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.

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Given a program and some input data, partial deduction computes a specialized program handling any remaining input more efficiently. However, controlling the process well is a rather difficult problem. In this article, we elaborate global control for partial deduction: for which atoms, among possibly infinitely many, should specialized relations be produced, meanwhile guaranteeing correctness as well as termination? Our work is based on two ingredients. First, we use the concept of a characteristic tree, encapsulating specialization behavior rather than syntactic structure, to guide generalization and polyvariance, and we show how this can be done in a correct and elegant way. Second, we structure combinations of atoms and associated characteristic trees in global trees registering "causal" relationships among such pairs. This allows us to spot looming nontermination and perform proper generalization in order to avert the danger, without having to impose a depth bound on characteristic trees. The practical relevance and benefits of the work are illustrated through extensive experiments. Finally, a similar approach may improve upon current (on-line) control strategies for program transformation in general such as (positive) supercompilation of functional programs. It also seems valuable in the context of abstract interpretation to handle infinite domains of infinite height with more precision.

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Partial deduction in the Lloyd±Shepherdson framework cannot achieve certain optimisations which are possible by unfold/fold transformations. We introduce conjunctive partial deduction, an extension of partial deduction accommodating such optimisations, e.g., tupling and deforestation. We ®rst present a framework for conjunctive partial deduction, extending the Lloyd±Shepherdson framework by considering conjunctions of atoms (instead of individual atoms) for specialisation and renaming. Correctness results are given for the framework with respect to computed answer semantics, least Herbrand model semantics, and ®nite failure semantics. Maintaining the well-known distinction between local and global control, we describe a basic algorithm for conjunctive partial deduction, and re®ne it into a concrete algorithm for which we prove termination. The problem of ®nding suitable renamings which remove redundant arguments turns out to be important, so we give an independent technique for this. A fully automatic implementation has been undertaken, which always terminates. Dierences between the abstract semantics and Prolog's left-to-right execution motivate deviations from the abstract technique in the actual implementation, which we discuss. The implementation has been tested on an extensive set of benchmarks which demonstrate that conjunctive partial