Backtracking

Iterating over the elements of an abstract collection is usu ally done in ML using a fold-like higher-order function provided by th e data structure. This article discusses a different paradigm of i teration based on purely functional, immutable cursors. Contrary to foldlike iterators, the iteration can be cleanly interrupted at any step. Contrary to imperative cursors (such as those found in C++ an d Java libraries) it is possible to backtrack the iterator to a previous step. Several ways to iterate over binary trees are examined a d close links with Gérard Huet’s Zipperare established. Incidentally, we show the well-known two-lists implementation of functio nal queues arising from a Zipper-based breadth-first traversal.