Program Repair by Stepwise Correctness Enhancement

Relative correctness is the property of a program to be more-correct than another with respect to a given specification. Whereas the traditional definition of (absolute) correctness divides candidate program into two classes (correct, and incorrect), relative correctness arranges candidate programs on the richer structure of a partial ordering. In other venues we discuss the impact of relative correctness on program derivation, and on program verification. In this paper, we discuss the impact of relative correctness on program testing; specifically, we argue that when we remove a fault from a program, we ought to test the new program for relative correctness over the old program, rather than for absolute correctness. We present analytical arguments to support our position, as well as an empirical argument in the form of a small program whose faults are removed in a stepwise manner as its relative correctness rises with each fault removal until we obtain a correct program.Comment: In Proceedings PrePost 2016, arXiv:1605.0809

Program Derivation by Correctness Enhacements

Relative correctness is the property of a program to be more-correct than another program with respect to a given specification. Among the many properties of relative correctness, that which we found most intriguing is the property that program P' refines program P if and only if P' is more-correct than P with respect to any specification. This inspires us to reconsider program derivation by successive refinements: each step of this process mandates that we transform a program P into a program P' that refines P, i.e. P' is more-correct than P with respect to any specification. This raises the question: why should we want to make P' more-correct than P with respect to any specification, when we only have to satisfy specification R? In this paper, we discuss a process of program derivation that replaces traditional sequence of refinement-based correctness-preserving transformations starting from specification R by a sequence of relative correctness-based correctness-enhancing transformations starting from abort.Comment: In Proceedings Refine'15, arXiv:1606.0134

What is a fault? and why does it matter?

Faults are an important concept in the study of system dependability, and most approaches to dependability can be characterized by the way in which they deal with faults (e.g., fault avoidance, fault removal, fault tolerance, fault forecasting). In their seminal work on modeling dependable computing, Laprie et al. define a fault as the adjudged or hypothesized cause of an error. In this paper, we propose a more formal definition of a fault in the context of software products and discuss some of its implications. 2017, Springer-Verlag London Ltd.Scopu

Relational mathematics for relative correctness

In earlier work, we had presented a definition of software fault as being any feature of a program that admits a substitution that would make the program more-correct. This definition requires, in turn, that we define the concept of relative correctness, i.e., what it means for a program to be more-correct than another with respect to a given specification. In this paper we broaden our earlier definition to encompass non-deterministic programs, or non-deterministic representations of programs; also, we study the mathematical properties of the new definition, most notably its relation to the refinement ordering, as well as its algebraic properties with respect to the refinement lattice.Fil: Desharnais, Jules. Laval University; CanadáFil: Diallo, Nafi. New Jersey Institute of Technology; Estados UnidosFil: Ghardallou, Wided. University of Tunis El Manar; TúnezFil: Frias, Marcelo Fabian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto Tecnológico de Buenos Aires; ArgentinaFil: Jaoua, Ali. Qatar University; QatarFil: Mili, Ali. New Jersey Institute of Technology; Estados Unido