Dedukti is a type-checker for the $\lambda$$\Pi$-calculus modulo rewriting, an extension of Edinburgh's logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF terms and types according to the rewrite rules given by the user.A key component of this engine is the matching algorithm to find which rules can be fired. In thispaper, we describe the class of rewrite rules supported by Dedukti and the new implementation ofthe matching algorithm. Dedukti supports non-linear rewrite rules on terms with binders usinghigher-order pattern-matching as in Combinatory Reduction Systems (CRS). The new matchingalgorithm extends the technique of decision trees introduced by Luc Maranget in the OCamlcompiler to this more general context.

中文翻译：

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Dedukti 的新重写引擎

Dedukti 是 $\lambda$$\Pi$-calculus 模重写的类型检查器，它是爱丁堡逻辑框架 LF 的扩展，其中函数和类型符号可以通过重写规则定义。因此，它包含一个引擎，用于根据用户给出的重写规则重写 LF 术语和类型。该引擎的一个关键组件是匹配算法，以查找可以触发哪些规则。在本文中，我们描述了Dedukti 支持的重写规则类和匹配算法的新实现。Dedukti 支持使用高阶模式匹配的绑定器的非线性重写规则，如组合归约系统 (CRS)。新的匹配算法将 Luc Maranget 在 OCamlcompiler 中引入的决策树技术扩展到这个更一般的上下文。