The role of logical interpretations on program development

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.The authors express their gratitude to the anonymous referees who raised a number of pertinent questions entailing a more precise characterisation of the paper's contributions and a clarification of their scope. This work was funded by HRDF - European Regional Development Fund through the COMPETE Programme (operational programme for competitiveness) and by National Funds through the FCT (Portuguese Foundation for Science and Technology) within project FCOMP-01-0124-FEDER-028923 (Nasoni) and the project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690 (CIDMA-UA). The first author also acknowledges the financial assistance by the projects GetFun, reference FP7-PEOPLE-2012-IRSES, and NOCIONES IDE COMPLETUD, reference FFI2009-09345 (MICINN - Spain). A. Madeira was supported by the FCT within the project NORTE-01-0124-FEDER-000060