Derivation of data intensive algorithms by formal transformation: the Schnorr-Waite graph marking algorithm

Ward, Martin

doi:10.1109/32.541437

Cited by 26 publications

(23 citation statements)

References 37 publications

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“…Examples of the use of the transformation based approach for forward engineering are given in [34,40], and for reverse engineering in [35,39,45]. A survey of work on transformation systems may be found in [42] and also in [27].…”

Section: Theoretical Foundationmentioning

confidence: 99%

Formal Methods to Aid the Evolution of Software

Ward

Bennett

1995

Int. J. Soft. Eng. Knowl. Eng.

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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 have developed a large catalogue of proven transformations, together with mechanically verifiable applicability conditions. These have been applied to many software development, reverse engineering and maintenance problems. In this paper, we focus on the results of using this approach in the reverse engineering of medium scale, industrial software, written mostly in languages such as assembler and JOVIAL. Results from both benchmark algorithms and heavily modified, geriatric software are summarised. We conclude that formal methods have an important practical role in software evolution.

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Section: Theoretical Foundationmentioning

confidence: 99%

Formal Methods to Aid the Evolution of Software

Ward

Bennett

1995

Int. J. Soft. Eng. Knowl. Eng.

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“…(5) Tackle some challenging program development and reverse engineering tasks to demonstrate the validity of this approach [31,33,37,39,42,46]; (6) Extend WSL with constructs for implementing program transformations (the result is called METAWSL);…”

Section: Slicing In Fermatmentioning

confidence: 99%

“…; (23) (24) funct @Slice(I, X) ≡ (25) var R := , new := , newX := : (26) if @ST(I) = Statements (27) then for S ∈ REVERSE(@Cs(I)) do (28) R := @Slice(S, X); (29) new := R[1] + + new; (30) X := R[2] od; (31) R := @Make(Statements, , new), X (32) elsif @ST(I) = Abort (33) then R := I, (34) elsif @GT(I) = Statement ∧ X ∩ @Assigned(I)) = (35) then R := @Skip, X (36) elsif @ST(I) = Assignment (37) then R := I, (X \ @Assigned(I)) ∪ @Used(I) (38) elsif @ST(I) = Cond ∨ @ST(I) = D If (39) then for guard ∈ @Cs(I) do (40) R := @Slice(guardˆ2, X); (41) new := @Make(Guarded, , guardˆ1,…”

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confidence: 99%

Slicing as a program transformation

Ward

Zedan

2007

ACM Trans. Program. Lang. Syst.

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The aim of this paper is to provide a unified mathematical framework for program slicing which places all slicing work, for sequential programs, on a sound theoretical foundation. The main advantage to a mathematical approach is that it is not tied to a particular representation. In fact the mathematics provides a sound basis for any particular representation. We use the WSL (Wide Spectrum Language) program transformation theory as our framework. Within this framework we define a new semantic relation, semi-refinement which lies between semantic equivalence and semantic refinement. Combining this semantic relation, a syntactic relation (called reduction) and WSL's remove statement, we can give mathematical definitions for backwards slicing, conditioned slicing, static and dynamic slicing and semantic slicing as program transformations in the WSL transformation theory. A novel technique of "encoding" operational semantics within a denotational semantics allows the framework to handle "operational slicing". The theory also enables the concept of slicing to be applied to nondeterministic programs. These transformations are implemented in the industry-strength FermaT transformation system.

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“…In [8][9][10] program transformations are used to derive a variety of efficient algorithms from abstract specifications. In [11] the same transformations are used in the reverse direction: starting with a small but tangled and obscure program we were able to use transformations to restructure the program and derive a concise abstract representation of its specification.…”

Section: Introductionmentioning

confidence: 99%

Recursion Removal/Introduction by Formal Transformation: An Aid to Program Development and Program Comprehension

Ward¹,

Bennett²

1999

The Computer Journal

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The transformation of a recursive program to an iterative equivalent is a fundamental operation in Computer Science. In the reverse direction, the task of reverse engineering (analysing a given program in order to determine its specification) can be greatly ameliorated if the program can be re-expressed in a suitable recursive form. But the existing recursion removal transformations, such as the techniques discussed by Knuth [1] and Bird [2], can only be applied in the reverse direction if the source program happens to match the structure produced by a particular recursion removal operation. In this paper we describe a much more powerful recursion removal and introduction operation which describes its source and target in the form of an action system (a collection of labels and calls to labels). A simple, mechanical, restructuring operation can be applied to a great many iterative programs which will put them in a suitable form for recursion introduction. Our transformation generates strictly more iterative versions than the standard methods, including those of Knuth and Bird [1,2]. With the aid of this theorem we prove a (somewhat counterintuitive) result for programs that contain sequences of two or more recursive calls: under a reasonable commutativity condition, "depth-first" execution is more general than "breadth-first" execution. In "depth-first" execution, the execution of each recursive call is completed, including all sub-calls, before execution of the next call is started. In "breadth-first" execution, each recursive call in the sequence is partially executed but any sub-calls are temporarily postponed. This result means that any breadth-first program can be reimplemented as a corresponding depth-first program, but the converse does not hold. We also treat the case of "random-first" execution, where the execution order is implementation dependent. For the more restricted domain of tree searching we show that breadth first search is the most general form. We also give two examples of recursion introduction as an aid to formal reverse engineering.

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Derivation of data intensive algorithms by formal transformation: the Schnorr-Waite graph marking algorithm

Cited by 26 publications

References 37 publications

Formal Methods to Aid the Evolution of Software

Formal Methods to Aid the Evolution of Software

Slicing as a program transformation

Recursion Removal/Introduction by Formal Transformation: An Aid to Program Development and Program Comprehension

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