A product line of theories for reasoning about safe evolution of product lines

A product line refinement theory formalizes safe evolution in terms of a refinement notion, which does not rely on particular languages for the elements that constitute a product line. Based on this theory, we can derive refinement templates to support safe evolution scenarios. To do so, we need to provide formalizations for particular languages, to specify and prove the templates. Without a systematic approach, this leads to many similar templates and thus repetitive verification tasks. We investigate and explore similarities between these concrete languages, which ultimately results in a product line of theories, where different languages correspond to features, and products correspond to theory instantiations. This also leads to specifying refinement templates at a higher abstraction level, which, in the long run, reduces the specification and proof effort, and also provides the benefits of reusing such templates for additional languages plugged into the theory. We use the Prototype Verification System to encode and prove soundness of the theories and their instantiations. Moreover, we also use the refinement theory to reason about safe evolution of the proposed product line of theories.