This paper introduces a uniform substitution calculus for $\mathsf{dL}_\text{CHP}$, the dynamic logic of communicating hybrid programs. Uniform substitution enables parsimonious prover kernels by using axioms instead of axiom schemata. Instantiations can be recovered from a single proof rule responsible for soundness-critical instantiation checks rather than being spread across axiom schemata in side conditions. Even though communication and parallelism reasoning are notorious for necessitating subtle soundness-critical side conditions, uniform substitution when generalized to $\mathsf{dL}_\text{CHP}$ manages to limit and isolate their conceptual overhead. Since uniform substitution has proven to simplify the implementation of hybrid systems provers substantially, uniform substitution for $\mathsf{dL}_\text{CHP}$ paves the way for a parsimonious implementation of theorem provers for hybrid systems with communication and parallelism.

翻译：本文介绍了$\mathsf{dL}_\text{CHP}$的一致替换演算，该逻辑用于通信混合程序的动态逻辑。一致替换通过使用公理而非公理模式，实现了简约的证明器内核。实例化可通过单一证明规则进行恢复，该规则负责对可靠性关键的实例化检查，而非分散在公理模式的附加条件中。尽管通信和并行推理因需要微妙的可靠性关键附加条件而闻名，但一致替换在推广到$\mathsf{dL}_\text{CHP}$时成功限制并隔离了其概念开销。由于一致替换已被证明能显著简化混合系统证明器的实现，$\mathsf{dL}_\text{CHP}$的一致替换为简约实现带通信与并行性的混合系统定理证明器铺平了道路。