Program Derivation by Correctness Enhacements

TL;DR

This paper explores a new approach to program derivation using relative correctness, focusing on correctness enhancements rather than traditional refinement, starting from an abort to achieve a more-correct program with respect to a given specification.

Contribution

It introduces a novel process of program derivation based on correctness enhancements via relative correctness, replacing traditional refinement-based methods.

Findings

Proposes a correctness-enhancement based derivation process

Shows that relative correctness relates to program refinement

Suggests starting from abort for derivation process

Abstract

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.