Iterating over the elements of an abstract collection is usually done in ML using a fold-like higher-order function provided by the data structure. This article discusses a different paradigm of iteration 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++ and Java libraries) it is possible to backtrack the iterator to a previous step. Several ways to iterate over binary trees are examined and close links with Gérard Huet’s Zipper are established. Incidentally, we show the well-known two-lists implementation of functional queues arising from a Zipper-based breadth-first traversal. Categories and Subject Descriptors D.1.1 [Programming Techniques]:

Traditional approaches to protecting computer systems from malicious or other misbehaved code typically involve (1) monitoring code for unacceptable behavior as it runs, or (2) detecting potentially misbehaved code and preventing it from running at all. These approaches are effective when unacceptable behavior can be detected in time to take remedial action, but in many settings and for many im-portant security policies this is computationally expensive or provably impossible. A third approach, termed in this dissertation program-rewriting, involves auto-matically rewriting code prior to running it in such a way that acceptable behavior is preserved but unacceptable behavior is not. Rewritten code can be run without further analysis or monitoring because it is guaranteed to exhibit only acceptable behavior. Program-rewriting has received recent attention in the literature in the form of in-lined reference monitors, which implement approach 1 above by in-lining security checks directly into the code being monitored. Program-rewriting generalizes in-lined reference monitoring, encompassing many other strategies for automatically rewriting programs as well.