One Vote for Type Families in Haskell!

Generalized Algebraic DataTypes (GADTs) allow programmers to capture important invariants of their data structures through type annotations on data constructors. However when working with GADTs, it is often difficult to concisely and precisely express the way complex data manipulations maintain those invariants. One can approach the problem in a few different ways, given the arsenal of GHC’s current type extensions. One approach is to use type classes with functional dependencies. Another approach is to introduce yet more GADTs to capture the behavior of individual functions. A third alternative is to use type families, a recent introduction of GHC by which functions over types can be defined directly, much like term-level functions, and appear in type signatures. In this paper we illustrate the use of type families in the context of a typepreserving compiler written in Haskell. We compare the results with an ad-hoc, all-GADT solution. We argue that type families promote a more direct programming style that eliminates much code bloat and translates into increased run-time performance. They offer better modularity and require fewer type annotations than type classes, which require that class constraints be propagated between compilation phases. We also describe a use of type families to capture more complex data structure invariants. We mention current limitations that we face with these more advanced uses, in which we need to convince the type checker that the type families we define satisfy certain properties. We sketch a proposal of a language extension to directly support such properties. ?Universite de Montreal, C.P. 6128, succ. Centre-Ville, Montreal, Quebec, Canada. ++1 (514) 343-6111 x3545; {guillelj,monnier}@iro.umontreal.ca