A theory of totally correct logic program transformations

ABSTRACT

We address the problem of proving total correctness of transformation rules for definite logic programs. We consider a general transformation rule, called clause replacement, which consists in transforming a program P into a new program Q by replacing a set Γ¹ of clauses occurring in P by a new set Γ² of clauses, provided that Γ¹ and Γ² are equivalent in the least Herbrand model M(P) of the program P.We propose a general method for proving that clause replacement is totally correct, that is, M(P)=M(Q). Our method consists in showing that the transformation of P into Q can be performed by: (i) adding extra arguments to predicates, thereby constructing from the given program P an annotated program α(P), (ii) applying clause replacements and transforming the annotated program α(P) into a terminating annotated program β(Q, and (iii) erasing the annotations from β(Q), thereby getting Q.Our method does not require that either P or Q terminates and it is parametric w.r.t. the annotations. By providing different definitions for these annotations, we can easily prove the total correctness of many versions of the unfolding, folding, and goal replacement rules proposed in the literature.

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INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.3 LOGICS AND MEANINGS OF PROGRAMS
      F.3.1 Specifying and Verifying and Reasoning about Programs

Additional Classification:
  D. Software
  D.1 PROGRAMMING TECHNIQUES
      D.1.2 Automatic Programming
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications
          Subjects: Constraint and logic languages

General Terms:
Languages, Theory, Verification

Keywords:
logic programming, partial and total correctness, program transformation rules, well-founded orderings