Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we investigate System Fat, or atomic System F, a very weak predicative fragment of System F whose typable terms coincide with the simply typable ones. We show that the type-checking problem for Fat is decidable and we propose an algorithm which sheds some new light on the source of undecidability in full System F. Moreover, we investigate free theorems and contextual equivalence in this fragment, and we show that the latter, unlike in the simply typed lambda-calculus, is undecidable.

中文翻译：

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关于（原子）多态性的决定

由于无法确定系统F的大多数类型相关属性（如类型居住或类型检查），因此对受限多态系统进行了广泛研究（最著名的是ML多态性）。在本文中，我们研究了系统胖，即原子系统F，它是系统F的非常弱的谓语片段，其可键入项与简单可键入项相吻合。我们证明Fat的类型检查问题是可判定的，并且我们提出了一种算法，该算法为整个系统F的不可判定性来源提供了一些新的认识。此外，我们研究了该片段中的自由定理和上下文等价关系，并且我们发现与简单类型的lambda微积分不同，后者是不可确定的。