The Constraint Logic Programming (CLP) Scheme merges logic programming with constraint solving over predefined domains. In this paper, we study proof methods for universal left termination of constraint logic programs. We provide a sound and complete characterization of left termination for ideal CLP languages which generalizes acceptability of logic programs. The characterization is then refined to the notion of partial acceptability, which is well-suited for automatic modular inference. We describe a theoretical framework for automation of the approach, which is implemented. For non-ideal CLP languages and without any assumption on their incomplete constraint solvers, even the most basic sound termination criterion from logic programming does not lift. We focus on a specific system, namely CLP(R), by proposing some additional conditions that make (partial) acceptability sound

A class of predicates is identified for which termination does not depend on left-to-right execution. The only assumption about the selection rule is that derivations are input-consuming, that is, in each derivation step, the input arguments of the selected atom do not become instantiated. This assumption is a natural abstraction of previous work on programs with delay declarations. The method for showing that a predicate is in that class is based on level mappings, closely following the traditional approach for LD-derivations. Programs are assumed to be well and nicely moded, which are two widely used concepts for verification. Many predicates terminate under such weak assumptions. Knowing these predicates is useful even for programs where not all predicates have this property.

We introduce the notion of bounded nondeterminism for logic programs and queries. A program and a query have bounded nondeterminism if there are finitely many refutations for them via any selection rule. We o#er a declarative characterization of the class of programs and queries that have bounded nondeterminism by defining bounded programs and queries. The characterization is provided in terms of Herbrand interpretations and level mappings, in the style of existing characterizations of universal termination.

We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to eliminate the well-known problem of speculative output bindings. The second approach is based on identifying the predicates for which the textual position of an atom using this predicate is irrelevant with respect to termination. Three features are distinctive of this work: it allows for predicates to be used in several modes; it shows that block declarations, which are a very simple delay construct, are sufficient to ensure the desired properties; it takes the selection rule into account, assuming it to be as in most Prolog implementations. The methods can be used to verify existing programs and assist in writing new programs.

This paper investigates the advantages of reasoning on logic programs and queries that have only successful derivations. We consider an extension of the logic programming paradigm that combines guarded clauses, in the style of concurrent logic languages, and dynamic selection rules. Some general conditions for a class of programs and queries are stated, which characterize when successful derivations only are present. A few practical instances of the general conditions are studied, and their applicability to real programs demonstrated. The main contributions of the proposed method are: (i) don't care non determinism can be safely adopted for programs that do not fail, (ii) termination of process networks expressed as logic programs can be proved, by means of a simple proof method developed for a fixed selection rule, and (iii) a strategy for parallelizing terminating Prolog programs is identified.

In logic programming, dynamic scheduling indicates the feature by means of which the choice of the atom to be selected at each resolution step is done at runtime and does not follow a fixed selection rule such as the left-to-right one of Prolog. Input consuming derivations were introduced to model dynamic scheduling while abstracting from the technical details. In this article, we provide a sufficient and necessary criterion for termination of input consuming derivations of simply moded logic programs. The termination criterion we propose is based on a denotational semantics for partial derivations which is defined in the spirit of model-theoretic semantics previously proposed for left-to-right derivations.