Formalization of the Equivalent Transformation Computation Model

In the equivalent transformation (ET) computation model, a specification provides background knowledge in a problem domain and defines a set of queries of interest; a program is a set of prioritized transformation rules; and computation consists in successive reduction of queries using meaningpreserving transformation with respect to given background knowledge. This paper presents a formalization of the ET model from the viewpoint of program synthesis, where not only computation but also program correctness and correctness relations are of central importance. The notion of program correctness defines “what it means for a program to be correct with respect to a specification”, while a correctness relation provides guidance on “how to obtain such a program”. The correctness relation of the ET model is established, based on which how the fundamental structure of the ET model facilitates program synthesis is discussed. Program synthesis strategies in the ET model are illustrated.