The Axiomatic Method of Hoare

Abstract

This chapter discusses the verification method of Hoare, well known for proving the partial correctness of while-programs. This method is usually presented in the form of a calculus, the so-called Hoare calculus. Essentially this approach is identical with the inductive assertions method introduced in the last chapter, as may become plausible from the following considerations. The inductive assertions method can be used on while-programs, since every while-program can be easily transformed to an equivalent flowchart program. Because this translation produces flowchart programs of a special form—namely flowchart programs without interleaved loops—the inductive assertions method can be simplified. This simplified form leads naturally to a calculus, namely the Hoare calculus. In the last section it will be seen how (a slight variant of) the well-founded sets method can be likewise incorporated in the Hoare calculus to achieve a method for proving the total correctness of while-programs.