A generic recursion toolbox for Haskell or: scrap your boilerplate systematically

Haskell programmers who deal with complex data types often need to apply functions to specific nodes deeply nested inside of terms. Typically, implementations for those applications require so-called boilerplate code, which recursively visits the nodes and carries the functions to the places where they need to be applied. The scrap-your-boilerplate approach proposed by Lämmel and Peyton Jones tries to solve this problem by defining a general traversal design pattern that performs the traversal automatically so that the programmers can focus on the code that performs the actual transformation.In practice we often encounter applications that require variations of the recursion schema and call for more sophisticated generic traversals. Defining such traversals from scratch requires a profound understanding of the underlying mechanism and is everything but trivial.In this paper we analyze the problem domain of recursive traversal strategies, by integrating and extending previous approaches. We then extend the scrap-your-boilerplate approach by rich traversal strategies and by a combination of transformations and accumulations, which leads to a comprehensive recursive traversal library Reclib in a statically typed framework.We define a two-layer library targeted at general programmers and programmers with knowledge in traversal strategies. The highlevel interface defines a universal combinator that can be customized to different one-pass traversal strategies with different coverage and different traversal order. The lower-layer interface provides a set of primitives that can be used for defining more sophisticated traversal strategies such as fixpoint traversals. The interfaceis simple and succinct. Like the original scrap-your-boilerplate approach, it makes use of rank-2 polymorphism and functional dependencies, implemented in GHC.