Formal Verification of Asymptotic Complexity Bounds for OCaml Programs

Program verification covers a wide range of techniques, frameworks and tools, interested in proving various properties about real world programs. Beyond basic safety properties (e.g. memory safety), program verification can be used to establish full functional correctness, meaning that, for every input, the program always behaves as expected. Yet, full functional correctness does not capture all the desired properties of a program. In particular, it does not give any form of guarantee on the execution time of the program. How useful would a mechanically-correct program be, if it does not delivers its output within reasonable amount of time? Estimating the real-life execution time of a program can be quite difficult given the complexity and underspecification of modern hardware, operating systems or even compilers. Without going that far, researchers have investigated the possibility of formally establishing asymptotic complexity bounds for programs. For example, some tools, such as RAML by Hoffmann and Hofmann [10], are capable of automatically inferring asymptotic bounds, but only for restricted classes of programs. Other lines of work (Danielsson’s Thunk library [7], Charguéraud’s CFML [4,3]) allow to establish execution cost bounds for arbitrary complex programs, thanks to the support of a proof assistant. However, they do not support reasoning on asymptotic complexity using Landau’s big-O notation.