Higher-Order Delta Modeling for Software Product Line Evolution

In software product lines (SPL), i.e., a family of similar software systems sharing common and variable artifacts, modeling evolution and reasoning about it is challenging, as not only a single system, but rather a set of system variants as well as their interdependencies change. An integrated modeling formalism for variability and evolution is required to allow the capturing of evolution operations that are applied to SPL artifacts, and to facilitate the impact analysis of evolution on the artifact level. Delta modeling is a flexible transformational variability modeling approach, where the variability and commonality between variants are explicitly documented and analyzable by means of transformations modeled as deltas. In this paper, we lift the notion of delta modeling to capture both, variability and evolution, by deltas. We evolve a delta model specifying a set of variants by applying higher-order deltas. A higher-order delta encapsulates evolution operations, i.e., additions, removals, or modifications of deltas, and transforms a delta model in its new version. In this way, we capture the complete evolution history of delta-oriented SPLs by higher-order delta models. By analyzing each higher-order delta application, we are further able to reason about the impact and, thus, the changes to the specified set of variants. We prototypically implement our formalism and show its applicability using a system from the automation engineering domain.