This article presents an example of correct circuit design through interactive transformation. Interactive transformation differs from traditional hardware design transformation frameworks in that it focuses on the issue of finding suitable hardware architecture for the specified system and the issue of architecture correctness. The transformation framework divides every transformation in designs into two steps. The first step is to find a proper architecture implementation. Although the framework does not guarantee existence of such an implementation, nor its discovery, it does provide a characterization of architectural implementation so that the question "is this a correct implementation?" can be answered by equational rewriting. The framework allows a correct architecture implementation to be automatically incorporated with control descriptions to obtain a new system description. The significance of this transformation framework lies in the fact that it requires simpler mechanism o...

In this paper we study final algebra semantics for constructive equational systems. A class of models of a constructive system is described, and proven to haveafinal algebra. Then wedevelop a method for proof by consistency with respect to the final model. Finally weshowthatthemethod contains the proof methods of Musser [11], Goguen [2], and Huet and Hullot [5] as special cases.