This paper addresses compositional and incremental type checking for object-oriented programming languages. Recent work achieved incremental type checking for structurally typed functional languages through co-contextual typing rules, a constraint-based formulation that removes any context dependency for expression typings. However, that work does not cover key features of object-oriented languages: Subtype polymorphism, nominal typing, and implementation inheritance. Type checkers encode these features in the form of class tables, an additional form of typing context inhibiting incrementalization. In the present work, we demonstrate that an appropriate co-contextual notion to class tables exists, paving the way to efficient incremental type checkers for object-oriented languages. This yields a novel formulation of Igarashi et al.'s Featherweight Java (FJ) type system, where we replace class tables by the dual concept of class table requirements and class table operations by dual operations on class table requirements. We prove the equivalence of FJ's type system and our co-contextual formulation. Based on our formulation, we implemented an incremental FJ type checker and compared its performance against javac on a number of realistic example programs. @en

Object-oriented programming languages feature static and dynamic overloading: Multiple methods share the same name but provide different implementations. Dynamic overloading (also know as dynamic dispatch) is resolved at run time based on the type of the receiver object. In this paper, we focus on static overloading, which is resolved at compile time based on the types of the method arguments. The challenge this paper addresses is to incrementalize static overload resolution in IDEs. IDEs resolve overloaded methods for the developer to help them discern which implementation a method call refers to. However, as the code changes, the IDE has to reconsider previously resolved method calls when they are affected by the code change. This paper clarifies when a method call is affected by a code change and how to re-resolve method calls with minimal computational effort. To this end, we explore and compare two approaches to incremental type checking: co-contextual type checking and IncA.@en