Axiomatic approach to total correctness of programs

Summary

We present here an axiomatic approach which enables one to prove by formal methods that his program is “totally correct” (i.e., it terminates and is logically correct—does what it is supposed to do). The approach is similar to Hoare's approach [3] for proving that a program is “partially correct” (i.e., that whenever it terminates it produces correct results). Our extension to Hoare's method lies in the possibility of proving both correctness and termination by one unified formalism. One can choose to prove total correctness by a single step, or by incremental proof steps, each step establishing more properties of the program.