This work extends a rule-based specification of nominal C-unification formalised in Coq to include ‘protected variables’ that cannot be instantiated during the unification process. By introducing protected variables, we are able to reuse the C-unification simplification rules to solve nominal C-matching (as well as equality check) problems. From the algorithmic point of view, this extension is sufficient to obtain a generalised C-unification procedure; however, it cannot be formally checked by simple reuse of the original formalisation. This paper describes the additional effort necessary in order to adapt the specification of the inference rules and reuse previous formalisations. We also generalise a functional recursive nominal C-unification algorithm specified in PVS with protected variables, effectively adapting this algorithm to the tasks of nominal C-matching and nominal equality check. The PVS formalisation is applied to test the correctness of a Python manual implementation of the algorithm.

中文翻译：

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用受保护变量形式化名义 C 统一

这项工作扩展了 Coq 中形式化的名义 C 统一的基于规则的规范，以包括在统一过程中无法实例化的“受保护变量”。通过引入受保护的变量，我们能够重用 C 统一简化规则来解决名义 C 匹配（以及相等检查）问题。从算法的角度来看，这个扩展足以获得一个广义的 C 统一过程；但是，不能通过简单地重用原始形式来对其进行正式检查。本文描述了调整推理规则规范和重用以前的形式化所需的额外工作。我们还用受保护的变量概括了 PVS 中指定的函数递归标称 C 统一算法，有效地使该算法适应名义 C 匹配和名义相等检查的任务。PVS 形式化用于测试 Python 手动实现算法的正确性。