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 let-polymorphic 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.