QuickChick: Property-Based Testing for Coq

Co-designing software or hardware systems and their formal proofs is an appealing idea, with the expectation that the rigor enforced by formal methods will percolate the whole design. In practice however, carrying out formal proofs while designing even a relatively simple system can be an exercise in frustration, with a great deal of time spent attempting to prove things about broken definitions, and countless iterations for discovering the correct lemmas and strengthening inductive invariants. We believe that property-based testing (PBT) can dramatically decrease the number of failed proof attempts and reduce the overall cost of producing formally verified systems. Despite the existence of experimental tools [Wil11], Coq is still lagging behind proof assistants like Isabelle, which provides several mature PBT tools (e.g. [Bul12]). We aim to improve the PBT support in Coq, while also investigating several innovations we could add into the mix like polarized mutation testing and a language-based approach to custom generation. We are also exploring whether PBT could bring more confidence to the implementation of Coq itself.