Bern Martens

CONJUNCTIVE PARTIAL DEDUCTION: FOUNDATIONS, CONTROL, ALGORITHMS, AND EXPERIMENTS

Abstract 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 first 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 finite failure semantics. Maintaining the well-known distinction between local and global control, we describe a basic algorithm for conjunctive partial deduction, and refine it into a concrete algorithm for which we prove termination. The problem of finding 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. Differences between the abstract semantics and Prologs 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 deduction indeed pays off, surpassing conventional partial deduction on a range of small to medium-size programs, while remaining manageable in an automatic and terminating system.

Controlling generalization and polyvariance in partial deduction of normal logic programs

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 andelegant 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 areillustrated 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.

A general criterion for avoiding infinite unfolding during partial deduction

Well-founded orderings are a commonly used tool for proving the termination of programs. We introduce related concepts specialised to SLD-trees. Based on these concepts, we formulate formal and practical criteria for controlling the unfolding during the construction of SLD-trees that form the basis of a partial deduction. We provide algorithms that allow to use these criteria in a constructive way. In contrast to the many ad hoc techniques proposed in the literature, our technique provides both a formal and practically applicable framework.

Global Control for Partial Deduction through Characteristic Atoms and Global Trees

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.

Automatic finite unfolding using well-founded measures

We elaborate on earlier work proposing general criteria to control unfolding during partial deduction of logic programs. We study several techniques relying on more general and more powerful well-founded orderings. In particular, we extend our framework to incorporate lexicographical priorities between argument positions in a goal. We show that this handles some remaining deficiencies in previous methods. We emphasize the development of fully automatic algorithms for finite unfolding, avoiding the use of ad hoc techniques. Through an extensive formalization, we convey an understanding of the common principles underlying the various algorithms. Finally, we exhibit how our structure-based unfolding framework can be adapted to cope with datalog-like constant manipulating predicates in a satisfactory way.

Conjunctive Partial Deduction in Practice

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”.

Termination Analysis for Tabled Logic Programming

We provide a theoretical basis for studying the termination of tabled logic programs executed under SLG-resolution using a left-to-right computation rule. To this end, we study the classes of quasi-terminating and LG-terminating programs (for a set of atomic goals S). These are tabled logic programs where execution of each call from S leads to only a finite number of different (i.e., non-variant) calls, and a finite number of different calls and computed answer substitutions for them, respectively. We then relate these two classes through a program transformation, and present a characterisation of quasi-termination by means of the notion of quasi-acceptability of tabled programs. The latter provides us with a practical method of proving termination and the method is illustrated on non-trivial examples of tabled logic programs.

Why untyped nonground metaprogramming is not (much of) a problem

Abstract We study a semantics for untyped, vanilla metaprograms, using the nonground representation for object level variables. We introduce the notion of language independence, which generalizes range restriction. We show that the vanilla metaprogram associated with a stratified normal object program is weakly stratified. For language independent, stratified normal object programs, we prove that there is a natural one-to-one correspondence between atoms p ( t 1 ,…, t r ) in the perfect Herbrand model of the object program and solve ( p ( t 1 ,…, t r )) atoms in the weakly perfect Herb and model of the associated vanilla metaprogram. Thus, for this class of programs, the weakly perfect Herbrand model provides a sensible semantics for the metaprogram. We show that this result generalizes to nonlanguage independent programs in the context of an extended Herbrand semantics, designed to closely mirror the operational behavior of logic programs. Moreover, we also consider a number of interesting extensions and/or variants of the basic vanilla metainterpreter. For instance, we demonstrate how our approach provides a sensible semantics for a limited form of amalgamation.

To Parse or Not To Parse

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.

A Sensible Least Herbrand Semantics for Untyped Vanilla Meta-Programming and its Extension to a Limited Form of Amalgamation

We study a semantics for untyped, vanilla meta-programs, using the non-ground representation for object level variables. We introduce the notion of language independence for definite programs, which generalises range restriction. For language independent, definite object programs, we prove that there is a natural one-to-one correspondence between atoms p(t1,..., tr) in the least Herbrand model of the object program and atoms of the form solve (p(t1,t r ) in the least Herbrand model of the associated vanilla met a-program. Thus, for this class of programs, the least Herbrand model provides a sensible semantics for the meta-program. The main attraction of our approach is that the results can be further extended — in a straightforward way — to provide a sensible semantics for a limited form of amalgamation.