Constraint-based termination analysis of logic programs

Abstract

Current norm-based automatic termination analysis techniques for logic programs can be split up into different components: inference of mode or type information, derivation of models, generation of well-founded orders, and verification of the termination conditions themselves. Although providing high-precision results, these techniques suffer from an efficiency point of view, as several of these analyses are often performed through abstract interpretation. We present a new termination analysis which integrates the various components and produces a set of constraints that, when solvable, identifies successful termination proofs. The proposed method is both efficient and precise. The use of constraint sets enables the propagation of information over all different phases while the need for multiple analyses is considerably reduced.

A polyvariant binding-time analysis for off-line partial deduction

“…In [10], Decorte and De Schreye describe how the constraint-based termination analysis of [11] can be adapted to generate a finite set of "most general" termination conditions (e.g. for append/3 they would generate rigidity w.r.t, the listlength norm of the first argument and rigidity w.r.t, the listlength norm of the third argument as the two most general termination conditions; for our funnyapp/3 they would generate rigidity of the first and second argument w.r.t.…”

On modular termination proofs of general logic programs

“…It is worth noting that if ¬A ∈ Call P (Q) and A is a ground atom, then A ∈ Call P (Q) too. Notice that, for definite programs, the set Call P (Q) coincides with the call set Call (P, {Q}) in (De Schreye, Verschaetse andBruynooghe 1992, Decorte, De Schreye andVandecasteele 1999).…”

Characterisations of Termination in Logic Programming

“…Approaches to the automatic inference of level mappings and models are briefly recalled in the next section. Pedreschi & Ruggieri [58] give an example showing how the approach of Decorte et al [29] could be rephrased to infer boundedness.…”

“…Under this classification, this survey paper has been mainly concerned with the first type. While we do not even try to survey the large amount of literature on automatic or semi-automatic approaches [14,21,29,23,44,52,53,71], it must be observed that existing tools typically implement conditions for checking proof obligations of the characterisations we surveyed. As an example, a challenging topic of the research in automatic termination inference consists in finding standard forms of level mappings and models, so that the solution of the resulting proof obligations can be reduced to known problems for which efficient algorithms exist.…”