Total Correctness of Logic Programs: A Formal Approach

This paper presents a deductive system in which one can prove total correctness of pure Prolog programs with negation. Total correctness of logic programs means two things: termination and partial correctness with respect to a specification. The deductive system we use is a Clark-like completion augmented with induction. It is called the inductive extension of a logic program. The connections between Clark’s completion and Prolog have been doubted before, since Prolog uses a special literal selection rule and a special search strategy. Also the possibility of using first-order predicate logic with induction for proving termination has rarely been used. We demonstrate the usefulness of the deductive system by giving a complete, fully formalized correctness proof of a program for TAUT. The example program uses negation as failure and backtracking in a non-trivial way and is therefore a typical Prolog program.