Higher-order symbolic execution for contract verification and refutation

Abstract

We present a new approach to automated reasoning about higher-order programs by endowing symbolic execution with a notion of higher-order, symbolic values. Our approach is sound and relatively complete with respect to a first-order solver for base type values. Therefore, it can form the basis of automated verification and bug-finding tools for higher-order programs. To validate our approach, we use it to develop and evaluate a system for verifying and refuting behavioral software contracts of components in a functional language, which we call soft contract verification. In doing so, we discover a mutually beneficial relation between behavioral contracts and higher-order symbolic execution. Our system uses higher-order symbolic execution, leveraging contracts as a source of symbolic values including unknown behavioral values, and employs an updatable heap of contract invariants to reason about flow-sensitive facts. Whenever a contract is refuted, it reports a concrete counterexample reproducing the error, which may involve solving for an unknown function. The approach is able to analyze first-class contracts, recursive data structures, unknown functions, and control-flow-sensitive refinements of values, which are all idiomatic in dynamic languages. It makes effective use of an off-the-shelf solver to decide problems without heavy encodings. The approach is competitive with a wide range of existing tools---including type systems, flow analyzers, and model checkers---on their own benchmarks. We have built a tool which analyzes programs written in Racket, and report on its effectiveness in verifying and refuting contracts.

This paper unifies and expands upon the work presented in the papers "Soft contract verification" [arXiv:1307.6239], and "Relatively complete counterexamples for higher-order programs" [arXiv:1411.3967]. It also subsumes the work in the paper "Higher-order symbolic execution via contracts" [arXiv:1103.1362]