graph rewriting, table algebra and transformational design is new. Also new is the use of PVS (a theorem prover of SRI) to assist in the correctness proofs of the transformations.