A practical procedure for computing a regular approximation of a logic program is given. Regular approximations are useful in a variety of tasks in debugging, program specialisation and compile-time optimisation. The algorithm shown here incorporates optimisations taken from deductive database fixpoint algorithms and efficient bottom-up abstract interpretation techniques. Frameworks for defining regular approximations have been put forward in the past, but the emphasis has usually been on theoretical aspects. Our results contribute mainly to the development of effective analysis tools that can be applied to large programs. Precision of the approximation can be greatly improved by applying query-answer transformations to a program and a goal, thus capturing some argument dependency information. A novel technique is to use transformations based on computation rules other than left-to-right to improve precision further. We give performance results for our procedure on a range of programs. 1

Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle of functional languages and the resolution principle of logic languages. Formal methods of transformation of functional logic programs can be based on this well-established operational semantics. In this paper, we present a partial evaluation scheme for functional logic languages based on an automatic unfolding algorithm which builds narrowing trees. We study the semantic properties of the transformation and the conditions under which the technique terminates, is sound and complete, and is also generally applicable to a wide class of programs. We illustrate our method with several examples and discuss the relation with Supercompilation and Partial Evaluation. To the best of our knowledge this is the first formal approach to partial evaluation of functional logic programs.

This paper presents a termination technique for positive supercompilation, based on notions from term algebra. The technique is not particularily biased towards positive supercompilation, but also works for deforestation and partial evaluation. It appears to be well suited for partial deduction too. The technique guarantees termination, yet it is not overly conservative. Our technique can be viewed as an instance of Martens ' and Gallagher's recent framework for global termination of partial deduction, but it is more general in some important respects, e.g. it uses well-quasi orderings rather than well-founded orderings. Its merits are illustrated on several examples.

The control of polyvariance is a key issue in partial deduction of logic programs. Certainly, only finitely many specialised versions of any procedure should be generated, while, on the other hand, overly severe limitations should not be imposed. In this paper, well-founded orderings serve as a starting point for tackling this so-called "global termination" problem. Polyvariance is determined by the set of distinct "partially deduced" atoms generated during partial deduction. Avoiding ad-hoc techniques, we formulate a quite general framework where this set is represented as a tree structure. Associating weights with nodes, we define a well-founded order among such structures, thus obtaining a foundation for certified global termination of partial deduction. We include an algorithm template, concrete instances of which can be used in actual implementations, prove termination and correctness, and report on the results of some experiments. Finally, we conjecture that the proposed framewor...

Recently well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper,

Abstract. Recently, considerable advances have been made in the (online) control of logic program specialisation. A clear conceptual distinction has been established between local and global control and on both levels concrete strategies as well as general frameworks have been proposed. For global control in particular, recent work has developed concrete techniques based on the preservation of characteristic trees (limited, however, by a given, arbitrary depth bound) to obtain a very precise control of polyvariance. On the other hand, the concept of an m-tree has been introduced as a refined way to trace “relationships ” of partially deduced atoms, thus serving as the basis for a general framework within which global termination of partial deduction can be ensured in a non ad hoc way. Blending both, formerly separate, contributions, in this paper, we present an elegant and sophisticated technique to globally control partial deduction of normal logic programs. Leaving unspecified the specific local control one may wish to plug in, we develop a concrete global control strategy combining the use of characteristic atoms and trees with global (m-)trees. We thus obtain partial deduction that always terminates in an elegant, non ad hoc way, while providing excellent specialisation as well as fine-grained (but reasonable) polyvariance. We conjecture that a similar approach may contribute to improve upon current (on-line) control strategies for functional program transformation methods such as (positive) supercompilation. 1

Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial deduction, is to exploit partial knowledge about the input. It is achieved through a well-automated application of parts of the Burstall-Darlington unfold/fold transformation framework. The main challenge in developing systems is to design automatic control that ensures correctness, efficiency, and termination. This survey and tutorial presents the main developments in controlling partial deduction over the past 10 years and analyses their respective merits and shortcomings. It ends with an assessment of current achievements and sketches some remaining research challenges.

Partial deduction and driving are two methods used for program specialization in logic and functional languages, respectively. We argue that both techniques achieve essentially the same transformational effect by unification-based information propagation. We show their equivalence by analyzing the definition and construction principles underlying partial deduction and driving, and by giving a translation from a functional language to a definite logic language preserving certain properties. We discuss residual program generation, termination issues, and related other techniques developed for program specialization in logic and functional languages.

This paper is concerned with the problem of removing, from a given logic program, redundant arguments. These are arguments which can be removed without affecting correctness. Most program specialisation techniques, even though they perform argument filtering and redundant clause removal, fail to remove a substantial number of redundant arguments, yielding in some cases rather inefficient residual programs. We formalise the notion of a redundant argument and show that one cannot decide effectively whether a given argument is redundant. We then give a safe, effective approximation of the notion of a redundant argument and describe several simple and efficient algorithms calculating based on the approximative notion. We conduct extensive experiments with our algorithms on mechanically generated programs illustrating the practical benefits of our approach.

The so called “cogen approach” to program specialisation, writing a compiler generator instead of a specialiser, has been used with considerable success in partial evaluation of both functional and imperative languages. This paper demonstrates that this approach is also applicable to partial evaluation of logic programming languages, also called partial deduction. Self-application has not been as much in focus in logic programming as for functional and imperative languages, and the attempts to self-apply partial deduction systems have, of yet, not been altogether that successful. So, especially for partial deduction, the cogen approach should prove to have a considerable importance when it comes to practical applications. This paper first develops a generic offline partial deduction technique for pure logic programs, notably supporting partially instantiated datastructures via binding types. From this a very efficient cogen is derived, which generates very efficient generating extensions (executing up to several orders of magnitude faster than current online systems) which in turn perform very good and non-trivial specialisation, even rivalling existing online systems. All this is supported by extensive benchmarks. Finally, it is shown how the cogen can be extended to directly support a large part of Prolog’s declarative and non-declarative features and how semi-online specialisation can be efficiently integrated.