Static analyses predominantly use discrete modes of logical reasoning to derive facts about programs. Despite significant strides, this form of reasoning faces new challenges in modern software applications and practices. These challenges concern not only traditional analysis objectives such as scalability, accuracy, and soundness, but also emerging ones such as tailoring analysis conclusions based on relevance or severity of particular code changes, and needs of individual programmers.

We advocate seamlessly extending static analyses to leverage continuous modes of logical reasoning in order to address these challenges. Central to our approach is expressing the specification of the static analysis in a constraint language that is amenable to computing provenance information. We use the logic programming language Datalog as proof-of-concept for this purpose. We illustrate the benefits of exploiting provenance even in the discrete setting. Moreover, by associating weights with constraints, we show how to amplify these benefits in the continuous setting.

We also present open problems in aspects of analysis usability, language expressiveness, and solver techniques. The overall process constitutes a fundamental rethinking of how to design, implement, deploy, and adapt static analyses.