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Gradual verification, which supports explicitly partial specifications and verifies them with a combination of static and dynamic checks, makes verification more incremental and provides earlier feedback to developers. While an abstract, weakest precondition-based approach to gradual verification was previously proven sound, the approach did not provide sufficient guidance for implementation and optimization of the required run-time checks. More recently, gradual verification was implemented using symbolic execution techniques, but the soundness of the approach (as with related static checkers based on implicit dynamic frames) was an open question. This paper puts practical gradual verification on a sound footing with a formalization of symbolic execution, optimized run-time check generation, and run time execution. We prove our approach is sound; our proof also covers a core subset of the Viper tool, for which we are aware of no previous soundness result. Our formalization enabled us to find a soundness bug in an implemented gradual verification tool and describe the fix necessary to make it sound. 

Static verification is used to ensure the correctness of programs. While useful in critical applications, the high overhead associated with writing specifications limits its general applicability. Similarly, the run-time costs introduced by dynamic verification limit its practicality. Gradual verification validates partially specified code statically where possible and dynamically where necessary. As a result, software developers gain granular control over the trade-offs between static and dynamic verification. This paper contains an end-to-end presentation of gradual verification in action, with a focus on applying it to 𝐶0 (a safe subset of C) and implementing the required dynamic verification.