黑田的 λΠ-Calculus 模数理论和 Dedukti 翻译

Q4 Computer Science

Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-07-08 DOI:10.4204/EPTCS.404.3

Thomas Traversi'e

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引用次数: 0

摘要

黑田的翻译通过插入双重否定，将经典一阶逻辑嵌入了直觉逻辑。最近，布朗和里兹卡拉将这一翻译扩展到了高阶逻辑。在本文中，我们将其调整为 lambdaPi-calculus modulo 理论中的高阶逻辑编码理论，这是一个逻辑框架，用依赖类型和用户定义的重写规则扩展了 lambda-calculus 。我们开发了一种工具，为基于 lambdaPi-calculus modulo 理论的证明语言 Dedukti 编写的证明实现了黑田的翻译。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Kuroda's Translation for the λΠ-Calculus Modulo Theory and Dedukti

Kuroda's translation embeds classical first-order logic into intuitionistic logic, through the insertion of double negations. Recently, Brown and Rizkallah extended this translation to higher-order logic. In this paper, we adapt it for theories encoded in higher-order logic in the lambdaPi-calculus modulo theory, a logical framework that extends lambda-calculus with dependent types and user-defined rewrite rules. We develop a tool that implements Kuroda's translation for proofs written in Dedukti, a proof language based on the lambdaPi-calculus modulo theory.

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