There are two ways to describe a state machine as an algebraic specification: a behavioral specification and a rewrite specification. In this study, we propose a translation system from behavioral specifications to rewrite specifications to obtain a verification system which has the strong points of verification techniques for both specifications. Since our translation system is complete with respect to invariant properties, it helps us to obtain a counter-example for an invariant property through automatic exhaustive searching for a rewrite specification.

In this paper, we give a denotational semantics of imperative programming languages as a CafeOBJ behavioral specification. Since CafeOBJ is an executable algebraic specification language, not only execution of programs but also semi-automatic verification of programs properties can be done. We first describe an imperative programming language with integer and Boolean types, called IPL. Next we discuss about how to extend IPL, that is, IPL with user-defined types. We give a notion of equivalent programs, which is defined by using the notion of the behavioral equivalence of behavioral specifications. We show a sufficient condition for the equivalence relation of programs, which reduces the task to prove programs to be equivalent.