In this paper we explore a family of type isomorphisms in System F whose validity corresponds, semantically, to some form of the Yoneda isomorphism from category theory. These isomorphisms hold under theories of equivalence stronger than beta-eta-equivalence, like those induced by parametricity and dinaturality. We show that the Yoneda type isomorphisms yield a rewriting over types, that we call Yoneda reduction, which can be used to eliminate quantifiers from a polymorphic type, replacing them with a combination of monomorphic type constructors. We establish some sufficient conditions under which quantifiers can be fully eliminated from a polymorphic type, and we show some application of these conditions to count the inhabitants of a type and to compute program equivalence in some fragments of System F.

中文翻译：

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多态类型的米田归约（扩展版）

在本文中，我们探讨了系统 F 中的一系列类型同构，其有效性在语义上对应于来自范畴论的某种形式的米田同构。这些同构在比 beta-eta-等价更强大的等价理论下成立，就像那些由参数化和非自然性引起的。我们展示了 Yoneda 类型同构产生了对类型的重写，我们称之为 Yoneda 约简，它可用于从多态类型中消除量词，用单态类型构造函数的组合替换它们。我们建立了一些充分条件，在这些条件下，量词可以从多态类型中完全消除，并且我们展示了这些条件在计算类型的居民和计算系统 F 的某些片段中的程序等效性的一些应用。