The parallel scan algorithm plays an important role in parallel programming, but previous explanations of it generally rely on informal methods that fail to establish its correctness. Equational reasoning in a pure functional language provides a formal vehicle for stating the parallel scan algorithm and proving that a parallel architecture executes it correctly. The two key ideas in the proof are (1) a collection of lemmas that show how folds and scans can be decomposed into smaller problems, supporting a divide-and-conquer strategy, and (2) a formal specification of the abstract parallel architecture in the same language used to specify the problem, making it possible to reason formally about how the architecture executes the algorithm.