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Journal Articles Annals of Pure and Applied Logic Year : 1997

Comparing cubes of typed and type assignment systems


We study the cube of type assignment systems, as introduced in [10], and confront it with Barendregt's typed λ-cube [3]. 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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hal-01154638 , version 1 (22-05-2015)



Steffen van Bakel, Luigi Liquori, Simona Ronchi Della Rocca, Pawel Urzyczyn. Comparing cubes of typed and type assignment systems. Annals of Pure and Applied Logic, 1997, 86 Issue 3, pp.267-303. ⟨10.1016/S0168-0072(96)00036-X⟩. ⟨hal-01154638⟩


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