Reusable Metatheory for Program Analysis

The design and implementation of static analyzers have becoming increasingly systematic. In fact, for large classes of analyzers, design and implementation have remained seemingly (and now stubbornly) on the verge of full mechanization for several years. A stumbling block in full mechanization has been the ad hoc nature of soundness proofs accompanying each analyzer. While design and implementation is largely systematic, soundness proofs can change significantly with seemingly minor changes to the semantics or analyzers. An achievement of this work is to systematize, parameterize and modularize the proofs of soundness, so as to make them composable across analytic properties. We solve the problem of systematically constructing static analyzers by introducing Galois transformers: monad transformers that transports Galois connection properties. In concert with a monadic interpreter, we define a library of monad transformers that implement building blocks for classic analysis parameters like context-, path-, and heap(in-)sensitivity. Moreover, these can be composed together independent of the language being analyzed. Significantly, a Galois transformer can be proved sound once and for all, making it a reusable analysis component. As new analysis features and abstractions are developed and mixed in, soundness proofs need not be reconstructed, as the composition of a monad transformer stack is sound by virtue of its constituents. Galois transformers provide a viable foundation for reusable and composable metatheory for program analysis. Finally, these Galois transformers shift the level of abstraction in analysis design and implementation to a level where non-specialists have the ability to synthesize sound analyzers over a number of parameters.