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Both static and dynamic program verification approaches have significant disadvantages when considered in isolation. Inspired by research on gradual typing, we propose gradual verification to seamlessly and flexibly combine static and dynamic verification. Drawing on general principles from abstract interpretation, and in particular on the recent Abstracting Gradual Typing methodology of Garcia et al., we systematically derive a gradual verification system from a static one. This approach yields, by construction, a gradual verification system that is compatible with the original static system, but overcomes its rigidity by resorting to dynamic verification when desired. As with gradual typing, the programmer can control the trade-off between static and dynamic checking by tuning the (im)precision of pre- and postconditions. The formal semantics of the gradual verification system and the proofs of its properties …