非左线性非类型高阶重写理论中的合流

Gaspard Férey, J. Jouannaud
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引用次数: 0

摘要

我们开发了基于van Oostrom的递减图的技术,将合流证明简化为在纯lambda项上扩展β -约简的高阶重写规则的临界对的检验。我们证明,对于包含所有纯lambda项的项的大子集,合流是保留的。我们的结果被应用于著名的Klop在存在收敛重写规则的情况下的非融合行为的例子,以及在具有重写规则的依赖类型理论中具有多态宇宙构造演算的各种编码片段。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Confluence in Non-Left-Linear Untyped Higher-Order Rewrite Theories
We develop techniques based on van Oostrom’s decreasing diagrams that reduce confluence proofs to the checking of critical pairs for higher-order rewrite rules extending beta-reduction on pure lambda-terms. We show that confluence is preserved for a large subset of terms that contains all pure lambda terms. Our results are applied to famous Klop’s examples of non-confluent behaviours in presence of convergent rewrite rules and to fragments of various encodings, in a dependent type theory with rewrite rules, of the Calculus of Constructions with polymorphic universes.
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