The role of logical interpretations in program development

Abstract

Abstract. Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant transformations in the context of software design, reuse, and adaptation. This paper proposes a new approach to refinement in which signature morphisms are replaced by logical interpretations as a means to witness refinements. The approach is first presented in the context of equational logic, and later generalised to deductive systems of arbitrary dimension. This allows, for example, refining sentential into equational specifications and the latter into modal ones.

Simulation-based matching of cloud applications

“…A similar problem has been faced in the area of algebraic development techniques. For instance, Martins et al [21,22] show that the standard notion of signature morphism (which can be thought morally as our notion of syntactic plug-in matching) is often not flexible enough to deal with the problems of software reuse and refinement. In analogy with our work, the Martin et al propose a notion of refinement based on the more flexible logical interpretations.…”

Behavioral equivalence of hidden k-logics: An abstract algebraic approach

“…This notion of interpretation has been successfully used in the abstract development of software systems (by providing a broad concept of refinement that accommodates several crucial transformation approaches in software development (see [37,38,39])), as well as in a variety of other contexts (see for example [43,12]). …”