Associated types with class (Manuel M. T. Chakravarty, Gabriele Keller, Simon Peyton Jones, Simon Marlow) In POPL '05: Proceedings of the 32nd ACM SIGPLAN-SIGACT sysposium on Principles of programming languages, pages 1--13, Long Beach, California, USA, ACM Press, 2005

Haskell's type classes allow ad-hoc overloading, or typeindexing, of functions. A natural generalisation is to allow type-indexing of data types as well. It turns out that this idea directly supports a powerful form of abstraction called associated types, which are available in C++ using traits classes. Associated types are useful in many applications, especially for self-optimising libraries that adapt their data representations and algorithms in a type-directed manner.

In this paper, we introduce and motivate associated types as a rather natural generalisation of Haskell's existing type classes. Formally, we present a type system that includes a type-directed translation into an explicitly typed target language akin to System F; the existence of this translation ensures that the addition of associated data types to an existing Haskell compiler only requires changes to the front end.