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Totally correct logic program transformations via well-founded annotations

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Higher-Order and Symbolic Computation

An Erratum to this article was published on 23 May 2008

An Erratum to this article was published on 23 May 2008

Abstract

We address the problem of proving the total correctness of transformations of 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 Γ 1 of clauses occurring in P by a new set Γ 2 of clauses, provided that Γ 1 and Γ 2 are equivalent in the least Herbrand model M(P) of the program P.

We propose a general method for proving that transformations based on clause replacement are 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 deriving from the given program P an annotated program \(\overline{P}\) , (ii) applying a variant of the clause replacement rule and transforming the annotated program \(\overline{P}\) into a terminating annotated program \(\overline{Q}\) , and (iii) erasing the annotations from \(\overline{Q}\) , thereby getting Q.

Our method does not require that either P or Q are terminating and it is parametric with respect to the annotations. By providing different annotations we can easily prove the total correctness of program transformations based on various versions of the popular unfolding, folding, and goal replacement rules, which can all be viewed as particular cases of our clause replacement rule.

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Authors and Affiliations

  1. DISP, University of Roma Tor Vergata, Via del Politecnico 1, 00133, Roma, Italy

    Alberto Pettorossi

  2. IASI-CNR, Viale Manzoni 30, Roma, Italy

    Maurizio Proietti

Authors
  1. Alberto Pettorossi
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  2. Maurizio Proietti
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Correspondence to Alberto Pettorossi.

Additional information

A preliminary version of this paper appears as: A Theory of Totally Correct Logic Program Transformations. In: Proceedings of the ACM SIGPLAN Symposium on Partial Evaluation and Semantics-Based Program Manipulation, August 24–25, 2004, Verona, Italy, ACM Press, 2004, pp. 159–168.

An erratum to this article can be found at http://dx.doi.org/10.1007/s10990-008-9031-7

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Pettorossi, A., Proietti, M. Totally correct logic program transformations via well-founded annotations. Higher-Order Symb Comput 21, 193–234 (2008). https://doi.org/10.1007/s10990-008-9024-6

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