Model Checking Higher-Order Programs

Abstract

We propose a novel verification method for higher-order functional programs based on higher-order model checking, or more precisely, model checking of higher-order recursion schemes (recursion schemes, for short). The most distinguishing feature of our verification method for higher-order programs is that it is sound, complete, and automatic for the simply typed λ-calculus with recursion and finite base types, and for various program verification problems such as reachability, flow analysis, and resource usage verification. We first show that a variety of program verification problems can be reduced to model checking problems for recursion schemes, by transforming a program into a recursion scheme that generates a tree representing all the interesting possible event sequences of the program. We then develop a new type-based model-checking algorithm for recursion schemes and implement a prototype recursion scheme model checker. To our knowledge, this is the first implementation of a recursion scheme model checker. Experiments show that our model checker is reasonably fast, despite the worst-case time complexity of recursion scheme model checking being hyperexponential in general. Altogether, the results provide a new, promising approach to verification of higher-order functional programs.