《抽象代数基础》封面

抽象代数基础

Elements of abstract algebra

Allan Clark · 初版 1971 年

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  • ……定理的自然语言描述,模型就能自动形式化吗?如果证明成功,我能拿到 Lean 证明的自然语言解释吗?——我正琢磨着用它来刷一遍《抽象代数基础》(Elements of Abstract Algebra),但不确定它有没有这么广的通用性?

    …description of the theorem to be proven and the model will automatically formalize it? And can I get a natural language interpretation of the Lean proof in case of success? --- I'm thinking of working through Elements of Abstract Algebra with this, but not sure if it has such general applicability?

  • 这模型做高中竞赛数学挺在行的。《抽象代数基础》里“集合论”和“自然数”这两章的题,用 Kimina-Prover 应该能搞定,再往后的就不行了,因为它不懂西罗定理(Sylow theorem)之类的,而且实际也没在 Lean 4 里用过这些数学对象。你可以先从一段自然语言描述开始……

    The model does well on highschool competition maths. Problems in the "Set Theory" and "Natural Numbers" chapters of Elements of Abstract Algebra may be doable with Kimina-Prover, nothing beyond because it doesn't know Sylow theorem etc. and hasn't used these objects with Lean 4 in practice. You can start with a natural language description of…

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