Single and Loving It: Must-Alias Analysis for Higher-Order Languages

Abstract

In standard control-flow analyses for higher-order languages, a single abstract binding for a variable represents a set of exact bindings, and a single abstract reference cell represents a set of exact reference cells. While such analyses provide useful may-alias information, they are unable to answer mustalias questions about variables and cells, as these questions ask about equality of specific bindings and references.In this paper, we present a novel program analysis for higher-order languages that answers must-alias questions. At every program point, the analysis associates with each variable and abstract cell a cardinality, which is either single or multiple. If variable x is single at program point p, then all bindings for x in the heap reachable from the environment at p hold the same value. If abstract cell r is single at p, then at most one exact cell corresponding to r is reachable from the environment at p.Must-alias information facilitates various program optimizations such as lightweight closure conversion [19]. In addition, must-alias information permits analyses to perform strong updates [3] on abstract reference cells known to be single. Strong updates improve analysis precision for programs that make significant use of state.A prototype implementation of our analysis yields encouraging results. Over a range of benchmarks, our analysis classifies a large majority of the variables as single.