A Finitary Subsystem of the Polymorphic λ-Calculus
We give a finitary normalisation proof for the restriction of system F where we quantify only over first-order type. As an application, the functions representable in this fragment are exactly the ones provably total in Peano Arithmetic. This is inspired by the reduction of π1 1-comprehension to inductive definitions presented in [Buch2] and this complements a result of [Leiv]. The argument uses a finitary model of a fragment of the system AF2 considered in Kriv,Leiv.
KeywordsKripke Model Proof Theory Finitary Model Peano Arithmetic Implicative Algebra
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