Coinductive reasoning about infinitary structures such as streams is widely applicable. However, practical frameworks for developing coinductive proofs and finding reasoning principles that help structure such proofs remain a challenge, especially in the context of machine-checked formalization. This paper gives a novel presentation of an equational theory for reasoning about structures up to weak bisimulation. The theory is both compositional, making it suitable for defining general-purpose lemmas, and also incremental, meaning that the bisimulation can be created interactively. To prove the theory's soundness, this paper also introduces generalized parameterized coinduction, which addresses expressivity problems of earlier works and provides a practical framework for coinductive reasoning. The paper presents the resulting equational theory for streams, but the technique applies to other structures too. All of the results in this paper have been proved in Coq, and the generalized parameterized coinduction framework is available as a Coq library.

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基于广义参数化联合归纳的弱互模拟方程理论

关于无限结构（如流）的共归纳推理是广泛适用的。然而，用于开发共归纳证明和寻找有助于构建此类证明的推理原理的实用框架仍然是一个挑战，尤其是在机器检查形式化的背景下。本文给出了一种方程理论的新颖介绍，用于推理结构直至弱互模拟。该理论既是组合式的，适用于定义通用引理，又是增量式的，这意味着可以交互地创建互模拟。为了证明该理论的合理性，本文还引入了广义参数化联合归纳，它解决了早期工作的表达性问题，并为联合推理提供了一个实用的框架。该论文介绍了由此产生的流方程理论，但该技术也适用于其他结构。本文的所有结果都在 Coq 中得到了证明，并且广义参数化共归纳框架可作为 Coq 库使用。