A type theory for productive coprogramming via guarded recursion

Rasmus Ejlers Møgelberg
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引用次数: 36

Abstract

To ensure consistency and decidability of type checking, proof assistants impose a requirement of productivity on corecursive definitions. In this paper we investigate a type-based alternative to the existing syntactic productivity checks of Coq and Agda, using a combination of guarded recursion and quantification over clocks. This approach was developed by Atkey and McBride in the simply typed setting, here we extend it to a calculus with dependent types. Building on previous work on the topos-of-trees model we construct a model of the calculus using a family of presheaf toposes, each of which can be seen as a multi-dimensional version of the topos-of-trees. As part of the model construction we must solve the coherence problem for modelling dependent types in locally cartesian closed categories simulatiously in a whole family of locally cartesian closed categories. We do this by embedding all the categories in a large one and applying a recent approach to the coherence problem due to Streicher and Voevodsky.
基于保护递归的高效协同编程的类型理论
为了确保类型检查的一致性和可判定性,证明助手对共递归定义施加了生产率要求。在本文中,我们研究了一种基于类型的替代Coq和Agda现有的语法生产力检查,使用保护递归和时钟量化的组合。这种方法是由Atkey和McBride在简单类型设置中开发的,这里我们将其扩展到具有依赖类型的微积分。在之前关于树的拓扑模型的工作的基础上,我们使用一组presheaf拓扑构建了一个微积分模型,每个拓扑都可以被看作是树的拓扑的多维版本。作为模型构建的一部分,我们必须解决局部笛卡儿封闭范畴中依赖类型在整个局部笛卡儿封闭范畴中模拟的相干性问题。我们通过将所有类别嵌入到一个大的类别中,并应用Streicher和Voevodsky提出的一种最新方法来解决相干性问题来做到这一点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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