An Interval-Based Inference of Variant Parametric Types

Variant parametric types represent the successful integration of subtype and parametric polymorphism to support a more flexible subtyping for Javalike languages. A key feature that helps strengthen this integration is the use-site variance. Depending on how the fields are used, each variance denotes a covariant, a contravariant, an invariant or a bivariant subtyping. By annotating variance properties on each type argument to a parametric class, programmers can choose various desirable variance properties for each use of the parametric class. Although Java library classes have been successfully refactored to use variant parametric types, these mechanisms are often criticized, due to the difficulty of choosing appropriate variance annotations. Several algorithms have been proposed for automatically refactoring legacy Java code to use generic libraries, but none can support the full flexibility of the use-site variance-based subtyping. This paper addresses this difficulty by proposing a novel interval-based approach to inferring both the variance annotations and the type arguments. Each variant parametric type is regarded as an interval type with two type bounds, a lower bound for writing and an upper bound for reading. We propose a constraint-based inference algorithm that works on a per method basis, as a summary-based analysis.