Modular verification of higher-order functional programs

Fully automated verification methods for higher-order functional programs have recently been proposed based on higher-order model checking and/or refinement type inference. Most of those methods are, however, whole program analyses, suffering from the scalability problem. To address the problem, we propose a modular method for fully automated verification of higher-order programs. Our method takes a program consisting of multiple top-level functions as an input, and repeatedly applies procedures for (i) guessing refinement intersection types of each function in a counterexample-guided manner, and (ii) checking that each function indeed has the guessed refinement intersection types, until the whole program is proved/disproved to be safe. To avoid the whole program analysis, we introduce the notion of modular counterexamples, and utilize them in (i), and employ Sato et al.’s technique of reducing refinement type checking to assertion checking in (ii). We have implemented the proposed method as an extension to MoCHi, and confirmed its effectiveness through experiments.