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.

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.

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. Recently, partial deduction of logic programs has been extended to conceptually embed folding. To this end, partial deductions are no longer computed of single atoms, but rather of entire conjunctions; Hence the term "conjunctive partial deduction". Conjunctive partial deduction aims at achieving unfold/fold-like program transformations such as tupling and deforestation within fully automated partial deduction. However, its merits greatly surpass that limited context: Also other major efficiency improvements are obtained through considerably improved side-ways information propagation. In this extended abstract, we investigate conjunctive partial deduction in practice. We describe the concrete options used in the implementation(s), look at abstraction in a practical Prolog context, include and discuss an extensive set of benchmark results. From these, we can conclude that conjunctive partial deduction indeed pays off in practice, thoroughly beating its conventional precursor on a wide...

The relation between partial deduction and the unfold/fold approach has been a matter of intense discussion. In this paper we consolidate the advantages of the two approaches and provide an extended partial deduction framework in which most of the tupling and deforestation transformations of the fold/unfold approach, as well the current partial deduction transformations, can be achieved. Moreover, most of the advantages of partial deduction, e.g. lower complexity and a more detailed understanding of control issues, are preserved. We build on well-defined concepts in partial deduction and present a conceptual embedding of folding into partial deduction, called conjunctive partial deduction. Two minimal extensions to partial deduction are proposed: using conjunctions of atoms instead of atoms as the principle specialisation entity and also renaming conjunctions of atoms instead of individual atoms. Correctness results for the extended framework (with respect to computed answer semantics and finite failure semantics) are given. Experiments with a prototype implementation are presented, showing that, somewhat to our surprise, conjunctive partial deduction not only handles the removal of unnecessary variables, but also leads to substantial improvements in specialisation for standard partial deduction examples. 1

Partial deduction strategies for logic programs often use an abstraction operator to guarantee the finiteness of the set of goals for which partial deductions are produced. Finding an abstraction operator which guarantees finiteness and does not lose relevant information is a difficult problem. In earlier work Gallagher and Bruynooghe proposed to base the abstraction operator on characteristic paths and trees, which capture the structure of the generated incomplete SLDNF-tree for a given goal. In this paper we exhibit the advantages of characteristic trees over purely syntactical measures: if characteristic trees can be preserved upon generalisation, then we obtain an almost perfect abstraction operator, providing just enough polyvariance to avoid any loss of local specialisation. Unfortunately, the abstraction operators proposed in earlier work do not always preserve the characteristic trees upon generalisation. We show that this can lead to important specialisation losses as well as to non-termination of the partial deduction algorithm. Furthermore, this problem cannot be adequately solved in the ordinary partial deduction setting. We therefore extend the expressivity and precision of the Lloyd and Shepherdson partial deduction framework by integrating constraints. We provide formal correctness results for the so obtained generic framework of constrained partial deduction. Within this new framework we are, among others, able to overcome the above mentioned problems by introducing an alternative abstraction operator, based on so called pruning constraints. We thus present a terminating partial deduction strategy which, for purely determinate unfolding rules, induces no loss of local specialisation due to the abstraction while ensuring correctness o...

. The aim of this work is to compute descriptions of successful computation paths in logic or functional program executions. Computation paths are represented as terms, built from special constructor symbols, each constructor symbol corresponding to a specific clause or equation in a program. Such terms, called trace-terms, are abstractions of computation trees, which capture information about the control flow of the program. A method of approximating trace-terms is described, based on well-established methods for computing regular approximations of terms. The special function symbols are first introduced into programs as extra arguments in predicates or functions. Then a regular approximation of the program is computed, describing the terms occurring in some set of program executions. The approximation of the extra arguments (the trace-terms) can then be examined to see what computation paths were followed during the computation. This information can then be used to control both off-l...

Integrity constraints are very useful in many contexts, such as, for example, deductive databases, abductive and inductive logic programming. However, fully testing the integrity constraints after each update or modification can be very expensive and methods have been developed which simplify the integrity constraints. In this paper, we pursue the goal of writing this simplification procedure as a meta-program in logic programming and then using partial deduction to obtain pre-compiled integrity checks for certain update patterns. We argue that the ground representation has to be used to write this metaprogram declaratively. We however also show that, contrary to what one might expect, current partial deduction techniques are then unable to specialise this meta-interpreter in an interesting way and no pre-compilation of integrity checks can be obtained. In fact, we show that partial deduction (alone) is not able to perform any (sophisticated) specialisation at the object-level for meta...

. In this paper, we reconsider the problem of specialising the vanilla meta interpreter through fully automatic and completely general partial deduction techniques. In particular, we study how the homeomorphic embedding relation guides specialisation of the interpreter. We focus on the so-called parsing problem, i.e. removing all parsing overhead from the program, and demonstrate that further refinements in the control of general partial deduction are necessary to properly deal with it. In particular, we modify local control on the basis of information imported from the global level. The resulting control strategy, while remaining fully general, leads to excellent specialisation of vanilla like meta programs. Parsing is always specialised, but -- appropriately, as we will show -- not always completely removed. As a concrete application, we subject an extended vanilla meta interpreter capable of dealing with compositions of programs to our techniques, showing we equal or surpass results obtained through a more ad hoc approach. 1