An unfold/fold transformation framework for definite logic programs

Abstract

Given a logic program P , an unfold/fold program transformation system derives a sequence of programs P = P 0 , P 1 , . . . , P n , such that P i+1 is derived from P i by application of either an unfolding or a folding step. Unfold/fold transformations have been widely used for improving program efficiency and for reasoning about programs. Unfolding corresponds to a resolution step and hence is semantics-preserving. Folding, which replaces an occurrence of the right hand side of a clause with its head, may on the other hand produce a semantically different program. Existing unfold/fold transformation systems for logic programs restrict the application of folding by placing (usually syntactic) conditions that are sufficient to guarantee the correctness of folding. These restrictions are often too strong, especially when the transformations are used for reasoning about programs. In this article we develop a transformation system (called SCOUT) for definite logic programs that is provably more powerful (in terms of transformation sequences allowed) than existing transformation systems. This extra power is needed for a novel use of logic program transformations: for the verification of a specific class of concurrent systems, called parameterized concurrent systems.Our transformation system is constructed by developing a framework, which is parameterized by a "measure space" and associated measure functions. This framework places no syntactic restriction on the application of folding, and it can be used to derive transformation systems (by fixing the measure space and functions). The power of the system is determined by the choice of the measure space and functions; thus the relative power of different transformation systems can be compared by considering their measure spaces and functions. The correctness of these transformation systems follows from the correctness of the framework. We show that various existing transformation A preliminary version of this article appeared in the • 465 systems can be obtained as instances of our framework. We extend the unfold/fold transformation framework with a goal replacement transformation that allows semantically equivalent conjunctions of atoms to be interchanged. We then derive a new transformation system SCOUT as an instance of the framework and show its power relative to the existing transformation systems. SCOUT has been used to inductively prove temporal properties of parameterized concurrent systems (infinite families of finite state concurrent systems). We demonstrate the use of the additional power of SCOUT in constructing such induction proofs.

Totally correct logic program transformations via well-founded annotations

“…Since the pioneering work by Tamaki and Sato [28], various authors have proposed suitable extra conditions which guarantee the total correctness of transformations determined by applications of the unfolding, folding, and goal replacement rules [5,8,11,13,16,24,28,29]. The essential idea presented by Tamaki and Sato in [28] is that the replacement of G 1 by G 2 determines a totally correct transformation if, in addition to the condition M(P ) |= ∀X(∃Y 1 G 1 ↔ ∃Y 2 G 2 ), we have that, for every ground substitution σ for the variables in X, if there exist a ground substitution ϑ 1 for the variables in Y 1 and a proof π 1 of G 1 σ ϑ 1 in P , then there exist a ground substitution ϑ 2 for the variables in Y 2 and a proof π 2 of G 2 σ ϑ 2 in P , such that the measure of π 2 is not larger than the measure of π 1 .…”

“…Thus, the replacement of p(f (X)) by q(X) satisfies the condition by Tamaki and Sato (and, indeed, this transformation is totally correct), while the replacement of q(X) by p(f (X)) does not satisfy that condition (and, indeed, this transformation is not totally correct). More sophisticated proof measures are defined in [24,29]. However, in [24,29] and also in [28] one cannot find any general methodology for comparing proof measures and checking the conditions which ensure the total correctness of the transformations based on goal replacements.…”

“…More sophisticated proof measures are defined in [24,29]. However, in [24,29] and also in [28] one cannot find any general methodology for comparing proof measures and checking the conditions which ensure the total correctness of the transformations based on goal replacements.…”

“…Much work has been devoted to the study of the correctness of program transformations of definite programs (see, for instance, [5,8,11,13,16,24,28,29]). Two correctness properties have been considered: partial correctness and total correctness.…”

Specialization of Concurrent Guarded Multi-set Transformation Rules

“…-In concurrent languages like CHR, we also can eliminate communication channels, synchronization points and don't care nondeterminism [EGM01]. -Verification and model checking can be done by program transformation [DP99,FPP01,RKRR04]. -Agent can be specialized to a specific context (Example in [EGM01]).…”