CSP# (communicating sequential programs) is a modelling language designed for specifying concurrent systems by integrating CSP-like compositional operators with sequential programs updating shared variables. In this work, we define an observation-oriented denotational semantics in an open environment for the CSP# language based on the UTP framework. To deal with shared variables, we lift traditional event-based traces into mixed traces which consist of state-event pairs for recording process behaviours. To capture all possible concurrency behaviours between action/channel-based communications and global shared variables, we construct a comprehensive set of rules on merging traces from processes which run in parallel/interleaving. We also define refinement to check process equivalence and present a set of algebraic laws which are established based on our denotational semantics. We further encode our proposed denotational semantics into the PVS theorem prover. The encoding not only ensures the semantic consistency, but also builds up a theoretic foundation for machine-assisted verification of CSP# specifications.

中文翻译：

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用于与共享变量通信进程的 UTP 语义及其在 PVS 中的形式编码

CSP#（通信顺序程序）是一种建模语言，旨在通过将类似 CSP 的组合运算符与更新共享变量的顺序程序集成来指定并发系统。在这项工作中，我们在基于 UTP 框架的 CSP# 语言的开放环境中定义了一个面向观察的指称语义。为了处理共享变量，我们将传统的基于事件的跟踪提升为由用于记录过程行为的状态-事件对组成的混合跟踪。为了捕捉基于动作/通道的通信和全局共享变量之间所有可能的并发行为，我们构建了一套全面的规则来合并来自并行/交错运行的进程的跟踪。我们还定义了细化以检查过程等价性，并提出了一组基于我们的指称语义建立的代数定律。我们进一步将我们提出的指称语义编码到 PVS 定理证明器中。该编码不仅保证了语义的一致性，而且为CSP#规范的机器辅助验证奠定了理论基础。