We propose proof script refactorings as a robust tool for constructing, restructuring, and maintaining formal proof developments. We argue that a formal approach is vital, and illustrate by defining and proving correct a number of valuable refactorings in a simplified proof script and declarative proof language of our own design.
Deep Neural Networks (DNNs) are finding important applications in safety-critical systems such as Autonomous Vehicles (AVs), where perceiving the environment correctly and robustly is necessary for safe operation. Raising unique challenges for assurance due to their black-box nature, DNNs pose a fundamental problem for regulatory acceptance of these types of systems. Robust training -training to minimize excessive sensitivity to small changes in input -has emerged as one promising technique to address this challenge. However, existing robust training tools are inconvenient to use or apply to existing codebases and models: they typically only support a small subset of model elements and require users to extensively rewrite the training code. In this paper we introduce a novel framework, PaRoT, developed on the popular TensorFlow platform, that greatly reduces the barrier to entry. Our framework enables robust training to be performed on existing DNNs without rewrites to the model. We demonstrate that our framework's performance is comparable to prior art, and exemplify its ease of use on off-the-shelf, trained models and its testing capabilities on a realworld industrial application: a traffic light detection network.
Design patterns are a highly successful technique in software engineering, giving a reusable 'best practice' solution to commonly occurring problems in software design. Taking inspiration, this paper introduces proof patterns, which aim to provide a common vocabulary for solving formal methods proof obligations by capturing and describing solutions to common patterns of proof, hence increasing effectiveness.
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