This paper presents an overview and a survey of logic program synthesis. Logic program synthesis is interpreted here in a broad way; it is concerned with the following question: given a specification, how do we get a logic program satisfying the specification? Logic programming provides a uniquely nice and uniform framework for program synthesis since the specification, the synthesis process and the resulting program can all be expressed in logic. Three main approaches to logic program synthesis by formal methods are described: constructive synthesis, deductive synthesis and inductive synthesis. Related issues such as correctness and verification as well as synthesis by informal methods are briefly presented. Our presentation is made coherent by employing a unified framework of terminology and notation, and by using the same running example for all the approaches covered. This paper thus intends to provide an assessment of existing work and a framework for future research in logic program synthesis.

Program transformation is a methodology for deriving correct and efficient programs from specifications. In this chapter, we will look at the so called 'rules + strategies' approach, and we will report on the main techniques which have been introduced in the literature for that approach, in the case of logic programs. We will also present some examples of program transformation, and we hope that through those examples the reader may acquire some familiarity with the techniques we will describe.

"Classical" partial deduction, within the framework by Lloyd and Shepherdson, computes partial deduction for separate atoms independently. As a consequence, a number of program optimisations, known from unfold/fold transformations and supercompilation, cannot be achieved. In this paper, we show that this restriction can be lifted through (polygenetic) specialisation of entire atom conjunctions. We present a generic algorithm for such partial deduction and discuss its correctness in an extended formal framework. We concentrate on novel control challenges specific to this "conjunctive" partial deduction. We refine the generic algorithm into a fully automatic concrete one that registers partially deduced conjunctions in a global tree, and prove its termination and correctness. We discuss some further control refinements and illustrate the operation of the concrete algorithm and/or some of its possible variants on interesting transformation examples.

We present a method for proving properties of definite logic programs. This method is called unfold/fold proof method because it is based on the unfold/fold transformation rules...

Given a program P, an unfold/fold program transformation system derives a sequence of programs P = P0, P1,:::, Pn, such that Pi+1 is derived from Pi by application of either an unfolding or a folding step. Existing unfold/fold transformation systems for definite logic programs differ from one another mainly in the kind of folding transformations they permit at each step. Some allow folding using a single (possibly recursive) clause while others permit folding using multiple non-recursive clauses. However, none allow folding using multiple recursive clauses that are drawn from some previous program in the transformation sequence. In this paper we develop a parameterized framework for unfold/fold transformations by suitably abstracting and extending the proofs of existing transformation systems. Various existing unfold/fold transformation systems can be obtained by instantiating the parameters of the framework. This framework enables us to not only understand the relative strengths and limitations of these systems but also construct new transformation systems. Specifically we present a more general transformation system that permits folding using multiple recursive clauses that can be drawn from any previous program in the transformation sequence. This new transformation system is also obtained by instantiating our parameterized framework.

. An unfold/fold program transformation system which extends the unfold/fold transformations of H. Tamaki and T. Sato is presented in this paper. The system consists of unfolding, simultaneous folding, and generalization + equality introduction rules. The simultaneous folding rule permits the folding of a set of folded clauses into a single clause, using a set of folding clauses, while the generalization + equality introduction rule facilitates the application of the simultaneous folding rule by performing appropriate abstractions. A proof of the correctness of the proposed transformations in the sense of the least Herbrand model semantics of the program is also presented. 1 Introduction Unfold/fold transformations were first proposed by R. Burstall and J. Darlington [BD77] in the context of a functional language. In the context of logic programming, H. Tamaki and T. Sato [TS84, TS86] formulated unfold/fold transformations for definite clause programs so as to preserve the equivalence...

This report is a revised version of my thesis of the same title, which was accepted for the Ph.D. degree in Computer Science at University of Aarhus, Denmark, in June 1993

. We address the problem of specializing logic programs w.r.t. the contexts where they are used. We assume that these contexts are specified by means of computable properties of the input data. We describe a general method by which, given a program P , we can derive a specialized program P 1 such that P and P 1 are equivalent w.r.t. every input data satisfying a given property. Our method extends the techniques for partial evaluation of logic programs based on Lloyd and Shepherdson 's approach, where a context can only be specified by means of a finite set of bindings for the variables of the input goal. In contrast to most program specialization techniques based on partial evaluation, our method may achieve superlinear speedups, and it does so by using a novel generalization technique. 1 Introduction Program specialization is a technique which can be used for deriving from a given program, a new and hopefully more efficient program, by exploiting the knowledge of the context in w...

Unfold/fold transformation systems for logic programs have been extensively investigated. Existing unfold/fold transformation systems for normal logic programs allow only Tamaki-Sato style folding using clauses from a previous program in the transformation sequence: i.e., they fold using a single, non-recursive clause. In this paper we present a transformation system that permits folding in the presence of recursion, disjunction, as well as negation. We show that the transformations are correct with respect to various semantics of negation including the well-founded model and stable model semantics.

We consider the problem of specializing constraint logic programs w.r.t. constrained queries. We follow a transformational approach based on rules and strategies. The use of the rules ensures that the specialized program is equivalent to the initial program w.r.t. a given constrained query. The strategies guide the application of the rules so to derive an efficient specialized program. In this paper we address various issues concerning the development of an automated transformation strategy. In particular, we consider the problems of when and how we should unfold, replace constraints, introduce generalized clauses, and apply the contextual constraint replacement rule. We propose a solution to these problems by adapting to our framework various techniques developed in the field of constraint programming, partial evaluation, and abstract interpretation. In particular, we use: (i) suitable solvers for simplifying constraints, (ii) well-quasi-orders for ensuring the termination...