The Russell-Prawitz embedding and the atomization of universal instantiation

Espírito Santo, José; Ferreira, Gilda

http://hdl.handle.net/10400.2/10493

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Authors

Espírito Santo, José

Ferreira, Gilda

Abstract(s)

Given the recent interest in the fragment of system F where universal instantiation is restricted to atomic formulas, a fragment nowadays named system Fat, we study directly in system F new conversions whose purpose is to enforce that restriction. We show some benefits of these new atomization conversions: (1) They help achieving strict simulation of proof reduction by means of the Russell-Prawitz embedding of IPC into system F; (2) They are not stronger than a certain “dinaturality” conversion known to generate a consistent equality of proofs; (3) They provide the bridge between the Russell-Prawitz embedding and another translation, due to the authors, of IPC directly into system Fat; (4) They give means for explaining why the Russell-Prawitz translation achieves strict simulation whereas the translation into Fat does not.