Higher-Order Symbolic Execution via Contracts

TL;DR

This paper introduces a novel symbolic execution method that uses behavioral contracts as symbolic values, enabling automated reasoning about higher-order programs with complex specifications.

Contribution

It extends symbolic execution with contract-based symbolic values, providing an operational semantics that soundly predicts behavior and scales to expressive contract languages.

Findings

Successfully verifies contract correctness in complex higher-order programs

Scales to expressive contract languages including recursive and dependent contracts

Enables automated contract verification and optimization justification

Abstract

We present a new approach to automated reasoning about higher-order programs by extending symbolic execution to use behavioral contracts as symbolic values, enabling symbolic approximation of higher-order behavior. Our approach is based on the idea of an abstract reduction semantics that gives an operational semantics to programs with both concrete and symbolic components. Symbolic components are approximated by their contract and our semantics gives an operational interpretation of contracts-as-values. The result is a executable semantics that soundly predicts program behavior, including contract failures, for all possible instantiations of symbolic components. We show that our approach scales to an expressive language of contracts including arbitrary programs embedded as predicates, dependent function contracts, and recursive contracts. Supporting this feature-rich language of specifications leads to powerful symbolic reasoning using existing program assertions. We then apply our approach to produce a verifier for contract correctness of components, including a sound and computable approximation to our semantics that facilitates fully automated contract verification. Our implementation is capable of verifying contracts expressed in existing programs, and of justifying valuable contract-elimination optimizations.