Type-based flow analysis and context-free language reachability

Abstract

We present a novel approach to computing the context-sensitive flow of values through procedures and data structures. Our approach combines and extends techniques from two seemingly disparate areas: polymorphic subtyping and interprocedural dataflow analysis based on context-free language reachability. The resulting technique offers several advantages over previous approaches: it works directly on higher-order programs; provides demand-driven interprocedural queries; and improves the asymptotic complexity of a known algorithm based on polymorphic subtyping fromO(n8) toO(n3) for computing all queries. For intra-procedural flow restricted to equivalence classes, our algorithm yields linear inter-procedural flow queries.