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

Termination, correctness and relative correctness

Over the last decade, research in verification and formal methods has been the subject of increased interest with the need of more secure and dependable software. At the heart of software dependability is the concept of software fault, defined in the literature as the adjudged or hypothesized cause of an error. This definition, which lacks precision, presents at least two challenges with regard to using formal methods: (1) Adjudging and hypothesizing are highly subjective human endeavors; (2) The concept of error is itself insufficiently defined, since it depends on a detailed characterization of correct system states at each stage of a computation (which is usually unavailable). In the process of defining what a software fault is, the concept of relative correctness, the property of a program to be more-correct than another with respect to a given specification, is discussed. Subsequently, a feature of a program is a fault (for a given specification) only because there exists an alternative to it that would make the program more-correct with respect to the specification. Furthermore, the implications and applications of relative correctness in various software engineering activities are explored. It is then illustrated that in many situations of software testing, fault removal and program repair, testing for relative correctness rather than absolute correctness leads to clearer conclusions and better outcomes. In particular, debugging without testing, a technique whereby, a fault can be removed from a program and the new program proven to be more-correct than the original, all without any testing (and its associated uncertainties/imperfections) is introduced. Given that there are orders of magnitude more incorrect programs than correct programs in use nowadays, this has the potential to expand the scope of proving methods significantly. Another technique, programming without refining, is also introduced. The most important advantage of program derivation by correctness enhancement is that it captures not only program construction from scratch, but also virtually all activities of software evolution. Given that nowadays most software is developed by evolving existing assets rather than producing new assets from scratch, the paradigm of software evolution by correctness enhancements stands to yield significant gains, if we can make it practical