Polyvariance, polymorphism and flow analysis

Abstract

Flow analysis is a potentially very useful analysis for higher order functional languages, but its practical application has been slow in coining, partially hindered by shortcomings of the current analysis techniques. Among these are the limited precision, long analysis times, incompatibility with separate compilation, inapplicability to untyped languages and sensitivity to program structure associated with various earlier formulations.

We address these shortcomings with an approach based on a novel type system integrating recursive types, subtyping with liberal union types, and system F style polymorphism, in a constraint based formulation. The type system is “soft” in the sense that it does not reject programs. It is also not decidable, but there is a broad spectrum of sound and terminating, though incomplete, algorithms whose precision can be characterized by restricting the substitutions used for instantiation of type schemes. We give an inference algorithm which simplifies constraints incrementally, rather than postponing all constraint solving until all of the constraints are generated. In this way we hope to avoid in practice the exponential growth in the size of constraint sets caused by repeated instantiation of unsimplified type schemes. Type schemes are also a suitable representation for communicationg the analysis result over module boundaries, making separate compilation feasible.