Debugging without Testing

It is so inconceivable to debug a program without testing it that these two words are used nearly interchangeably. Yet we argue that using the concept of relative correctness we can indeed remove a fault from a program and prove that the fault has been removed, by proving that the new program is more correct than the original. This is a departure from the traditional roles of proving and testing methods, whereby static proof methods are applied to a correct program to prove its correctness, and dynamic testing methods are applied to an incorrect program to expose its faults.