A Formal Framework of Software Product Line Analyses

A number of product-line analysis approaches lift analyses such as type checking, model checking, and theorem proving from the level of single programs to the level of product lines. These approaches share concepts and mechanisms that suggest an unexplored potential for reuse of key analysis steps and properties, implementation, and verification efforts. Despite the availability of taxonomies synthesizing such approaches, there still remains the underlying problem of not being able to describe product-line analyses and their properties precisely and uniformly. We propose a formal framework that models product-line analyses in a compositional manner, providing an overall understanding of the space of family-based, feature-based, and product-based analysis strategies. It defines precisely how the different types of product-line analyses compose and inter-relate. To ensure soundness, we formalize the framework, providing mechanized specification and proofs of key concepts and properties of the individual analyses. The formalization provides unambiguous definitions of domain terminology and assumptions as well as solid evidence of key properties based on rigorous formal proofs. To qualitatively assess the generality of the framework, we discuss to what extent it describes five representative product-line analyses targeting the following properties: safety, performance, dataflow facts, security, and functional program properties.