We describe defret-mutual-generate, a utility for proving ACL2 theorems about large mutually recursive cliques of functions. This builds on previous tools such as defret-mutual and make-flag, which automate parts of the process but still require a theorem body to be written out for each function in the clique. For large cliques, this tends to mean that certain common hypotheses and conclusions are repeated many times, making proofs difficult to read, write, and maintain. This utility automates several of the most common patterns that occur in these forms, such as including hypotheses based on formal names or types. Its input language is rich enough to support forms that have some common parts and some unique parts per function. One application of defret-mutual-generate has been to support proofs about the FGL rewriter, which consists of a mutually recursive clique of 49 functions. The use of this utility reduced the size of the forms that express theorems about this clique by an order of magnitude. It also greatly has reduced the need to edit theorem forms when changing definitions in the clique, even when adding or removing functions.

中文翻译：

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从简明描述生成互归纳定理

我们描述了 defret-mutual-generate，这是一种用于证明关于大型相互递归函数团的 ACL2 定理的实用程序。这建立在以前的工具（例如 defret-mutual 和 make-flag）的基础上，这些工具可以自动化部分过程，但仍然需要为集团中的每个函数写出一个定理主体。对于大集团，这往往意味着某些常见的假设和结论被重复多次，使得证明难以阅读、编写和维护。此实用程序自动执行以这些形式出现的几种最常见模式，例如包括基于正式名称或类型的假设。它的输入语言足够丰富，可以支持每个功能具有一些公共部分和一些独特部分的表单。defret-mutual-generate 的一个应用是支持关于 FGL 重写器的证明，它由相互递归的 49 个函数组成。此实用程序的使用将表达有关该集团的定理的形式的大小减少了一个数量级。即使在添加或删除函数时，它也大大减少了在更改集团中的定义时编辑定理形式的需要。