Control-Flow Analysis of Function Calls and Returns by Abstract Interpretation

摘要

We derive a control-flow analysis that approximates the interprocedural control-flow of both function calls and returns in the presence of first-class functions and tail-call optimization. In addition to an abstract environment, our analysis computes for each expression an abstract control stack, effectively approximating where function calls return across optimized tail calls. The analysis is systematically calculated by abstract interpretation of the stack-based CaEK abstract machine of Flanagan et al. using a series of Galois connections. Abstract interpretation provides a unifying setting in which we 1) prove the analysis equivalent to the composition of a continuation-passing style (CPS) transformation followed by an abstract interpretation of a stack-less CPS machine, and 2) extract an equivalent constraint-based formulation, thereby providing a rational reconstruction of a constraint-based control-flow analysis from abstract interpretation principles.