Strongly-Typed Theory of Structures and Behaviours

This paper describes an approach to capturing the relation between circuits and their behaviours within a formal theory. The method exploits dependent types to achieve a rigorous yet theoretically simple connection between circuits (treated as graphs) and their behavioural speciications (treated as predicates). An example is given of a behavioural extraction function and it is shown how a type for modules can be deened that is suuciently ne to guarantee that the behaviour of a module will satisfy its behavioural speciication. The method is discussed in relation to VHDL and in relation to formal synthesis, (a process whereby one starts with a behavioural speciica-tion and, using an interactive goal-directed approach, ends up with a circuit and a formal proof that it satisses the given behavioural speciication).