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A software analysis is a computer program that takes some representation of asoftware product as input and produces some useful information about thatproduct as output. A software product line encompasses \emph{many} softwareproduct variants, and thus existing analyses can be applied to each of theproduct variations individually, but not to the entire product line as a whole.Enumerating all product variants and analyzing them one by one is usuallyintractable due to the combinatorial explosion of the number of productvariants with respect to product line features. Several software analyses(e.g., type checkers, model checkers, data flow analyses) have beenredesigned/re-implemented to support variability. This usually requires a lotof time and effort, and the variability-aware version of the analysis mighthave new errors/bugs that do not exist in the original one.  Given an analysis program written in a functional language based on PCF, inthis paper we present two approaches to transforming (lifting) it into asemantically equivalent variability-aware analysis. A light-weight approach(referred to as \emph{shallow lifting}) wraps the analysis program into avariability-aware version, exploring all combinations of its input arguments.Deep lifting, on the other hand, is a program rewriting mechanism where thesyntactic constructs of the input program are rewritten into theirvariability-aware counterparts. Compositionally this results in an efficientprogram semantically equivalent to the input program, modulo variability. Wepresent the correctness criteria for functional program lifting, together withcorrectness proof sketches of our program transformations. We evaluate ourapproach on a set of program analyses applied to the BusyBox C-language productline.

Automatic and Efficient Variability-Aware Lifting of Functional Programs