Equality-based flow analysis versus recursive types

Abstract

Equality-based control-flow analysis has been studied by Henglein, Bondorf and Jørgensen, DeFouw, Grove, and Chambers, and others. It is faster than the subset-based-0-CFA, but also more approximate. Heintze asserted in 1995 that a program can be safety checked with an equality-based control-flow analysis if and only if it can be typed with recursive types. In this article we falsify Heintze's assertion, and we present a type system equivalent to equality-based control-flow analysis. The new type system contains both recursive types and an unusual notion of subtyping. We have s ≤ t if s and t unfold to the same regular tree, and we have ⊥≤t≤⊤ where t is a function type. In particular, there is no nontrivial subtyping between function types.