The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on abstract fixed-point theory and compatible functions. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the pi-calculus, the lambda-calculus, and a (call-by-value) lambda-calculus with references.

中文翻译：

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通过一阶转换系统对高阶语言进行模块化联合归纳

可以通过采用“双向仿真”技术来增强互仿真证明方法。基于抽象定点理论和兼容函数，已经为一阶（即类似 CCS）标记的转换系统 (LTS) 和双相似性开发了这种增强的综合理论。我们将此理论传递到双相似性和 LTS 超出一阶模型的语言上。该方法包括展示更复杂的 LTS 和双相似性到一阶 LTS 的完全抽象转换。这使我们能够直接重用一阶 LTS 上可用的大型最新技术语料库。必须手动提供的唯一要素是特定于新语言的基本最新技术的兼容性。我们研究了 pi 演算的方法，