Cyber-physical systems (CPS) are assemblies of networked, heterogeneous, hardware, and software components sensing, evaluating, and actuating a physical environment. This heterogeneity induces complexity that makes CPSs challenging to model correctly. Since CPSs often have critical functions, it is however of utmost importance to formally verify them in order to provide the highest guarantees of safety. Faced with CPS complexity, model abstraction becomes paramount to make verification attainable. To this end, assume/guarantee contracts enable component model abstraction to support a sound, structured, and modular verification process. While abstractions of models by contracts are usually proved sound, none of the related contract frameworks themselves have, to the best of our knowledge, been formally proved correct so far. In this aim, we present the formalization of a generic assume/guarantee contract theory in the proof assistant Coq. We identify and prove theorems that ensure its correctness. Our theory is generic, or parametric, in that it can be instantiated and used with any given logic, in particular hybrid logics, in which highly complex cyber-physical systems can uniformly be described.

中文翻译：

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机械验证的合同理论

信息物理系统 (CPS) 是网络化、异构、硬件和软件组件的集合，用于感知、评估和驱动物理环境。这种异质性导致复杂性，使 CPS 难以正确建模。由于 CPS 通常具有关键功能，因此对它们进行正式验证以提供最高的安全保证至关重要。面对 CPS 的复杂性，模型抽象对于实现验证变得至关重要。为此，假设/保证合同使组件模型抽象能够支持健全、结构化和模块化的验证过程。虽然合同模型的抽象通常被证明是合理的，但据我们所知，到目前为止，没有一个相关的合同框架本身被正式证明是正确的。在这个目标中，我们在证明助手 Coq 中介绍了通用假设/保证合同理论的形式化。我们确定并证明确保其正确性的定理。我们的理论是通用的或参数化的，因为它可以实例化并与任何给定的逻辑一起使用，特别是混合逻辑，其中可以统一描述高度复杂的网络物理系统。