Non-termination Inference for Constraint Logic Programs

Abstract

We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized. We give syntactic criteria to statically identify such argument positions from the text of a program. Atomic left looping queries are generated bottom-up from selected subsets of the binary unfoldings of the program of interest. We propose a set of correct algorithms for automating the approach. Then, non-termination inference is tailored to attempt proofs of optimality of left termination conditions computed by a termination inference tool. An experimental evaluation is reported. When termination and non-termination analysis produce complementary results for a logic procedure, then with respect to the leftmost selection rule and the language used to describe sets of atomic queries, each analysis is optimal and together, they induce a characterization of the operational behavior of the logic procedure.

A non-termination criterion for binary constraint logic programs

“…In (Payet and Mesnard 2006) we have presented a technique to complement termination analysis with non-termination inside the logic programming paradigm. Our aim was to detect optimal termination conditions expressed in a language describing classes of queries.…”

“…Some termination analyses compute a finite over-approximation of the binary unfolding semantics, over a constraint domain such as CLP(N ). In contrast, the non-termination analysis we have presented in (Payet and Mesnard 2006) starts from a finite subset BP of the binary unfoldings of the concrete program P ; of course, a larger subset may increase the precision of the analysis ( (Payet and Mesnard 2006) provides some experimental evidence). This non-termination analysis first detects patterns of nonterminating atomic queries from the binary recursive clauses and then propagates this non-termination information to compute classes of atomic queries for which we have a finite proof that there exists at least one infinite derivation w.r.t.…”

“…P . The basic idea in (Payet and Mesnard 2006) relies on checking, for each recursive clause in BP , that the body is more general than the head; if this test succeeds, we can conclude that the head is an atomic query which has an infinite derivation w.r.t. BP .…”

“…The initial motivation in (Payet and Mesnard 2006) was to complement termination analysis with non-termination inside the logic programming paradigm in order to detect optimal termination conditions expressed in a language describing classes of queries. Although we obtained interesting experimental results, the overall approach remains quite syntactic, with an ad hoc flavor and tight links to some basic logic programming machinery such as the unification algorithm.…”

Nontermination inference of logic programs

“…Can we propose more abstract criteria for identifying neutral arguments? A first step in this direction is presented in [29]. Also, our work aims at inferring classes of atomic left looping queries, using a bottom-up point of view.…”