0137-2904

Instantiation overflow

Dinis

Bruno

author Ferreira

Gilda

author

Departamento de Matematica, Faculdade de Ciencias da Universidade de Lisboa, Campo Grande, Ed. C6, 1749-016, Lisboa, Portugal

Correspondence to: Bruno Dinis bmdinis@fc.ul.pt Correspondence to: Gilda Ferreira gmferreira@fc.ul.pt

14 09 2016

Number 51 2016 15 33

2016

The well-known embedding of full intuition- istic propositional calculus into the atomic polymorphic system Fat is possible due to the intriguing phenomenon of instantiation overflow. Instantiation overflow 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 overflow? In this paper we show that the answer is yes and we isolate a class of formulas with such property.

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