Working in a variant of the intersection type assignment system of Coppo, Dezani-Ciancaglini and Veneri [1981], we prove several facts about sets of terms having a given intersection type. Our main result is that every strongly normalizing term $M$ admits a *uniqueness typing*, which is a pair $(\Gamma,A)$ such that 1) $\Gamma \vdash M : A$ 2) $\Gamma \vdash N : A \Longrightarrow M =_{\beta\eta} N$ We also discuss several presentations of intersection type algebras, and the corresponding choices of type assignment rules.

中文翻译：

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交集类型的唯一性键入

在Coppo，Dezani-Ciancaglini和Veneri [1981]的交集类型分配系统的变体中，我们证明了关于具有给定交集类型的术语集的几个事实。我们的主要结果是，每个强规范化项$ M $都接受一个*唯一性键入*，它是一对$（\ Gamma，A）$，这样1）$ \ Gamma \ vdash M：A $ 2）$ \ Gamma \ vdash N：A \ Longrightarrow M = _ {\ beta \ eta} N $我们还将讨论交集类型代数的几种表示形式以及类型分配规则的相应选择。