Comparing Flow-Based Binding-Time Analyses

Binding-time analyses based on flow analysis have been presented by Bondorf, Consel, Bondorf and Jørgensen, and Schwartzbach and the present author. The analyses are formulated in radically different ways, making comparison non-trivial. In this paper we demonstrate how to compare such analyses. We prove that the first and the fourth analyses can be specified by constraint systems of a particular form, enabling direct comparison. As corollaries, we get that Bondorf’s analysis is more conservative than ours, that both analyses can be performed in cubic time, and that the core of Bondorf’s analysis is correct. Our comparison is of analyses that apply to the pure λ-calculus.