AbstractOne of the important aspects in the design of automation system is to establish some automatic transformation method from the specification by high‐level language, which is suitable for designer to the description at the circuit level. This paper formulates the circuit design as the transformation, from the recursion equation, which is a high‐level description, to the functional network FN, which is a circuit model based on the data‐flow operation. The purpose of this paper is to clarify the transformation rules for the automatic circuit design based on the theorem‐proving techniques. First, the recursion equation is formulated as the specification language, and the circuit description language for FN is designed. The theorem‐proving system for the automatic design of the circuit can be formulated as a logic system in which the axioms are the predicate expressions for the elements, and the inference rules are the transformation rules among elements. The transformation rules from the recursion equation to the circuit representation are constructed using the concept of schema corresponding to the type of the recursion equation. Since the transformation includes heuristic aspects, some transformation techniques from the schema to the circuit description (called schema transformation) as well as the decomposition‐synthesis rules in the circuit representation, are presented. A logic system based on the obtained result is presented, indicating that a theorem‐proving system for the automatic circuit design can b