Polyvariant Flow Analysis with Constrained Types

Abstract

The basic idea behind improving the quality of a monovariant control flow analysis such as 0CFAis the concept of polyvariant analyses such asAgesen’s Cartesian Product Algorithm (CPA) and Shivers’ nCFA. In this paper we develop a novel framework for polyvariant flow analysis based on Aiken-Wimmers constrained type theory. We develop instantiations of our framework to formalize various polyvariant algorithms, including nCFA and CPA. With our CPA formalization, we show the call-graph based termination condition for CPA will not always guarantee termination. We then develop a novel termination condition and prove it indeed leads to a terminating algorithm. Additionally, we show how data polymorphism can be modeled in the framework, by defining a simple extension to CPA that incorporates data polymorphism.