Associated Types with Class

Manuel M. T. Chakravarty, Gabriele Keller, Simon Peyton Jones, and Simon Marlow.

In Proceedings of The 32nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL'05), pages 1-13, ACM Press, 2005.

Abstract
Haskell's type classes allow ad-hoc overloading, or type-indexing, 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.

PostScript version (13 pages)
Proofs of Theorem 1 & 2 of the paper (PostScript) (14 pages)

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