Decomposable Type Highlighting for Bidirectional Type and Cast System

We explore how to provide programmers with an interactive interface for explaining the process by which static types and dynamic casts are derived, with the goal of improving the debugging of static and dynamic type errors. To this end, we define mathematical foundations for a decomposable highlighting system within a bidirectional system and show how these can be propagated through dynamic types in a cast system. Our prototype implementation in the gradually typed Hazel language includes a web-based user interface, through which we highlight the importance of type-level debugging.