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arXiv 2406.14719cs.PL
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深入理解 Sequent Calculus(函数式珍珠)

Grokking the Sequent Calculus (Functional Pearl)

David Binder, Marco Tzschentke, Marius Müller, Klaus Ostermann

AI总结:

本文面向编译器黑客与编程语言爱好者,通过编写将小型表层语言转换为 λμμ-calculus 的编译器,首次以非逻辑学家的视角介绍了 sequent calculus 及其作为编译器中间语言的优势。

摘要:

sequent calculus(序列演算)是一种证明系统,被设计为自然演绎的更对称的替代方案。λμμ-calculus 是 sequent calculus 的项指派系统,并且由于其一流地表示了求值上下文,是编译器中间语言的绝佳基础。遗憾的是,只有 sequent calculus 的专家才能欣赏其美感。为了弥补这一点,我们提出了首个 λμμ-calculus 的介绍,它不是面向类型理论家或逻辑学家,而是面向编译器黑客和编程语言爱好者。我们通过编写一个编译器来实现这一点,该编译器将一种小而有趣的表层语言转换为 λμμ-calculus,作为编译器中间语言。

英文摘要:

The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The λμμ-calculus is a term assignment system for the sequent calculus and a great foundation for compiler intermediate languages due to its first-class representation of evaluation contexts. Unfortunately, only experts of the sequent calculus can appreciate its beauty. To remedy this, we present the first introduction to the λμμ-calculus which is not directed at type theorists or logicians but at compiler hackers and programming-language enthusiasts. We do this by writing a compiler from a small but interesting surface language to the λμμ-calculus as a compiler intermediate language.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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