Instantiation overflow

The well-known embedding of full intuitionistic propositional calculus into the atomic polymorphic system Fat is possible due to the intriguing phenomenon of instantiation overow. Instantiation overow ensures that (in Fat) we can instantiate certain universal formulas by any formula of the system, not necessarily atomic. Until now only three types in Fat were identified with such property: the types that result from the Prawitz translation of the propositional connectives (, , ) into Fat (or Girard's system F). Are there other types in Fat with instantiation overow ? In this paper we show that the answer is yes and we isolate a class of formulas with such property.

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.