Uniqueness typing for intersection types

05/05/2021

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by   Richard Statman, et al.

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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 (Γ,A) such that 1) Γ⊢ M : A 2) Γ⊢ N : A ⟹ M =_βη N We also discuss several presentations of intersection type algebras, and the corresponding choices of type assignment rules.