Much of the work on developing program transformation systems has concentrated on systems to assist in program development. However, the four separate surveys carried out between 1977 and 1990 [18,20,22,24], summarised in [17], show that between 40% and 60% of all commercial software effort is devoted to software maintenance rather than the development of new systems. In this paper we describe a joint project between the University of Durham and CSM Ltd to develop a method and tool for reverse engineering and software maintenance based on program transformation theory. We present an example which illustrates how such a tool can extract a high-level abstract specification from the low-level source code of a program by a process of formal program transformation based on a theory of program equivalence [27]. All the code-level reverse engineering of the example progr...

In this paper we consider a particular class of algorithms which present certain difficulties to formal verification. These are algorithms which use a single data structure for two or more purposes, which combine program control information with other data structures or which are developed as a combination of a basic idea with an implementation technique. Our approach is based on applying proven semantics-preserving transformation rules in a wide spectrum language. Starting with a set theoretical specification of "reachability" we are able to derive iterative and recursive graph marking algorithms using the "pointer switching" idea of Schorr and Waite. There have been several proofs of correctness of the Schorr-Waite algorithm, and a small number of transformational developments of the algorithm. The great advantage of our approach is that we can derive the algorithm from its specification using only general-purpose transformational rules: without the need for complicated induction arg...

There is a vast collection of operational software systems which are vitally important to their users, yet are becoming increasingly difficult to maintain, enhance and keep up to date with rapidly changing requirements. For many of these so called legacy systems the option of throwing the system away an re-writing it from scratch is not economically viable. Methods are therefore urgently required which enable these systems to evolve in a controlled manner. The approach described in this paper uses formal proven program transformations, which preserve or refine the semantics of a program while changing its form. These transformations are applied to restructure ans simplify the legacy systems and to extract higher-level representations. By using an appropriate sequence of transformations, the extracted representation is guaranteed to be equivalent to the code. The method is based on a formal wide spectrum language, called WSL, with accompanying formal method. Over the last ten years we h...

Program transformation systems provide one means of formally deriving a program from its specification. The main advantage of this development method is that the executable program is correct by construction. In this paper we describe a tool called ReForm which is designed to address the inverse problem to support the extraction of a specification from existing program code, using transformations. This is an important activity during software maintenance. One of the problems of transformation systems is the scarcity of practical tools which can address industrial scale problems, rather than contrived laboratory itoyj problems. The main contribution of this paper is an analysis of the important software engineering factors that contribute to a successful transformation based tool. Results from using the tool are also presented.

In this paper we briey introduce a Wide Spectrum Language and its transformation theory and describe a recent success of the theory: a general recursion removal theorem. This theorem includes as special cases the two techniques discussed by Knuth [12] and Bird [7]. We describe some applications of the theorem to cascade recursion, binary cascade recursion, Gray codes, the Towers of Hanoi problem, and an inverse engineering problem. 1 Introduction In this paper we briey introduce some of the ideas behind the transformation theory we have developed over the last eight years at Oxford and Durham Universities and describe a recent result: a general recursion removal theorem. We use a Wide Spectrum Language (called WSL), developed in [19,20,21] which includes lowlevel programming constructs and high-level abstract specications within a single language. Working within a single language means that the proof that a program correctly implements a specication, or that a specication correct...

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In this paper we briefly introduce a Wide Spectrum Language and its transformation theory and describe a recent success of the theory: a general recursion removal theorem. Recursion removal often forms an important step in the systematic development of an algorithm from a formal specification. We use semantic-preserving transformations to carry out such developments and the theorem proves the correctness of many different classes of recursion removal. This theorem includes as special cases the two techniques discussed by Knuth [13] and Bird [7]. We describe some applications of the theorem to cascade recursion, binary cascade recursion, Gray codes, and an inverse engineering problem.

This paper uses Ackerman's function as a testbed to illustrate the operation of various program transformations which take recursive procedures to equivalent iterative forms. The transformations are taken from the author's DPhil thesis [19]. In this paper we illustrate that they can be successfully applied to even the most convoluted recursion. For many programs a recursive function is the most natural and clear specification while an iterative (or tail-recursive) form is the most efficient implementation. This paper illustrates how an efficient iterative program can be developed and verified by starting with a simple recursive program and using proven transformations to remove the recursion. The resulting iterative program will be correct by construction, so the problem of a direct verification of the iterative algorithm is avoided. This process can also throw light on the nature of the recursive specification. Several interesting properties of Ackermann's function and the iterative algorithms are derived in the course of this development.

The Maintainer's Assistant is a code analysis tool aimed at helping the maintenance programmer to understand and modify a given program. Program transformation techniques are employed by the Maintainer's Assistant both to derive a speci cation from a section of code and to transform a section of code into a logically equivalent form. The general structure of the tool is described and two examples of the application of program transformations are given. 1