Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today’s powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search, borrowing techniques from the world of first order theorem proving, but also the automatic search for counterexamples. They include a highly readable structured language of proofs and a unique interactive development environment for editing live proof documents. Everything rests on the foundation conceived by Robin Milner for Edinburgh LCF: a proof kernel, using abstract types to ensure soundness and eliminate the need to store proofs. Compared with the research prototypes of the 1970s, Isabelle is a practical and versatile tool. It is used by system designers, mathematicians and many others.

中文翻译：

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从 LCF 到 Isabelle/HOL

交互式定理证明器在过去的 4 年中发展迅速，从最初的开始到今天的强大系统。在这里，我们专注于 Isabelle/HOL 及其独特的优势。它们包括自动证明搜索、从一阶定理证明世界中借用技术，以及自动搜索反例。它们包括高度可读的结构化证明语言和用于编辑实时证明文档的独特交互式开发环境。一切都建立在 Robin Milner 为 Edinburgh LCF 构想的基础之上：证明内核，使用抽象类型来确保可靠性并消除存储证明的需要。与 1970 年代的研究原型相比，Isabelle 是一个实用且用途广泛的工具。它被系统设计师、数学家和许多其他人使用。