A software analysis is a computer program that takes some representation of a software product as input and produces some useful information about that product as output. A software product line encompasses \emph{many} software product variants, and thus existing analyses can be applied to each of the product variations individually, but not to the entire product line as a whole. Enumerating all product variants and analyzing them one by one is usually intractable due to the combinatorial explosion of the number of product variants with respect to product line features. Several software analyses (e.g., type checkers, model checkers, data flow analyses) have been redesigned/re-implemented to support variability. This usually requires a lot of time and effort, and the variability-aware version of the analysis might have new errors/bugs that do not exist in the original one.

Given an analysis program written in a functional language based on PCF, in this paper we present two approaches to transforming (lifting) it into a semantically equivalent variability-aware analysis. A light-weight approach (referred to as \emph{shallow lifting}) wraps the analysis program into a variability-aware version, exploring all combinations of its input arguments. Deep lifting, on the other hand, is a program rewriting mechanism where the syntactic constructs of the input program are rewritten into their variability-aware counterparts. Compositionally this results in an efficient program semantically equivalent to the input program, modulo variability.

We present the correctness criteria for functional program lifting, together with correctness proof sketches of shallow lifting. We evaluate our approach on a set of program analyses applied to the BusyBox C-language product line.