Locales, the module system of the theorem prover Isabelle, were designed so that developments in abstract algebra could be represented faithfully and concisely. Whether these goals were met is assessed through a case study. Parts of an algebra textbook, Jacobson’s Basic Algebra, that are challenging structurally were formalised. Key parts of the formalisation are presented in greater detail. An analysis of the work from both qualitative and quantitative perspectives substantiates that the design goals were met. In particular, the size ratio of formal to “pen and paper” text does not increase when going further into the book. The analysis also yields guidance on locales including patterns of use, which are identified and described.

中文翻译：

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使用语言环境探索代数文本的结构

Locales 是定理证明者 Isabelle 的模块系统，其设计目的是使抽象代数的发展能够忠实而简洁地表现出来。通过案例研究评估是否达到了这些目标。代数教科书雅各布森的《基本代数》中在结构上具有挑战性的部分已正式化。更详细地介绍了形式化的关键部分。从定性和定量的角度对工作进行的分析证实了设计目标得到了满足。特别是，正式文本与“笔和纸”文本的大小比例在进一步阅读本书时不会增加。该分析还提供了有关区域设置的指南，包括已识别和描述的使用模式。