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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.

Towards Unifying Partial Evaluation, Deforestation, Supercompilation, and GPC

We study four transformation methodologies which are automatic instances of Burstall and Darlingtons fold/unfold framework: partial evaluation, deforestation, supercompilation, and generalized partial computation (GPC). One can classify these and other fold/unfold based transformers by how much information they maintain during transformation.

Partial Deduction and Driving are Equivalent

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.

Perpetual Reductions in λ-Calculus

This paper surveys a part of the theory ofs-reduction in?-calculus which might aptly be calledperpetual reductions. The theory is concerned withperpetual reduction strategies, i.e., reduction strategies that compute infinite reduction paths from?-terms (when possible), and withperpetual redexes, i.e., redexes whose contraction in?-terms preserves the possibility (when present) of infinite reduction paths. The survey not only recasts classical theorems in a unified setting, but also offers new results, proofs, and techniques, as well as a number of applications to problems in?-calculus and type theory.

Redundant Argument Filtering of Logic Programs

This paper is concerned with the problem of removing redundant arguments from logic programs. Such arguments can be removed without affecting correctness, in a certain sense. Most program specialisation techniques, even though they filter arguments and remove clauses, 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 effectively remove all redundant arguments. We then give a safe, effective approximation of the notion of a redundant argument and describe several simple and efficient algorithms based on the approximative notion. We conduct extensive experiments with our algorithms on mechanically generated programs illustrating the practical benefits of our approach.

A Roadmap to Metacomputation by Supercompilation

This paper gives a gentle introduction to Turchins super-compilation and its applications in metacomputation with an emphasis on recent developments. First, a complete supercompiler, including positive driving and generalization, is defined for a functional language and illustrated with examples. Then a taxonomy of related transformers is given and compared to the supercompiler. Finally, we put supercompilation into the larger perspective of metacomputation and consider three metacomputation tasks: specialization, composition, and inversion.

AnnoDomini: from type theory to Year 2000 conversion tool

AnnoDomini is a source-to-source conversion tool for making COBOL programs Year 2000 compliant. It is technically and conceptually built upon type-theoretic techniques and methods: type-based specification, program analysis by type inference and type-directed transformation. These are combined into an integrated software reengineering tool and method for finding and fixing Year 2000 problems. AnnoDominis primary goals have been flexibility (support for multiple year representations), completeness (identifying all potential Year 2000 problems), correctness (correct fixes for Year 2000 problems) and a high degree of safe automation in all phases (declarative specification of conversions, no second-guessing or dangerous heuristics).In this paper we present the type-theoretic foundations of AnnoDomini: type system, type inference, unification theory, semantic soundness, and correctness of conversion. We also describe how these foundations have been applied and extended to a common COBOL mainframe dialect, and how AnnoDomini is packaged with graphical user interface and syntax-sensitive editor into a commercially available software tool.

Domain-free pure type systems

Pure type systems make use of domain-full λ-abstractions λx:D.M. We present a variant of pure type systems, which we call domain-free pure type systems, with domain-free λ-abstractions λx.M. Domain-free pure type systems have a number of advantages over both pure type systems and so-called type assignment systems (they also have some disadvantages), and have been used in theoretical developments as well as in implementations of proof-assistants. We study the basic properties of domain-free pure type systems, establish their formal relationship with pure type systems and type assignment systems, and give a number of applications of these correspondences.

Introduction to Supercompilation

This paper gives an introduction to Turchins supercompiler, a program transformer for functional programs which performs optimizations beyond partial evaluation and deforestation. More precisely, the paper presents positive supercompilation.

CPS Translations and Applications: The Cube and Beyond

Continuation passing style (CPS) translations of typed λ-calculi have numerous applications. However, the range of these applications has been confined by the fact that CPS translations are known for non-dependent type systems only, thus excluding well-known systems like the calculus of constructions (CC) and the logical frameworks (LF). This paper presents techniques for CPS translating systems with dependent types, with an emphasis on pure type-theoretical applications.In the first part of the paper we review several lines of work in which the need for CPS translations of dependent type systems has arisen, and discuss the difficulties involved with CPS translating such systems. One way of overcoming these difficulties is to work with so-called domain-free type systems. Thus, instead of Barendregts λ-cube we shall consider the domain-free λ-cube, and instead of traditional pure type systems, we shall consider domain-free pure type systems.We therefore begin the second part by reviewing the domain-free λ-cube, which includes domain-free versions of CC and LF, and then present CPS translations for all the systems of the domain-free λ-cube. We also introduce Direct Style (DS) (i.e., inverse CPS) translations for all the systems of the domain-free λ-cube; such DS translations, which have been used in a number of applications, were previously formulated for untyped and simply-typed languages only.In the third part we review domain-free pure type systems and generalize the CPS translations of the domain-free λ-cube to a large class of domain-free pure type systems which includes most of the systems that appear in the literature, including those of the domain-free λ-cube. Many translations that appear in the literature arise as special cases of ours.In the fourth part of the paper we present two approaches to CPS translations of traditional pure type systems. The first, indirect, technique lifts the CPS translation of domain-free pure type systems to the analogous class of traditional pure type systems by using results that relate derivations in domain-free and traditional pure type systems. The second, direct, approach translates derivations, requiring a certain order on derivations to be well-founded. Both techniques yield translations for most of the systems that appear in the literature, including those of Barendregts λ-cube.