Parametricity and Semi-Cubical Types

Hugo Moeneclaey
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引用次数: 2

Abstract

We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes.Our construction works not only for parametricity, but also for similar interpretations of type theory and in fact similar interpretations of any generalized algebraic theory. To be precise we consider a functor forgetting unary operations and equations defining them recursively in a generalized algebraic theory. We show that it has a right adjoint.We use techniques from locally presentable category theory, as well as from quotient inductive-inductive types.
参数型和半立方型
我们从任意一个类型理论模型出发,构造了一个具有参数性的类型理论模型。新模型中的类型是旧模型中的半立方体类型,说明了参数与立方体之间的对应关系。我们的构造不仅适用于参数性,也适用于类型论的类似解释,事实上也适用于任何广义代数理论的类似解释。更确切地说,我们考虑一个函子,在广义代数理论中忘记一元操作和递归定义一元操作的方程。我们证明了它有一个右伴随。我们使用了来自局部表象范畴论的技术,以及来自商归纳-归纳类型的技术。
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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