Dependent object types with implicit functions

DOT (Dependent Object Types) is an object calculus with path-dependent types and abstract type members, developed to serve as a theoretical foundation for the Scala programming language. As yet, DOT does not model all of Scala's features, but a small subset. We present the calculus DIF (DOT with Implicit Functions), which extends the set of features modelled by DOT to include implicit functions, a feature of Scala to aid modularity of programs. We show type safety of DIF, and demonstrate that the generic programming focused use cases for implicit functions in Scala are also expressible in DIF.