The expressiveness of dependent type theory can be extended by identifying types modulo some additional computation rules. But, for preserving the decidability of type-checking or the logical consistency of the system, one must make sure that those user-defined rewriting rules preserve typing. In this paper, we give a new method to check that property using Knuth-Bendix completion.

中文翻译：

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依赖类型中重写规则的类型安全

依赖类型理论的表达能力可以通过以一些额外的计算规则为模来识别类型来扩展。但是，为了保持类型检查的可判定性或系统的逻辑一致性，必须确保那些用户定义的重写规则保留类型。在本文中，我们提供了一种使用 Knuth-Bendix 完成检查该属性的新方法。