A functional approach to generic programming using adaptive traversals

Writing functions over complex user-defined datatypes can be tedious and error prone. Generic (or polytypic) programming and higher order functions like foldr have resolved some of these issues, but can be too general to be practically useful for larger collections of data types. In this paper we present a traversal-based approach to generic programming using function sets. Our traversal is an adaptive, higher-order function that employs an asymmetric type-based multiple dispatch to fold over arbitrarily complex structures. We introduce our approach in the context of our Scheme library implementation, present a typed model of our system, and provide a proof of type soundness, showing that our flexible, adaptive approach is both useful and safe.