Representational and denotational semantics of digital systems

The input/output transformation effected by digital systems can be considered as concrete realizations of abstract mathematical functions. The mappings between abstract functions and concrete realizations, if kept explicit throughout the formulation, constitute the necessary `handles´ (embodied by function definitions) for transformational reasoning about digital systems. Deductive reasoning can be factored out and reduced considerably. This is demonstrated by a functional recast of the major parts of digital systems theory. Since the emphasis of this study is on the method (transformational reasoning) rather than on new system concepts, examples are chosen from familiar areas. However, some new results are obtained