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Of the complex features of generic nominally-typed OO type systems, wildcardtypes and variance annotations are probably the hardest to fully grasp. Asdemonstrated when adding closures (a.k.a., lambdas) and when extending typeinference in Java, wildcard types and variance annotations make the developmentand progress of OO programming languages, and of their type systems inparticular, a challenging and delicate task.  In this work we build on our concurrent work, in which we model Javasubtyping using a partial graph product, to suggest how wildcard types in Javacan be generalized, and simplified, to interval types. In particular, intervaltypes correspond to endpoints of paths in the Java subtyping graph.  In addition to being a simple and more familiar notion, that is easier tograsp than wildcard types, interval types are strictly more expressive thanwildcard types. As such, we believe interval types, when developed and analyzedin full, will be a welcome addition to Java and other similar genericnominally-typed OO programming languages.

Towards Taming Java Wildcards and Extending Java with Interval Types