Native Type Theory

Christian Williams, Michael Stay
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引用次数: 1

Abstract

Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad class of languages, λ -theories with equality, by embedding such a theory into the internal language of its topos of presheaves. Native types provide total specification of the structure of terms; and by internalizing transition systems, native type systems serve to reason about structure and behavior simultaneously. The construction is functorial, thereby providing a shared framework of higher-order reasoning for many languages, including programming languages.
原生类型理论
原生类型系统是指类型构造函数派生自术语构造函数、谓词逻辑和直觉型理论的构造函数的类型系统。我们提出了一种方法,通过将λ -理论嵌入到其presheaves拓扑的内部语言中,为一类广泛的语言构造具有相等性的本地类型系统。原生类型提供了术语结构的总体规范;通过内化转换系统,原生类型系统可以同时对结构和行为进行推理。这种构造是功能性的,因此为许多语言(包括编程语言)提供了一个高阶推理的共享框架。
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