Lightweight Testing of Persistent Amortized Time Complexity in the Credit Monad

Persistent data structures are ubiquitous in functional programming languages and their designers frequently have to reason about amortized time complexity. But proving amortized bounds is difficult in a persistent setting, and pen-and-paper proofs give little assurance of correctness, while a full mechanization in a proof assistant can be too involved for the casual user. In this work, we define a strict domain specific language (DSL) for testing the amortized time complexity of persistent data structures using QuickCheck. Our DSL can give strong evidence of correctness, while imposing low overhead on the user. We have used our DSL to check the amortized time complexity of all lazy data structures in Okasaki's book. As a sign of our approach's effectiveness, we re-discovered a previously unreported gap in the analysis of persistent Finger Trees.