无穷组合归约系统：Confluence
Infinitary Combinatory Reduction Systems: Confluence
摘要：
我们研究了高阶无穷重写中的汇合，特别是无穷组合归约系统（iCRS）。我们证明了完全扩展的，正交的iCRS是合流模识别的hypercollapsing子项。作为推论，我们得到完全扩展的正交iCRS具有范式性质和唯一的范式性质（关于约简）。我们还表明，与一阶无穷重写的情况不同，几乎非崩溃的iCRS不一定是合流的。
英文摘要：
We study confluence in the setting of higher-order infinitary rewriting, in particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that fully-extended, orthogonal iCRSs are confluent modulo identification of hypercollapsing subterms. As a corollary, we obtain that fully-extended, orthogonal iCRSs have the normal form property and the unique normal form property (with respect to reduction). We also show that, unlike the case in first-order infinitary rewriting, almost non-collapsing iCRSs are not necessarily confluent.
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