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arXiv · 2105.02352

Uniqueness typing for intersection types

Richard Statman·Andrew Polonsky
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Abstract

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.

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Richard Statman, Andrew Polonsky. 2021-05-05. Uniqueness typing for intersection types. https://arxiv.org/abs/2105.02352

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