Proof pearl: Braun trees

Abstract

Braun trees are functional data structures for implementing extensible arrays and priority queues (and sorting functions based on the latter) efficiently. Some well-known functions on Braun trees have not yet been verified, including especially Okasaki’s linear time conversion from lists to Braun trees. We supply the missing proofs and verify all of these algorithms in Isabelle, including non-obvious time complexity claims. In particular we provide the first linear-time conversion from Braun trees to lists. We also state and verify a new characterization of Braun trees as the trees t whose index set is the interval {1, …, size of t}.

Topics & Concepts