A Recipe for Modular Verification of Generic Tree Traversals

Data structures based on trees and tree traversals are ubiquitous in computer systems. Many low-level programs, including some implementations of critical systems like page tables and the web browser DOM, rely on generic tree-traversal functions that traverse tree nodes in a pre-determined order, applying a client-provided operation to each visited node. Developing a general approach to specifying and verifying such traversals is tricky since the client-provided per-node operation can be stateful and may potentially depend on or modify the structure of the tree being traversed.