Theory of choreographic languages typically includes a number of complex results that are proved by structural induction. The high number of cases and the subtle details in some of them lead to long reviewing processes, and occasionally to errors being found in published proofs. In this work, we take a published proof of Turing completeness of a choreographic language and formalise it in Coq. Our development includes formalising the choreographic language and its basic properties, Kleene's theory of partial recursive functions, the encoding of these functions as choreographies, and proving this encoding correct. With this effort, we show that theorem proving can be a very useful tool in the field of choreographic languages: besides the added degree of confidence that we get from a mechanised proof, the formalisation process led us to a significant simplification of the underlying theory. Our results offer a foundation for the future formal development of choreographic languages.

中文翻译：

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在Coq中形式化图灵完整的编排语言

编舞语言理论通常包含许多复杂的结果，这些结果已通过结构归纳法得到证明。大量的案例和其中的一些细微细节导致漫长的审查过程，并偶尔导致在已发布的证据中发现错误。在这项工作中，我们获得了编舞语言的图灵完整性的已公开证明，并将其正式化为Coq。我们的发展包括形式化编排语言及其基本属性，Kleene的部分递归函数理论，将这些函数编码为编排并证明这种编码正确。通过这项工作，我们证明了定理证明在编排语言领域可能是一个非常有用的工具：除了我们从机械化证明中获得的更高的置信度之外，形式化过程使我们大大简化了基础理论。我们的研究结果为编排语言的未来正式发展奠定了基础。