We propose a structured mechanism to traverse recursive data types incrementally, in successive reactions to external input events. “traverse” is an iterator-like anonymous block that can be invoked recursively and suspended at any point, retaining the full state and stack frames alive. “traverse” is designed for the synchronous language Céu, inheriting all of its concurrency functionality and safety properties, such as parallel compositions with orthogonal abortion, static memory management, and bounded reaction time and memory usage. We discuss three applications in the domain of control-oriented DSLs that contain reactive and recursive behavior at the same time.