We present an overview of the program transformation methodology, focusing our attention on the so-called `rules + strategies' approach in the case of functional and logic programs. The paper is intended to offer an introduction to the subject. The various techniques we present are illustrated via simple examples. A preliminary version of this report has been published in: Moller, B., Partsch, H., and Schuman, S. (eds.): Formal Program Development. Lecture Notes in Computer Science 755, Springer Verlag (1993) 263--304. Also published in: ACM Computing Surveys, Vol 28, No. 2, June 1996. 3 1 Introduction The program transformation approach to the development of programs has first been advocated by [Burstall-Darlington 77], although the basic ideas were already presented in previous papers by the same authors [Darlington 72, Burstall-Darlington 75]. In that approach the task of writing a correct and efficient program is realized in two phases: the first phase consists in writing an in...

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A theorem proving system has been programmed for automating mildly complex proofs by structural induction. One purpose was to prove properties of simple functional programs without loops or assignments. One can see the formal system as a generalization of number theory: the formal language is typed and the induction rule is valid for all types. Proofs are generated by working backward from the goal. The induction strategy splits into two parts: (1) the selection of induction variables, which is claimed to be linked to the useful generalization of terms to variables, and (2) the generation of induction subgoals, in particular, the selection and specialization of hypotheses. Other strategies include a fast simplification algorithm. The prover can cope with situations as complex as the definition and correctness proof of a simple compiling algorithm for expressions. Descriptive Terms Program proving, theorem proving, data type, structural induction, generalization, simplification.

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.

. The so-called "Boyer-Moore Theorem Prover" (otherwise known as "Nqthm") has been used to perform a variety of verification tasks for two decades. We give an overview of both this system and an interactive enhancement of it, "Pc-Nqthm," from a number of perspectives. First we introduce the logic in which theorems are proved. Then we briefly describe the two mechanized theorem proving systems. Next, we present a simple but illustrative example in some detail in order to give an impression of how these systems may be used successfully. Finally, we give extremely short descriptions of a large number of applications of these systems, in order to give an idea of the breadth of their uses. This paper is intended as an informal introduction to systems that have been described in detail and similarly summarized in many other books and papers; no new results are reported here. Our intention here is merely to present Nqthm to a new audience. This research was supported in part by ONR Contract N...

We briefly review a mechanical theorem-prover for a logic of recursive functions over finitely generated objects including the integers, ordered pairs, and symbols. The prover, known both as NQTHM and as the Boyer-Moore prover, contains a mechanized principle of induction and implementations of linear resolution, rewriting, and arithmetic decision procedures. We describe some applications of the prover, including a proof of the correct implementation of a higher level language on a microprocessor defined at the gate level. We also describe the ongoing project of recoding the entire prover as an applicative function within its own logic.

Introduction: What is partial evaluation? Partial evaluation is a technique to partially execute a program, when only some of its input data are available. Consider a program p requiring two inputs, x 1 and x 2 . When specific values d 1 and d 2 are given for the two inputs, we can run the program, producing a result. When only one input value d 1 is given, we cannot run p, but can partially evaluate it, producing a version p d1 of p specialized for the case where x 1 = d 1 . Partial evaluation is an instance of program specialization, and the specialized version p d1 of p is called a residual program. For an example, consider the following C function p

Data Types and Software Validation ," Communications of the ACM, Vol. 21, No. 12, 1978, pp. 1048-1064.

Distributed systems are multi-processor information processing systems which do not rely on the central shared memory for communication. The importance of distributed systems has been growing with the advent of "computer

We introduce a framework for managing as a whole the space of a narrowing computation. The aim of our framework is to find a finite representation of an infinite narrowing space. This, in turn, allows us to replace an infinite enumeration of computed answers with an equivalent finite representation. We provide a semidecidable condition for this result. Our framework is intended to be used by implementations of functional logic programming languages. Our approach borrows from the memoization technique used in the implementation of functional languages. Since narrowing adds non-determinism and unifiers to functional evaluation, we develop a new approach based on graphs to memoize the outcome of a goal.