A Java-like Calculus with User-Defined Coeffects

We propose a Java-like calculus where declared variables can be annotated by coeffects specifying constraints on their use, such as linearity or privacy levels. Annotations are written in the language itself, as expressions of type Coeffect, a predefined class which can be extended by user-defined subclasses, modeling the coeffects desired for a specific application. We formalize the type system and prove subject reduction, which includes preservation of coeffects, and show several examples.