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Current static verification techniques such as separation logic support a wide range of programs. However, such techniques only support complete and detailed specifications, which places an undue burden on users. To solve this problem, prior work proposed gradual verification, which handles complete, partial, or missing specifications by soundly combining static and dynamic checking. Gradual verification has also been extended to programs that manipulate recursive, mutable data structures on the heap. Unfortunately, this extension does not reward users with decreased dynamic checking as more specifications are written and more static guarantees are made. In fact, all properties are checked dynamically regardless of any static guarantees. Additionally, no full-fledged implementation of gradual verification exists so far, which prevents studying its performance and applicability in practice. We present Gradual C0, the first practicable gradual verifier for recursive heap data structures, which targets C0, a safe subset of C designed for education. Static verifiers supporting separation logic or implicit dynamic frames use symbolic execution for reasoning; so Gradual C0, which extends one such verifier, adopts symbolic execution at its core instead of the weakest liberal precondition approach used in prior work. Our approach addresses technical challenges related to symbolic execution with imprecise specifications, heap ownership, and branching in both program statements and specification formulas. We also deal with challenges related to minimizing insertion of dynamic checks and extensibility to other programming languages beyond C0. Finally, we provide the first empirical performance evaluation of a gradual verifier, and found that on average, Gradual C0 decreases run-time overhead between 7.1 and 40.2% compared to the fully dynamic approach used in prior work (for context, the worst cases for the approach by Wise et al. [2020] range from 0.1 to 4.5 seconds depending on the benchmark). Further, the worst-case scenarios for performance are predictable and avoidable. This work paves the way towards evaluating gradual verification at scale. 

Static analysis tools typically address the problem of excessive false positives by requiring programmers to explicitly annotate their code. However, when faced with incomplete annotations, many analysis tools are either too conservative, yielding false positives, or too optimistic, resulting in unsound analysis results. In order to flexibly and soundly deal with partially-annotated programs, we propose to build upon and adapt the gradual typing approach to abstract-interpretation-based program analyses. Specifically, we focus on null-pointer analysis and demonstrate that a gradual null-pointer analysis hits a sweet spot, by gracefully applying static analysis where possible and relying on dynamic checks where necessary for soundness. In addition to formalizing a gradual null-pointer analysis for a core imperative language, we build a prototype using the Infer static analysis framework, and present preliminary evidence that the gradual null-pointer analysis reduces false positives compared to two existing null-pointer checkers for Infer. Further, we discuss ways in which the gradualization approach used to derive the gradual analysis from its static counterpart can be extended to support more domains. This work thus provides a basis for future analysis tools that can smoothly navigate the tradeoff between human effort and run-time overhead to reduce the number of reported false positives.