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Comparing Cubes of Typed and Type Assignment Systems

Steffen van Bakel, Luigi Liquori, Simona Ronchi delle Rocca, Pawel Urzyczyn

Journal Article
Annals of Pure and Applied Logic
Volume 86
Issue 3
July, 1997
DOI 10.1016/S0168-0072(96)00036-X

We study the Giannini-Honsell-Ronchi `cube of type assignment systems', and confront it with Barendregt's typed lambda-cube. The first is obtained from the latter through applying a natural type erasing function E to derivation rules, that erases type information from terms. In particular, we address the question whether a judgement, derivable in a type assignment system, is always an erasure of a derivable judgement in a corresponding typed system; we show that this property holds only for the systems without polymorphism. The type assignment systems we consider satisfy the properties `subject reduction' and `strong normalization'. Moreover, we define a new type assignment cube that is isomorphic to the typed one.

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