Quasi-terminating logic programs for ensuring the termination of partial evaluation

Abstract

Abstract. A logic program strongly quasi-terminates when only a finite number of distinct atoms (modulo variable renaming) are derivable from any given query and computation rule. This notion of quasi-termination, though stronger than related notions that only consider Prolog's computation rule, is essential for ensuring the termination of partial evaluation, where liberal selection policies are often mandatory to achieve a good specialization. In this paper, we introduce sufficient conditions for the strong termination and quasi-termination of logic programs which are based on the construction of size-change graphs. The class of strongly quasi-terminating logic programs, however, is too restricted. Therefore, we also introduce an annotation procedure that annotates those predicate arguments which are responsible of the non-quasi-termination. As a consequence, the annotated program behaves like a quasi-terminating program if annotated arguments are generalized (i.e., replaced by a fresh variable) when they occur in a computation. We illustrate the usefulness of our approach by designing a simple partial evaluator in which global termination is always ensured offline (i.e., statically). A prototype implementation demonstrates its viability.

Fast Offline Partial Evaluation of Large Logic Programs

“…In this section, we recall the basis of the size-change analysis of [13], which is used to check the (quasi-)termination of a program.…”

“…For this purpose, some ordering on terms is required. In [13], reduction orders ( , ) induced from symbolic norms || · || are used:…”

“…Theorem 1 (termination [13]). Let P be a program and let ( , ) be a reduction pair induced by a symbolic norm || · ||.…”

“…For this purpose, [13] adds an additional condition, namely that the considered norms || · || should be bounded, i.e., the set {s | ||t|| ||s||} should contain a finite number of nonvariant terms for any term t. Note that this condition excludes the use of some norms. For instance, the list-length norm is not bounded, a serious limitation of the results in [13].…”

“…-In addition to the implementation complexity, the technique is also very slow and does not scale to medium-sized examples. Recently, Vidal [13] has introduced a quasi-termination analysis for logic programs that is independent of the selection rule. This approach is less precise than other termination analyses that take into account a particular selection strategy but, as a counterpart, is also faster and well suited for partial evaluation (where flexible selection strategies are often mandatory, see, e.g., [1,8]).…”