Polyvariant Flow Analysis with Higher-ranked Polymorphic Types and Higher-order Effect Operators

We present a type and effect system for flow analysis that makes essential use of higher-ranked polymorphism. We show that, for higher-order functions, the expressiveness of higher-ranked types enables us to improve on the precision of conventional letpolymorphic analyses. Modularity and decidability of the analysis are guaranteed by making the analysis of each program parametric in the analyses of its inputs; in particular, we have that higher-order functions give rise to higher-order operations on effects. As flow typing is archetypical to a whole class of type and effect systems, our approach can be used to boost the precision of a wide range of type-based program analyses for higher-order languages.