Compositional data types

Reviewer: Jacques Carette

Modularity and extensibility are continuing concerns, and different programming paradigms have an effect on this: object-oriented and functional languages make it easy to add new data representations and new functions (respectively) to old data representations. This is the well-known expression problem. While there are many solutions to it, none can yet claim to be "the" solution (if there even is such a thing). The authors present compositional data types, an extension of Swierstra's data types ? la carte [1]. They then go far beyond to include more general recursion schemes, add generic programming, and show that the results are reasonably efficient. They show how to deal with mutually recursive types and generalized algebraic data types (GADTs), and also make the claim, with some supporting evidence, that this method is practical; on this last aspect, time will tell. The work is supported as well as guided by a lot of theory on data types, which is generally founded on a categorical formalism. This is comforting for experts and daunting for beginners. Whenever these advanced foundations leak into user space (as they often do in error messages), any claims that this is a practical solution become dubious. However, in theory, this is a very nice solution indeed. Written for domain experts, the paper is (for its audience) very well written. The problem and its solution are well motivated and carefully explained. The full code behind this work is also published on Hackage (http://hackage.haskell.org/package/compdata). The main drawback of this paper is that, at times, the authors stick too closely to Haskell details-for example, not noticing in section 4.1 that they are trying to perform a little bit of intensional analysis on terms. The use of contexts is a clever way to tame unbounded intensionality, but contexts otherwise appear here as an ad hoc solution even though they are not. Similarly, the link with universal algebra (or its categorical brethren), especially in section 4.3, would have been a welcome addition. Nevertheless, any expert in the data type generic programming domain should read this paper. Online Computing Reviews Service