具有类型相等判断的Martin-Lof类型理论的评价归一化

Andreas Abel, T. Coquand, P. Dybjer
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引用次数: 45

摘要

证明了具有罗素宇宙和类型化β -相等判断的马丁-洛夫型理论的相等性的可决性。这个结果的一个推论是,依赖函数类型的构造函数是内射的,这个属性对于建立类型检查算法的正确性至关重要。决策过程采用归一化求值算法,该算法首先解释具有无类型语义元素的领域中的术语,然后提取标准形式。利用per模型和语法与语义之间的逻辑关系来确定算法的正确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Normalization by Evaluation for Martin-Lof Type Theory with Typed Equality Judgements
The decidability of equality is proved for Martin-Lof type theory with a universe a la Russell and typed beta-eta- equality judgements. A corollary of this result is that the constructor for dependent function types is injective, a property which is crucial for establishing the correctness of the type-checking algorithm. The decision procedure uses normalization by evaluation, an algorithm which first interprets terms in a domain with untyped semantic elements and then extracts normal forms. The correctness of this algorithm is established using a PER-model and a logical relation between syntax and semantics.
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