LARGE-SCALE INFORMATICS SYSTEMS LABORATORY

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Publications

The Russell-Prawitz embedding and the atomization of universal instantiation

Publication . Espírito Santo, José; Ferreira, Gilda

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.

2020Journal article

Open access

A refined interpretation of intuitionistic logic by means of atomic polymorphism

Publication . Espírito Santo, José; Ferreira, Gilda

We study an alternative embedding of IPC into atomic system F whose translation of proofs is based, not on instantiation overflow, but instead on the admissibility of the elimination rules for disjunction and absurdity (where these connectives are defined according to the Russell- Prawitz translation). As compared to the embedding based on instantiation overflow, the alternative embedding works equally well at the levels of provability and preservation of proof identity, but it produces shorter derivations and shorter simulations of reduction sequences. Lambda-terms are employed in the technical development so that the algorithmic content is made explicit, both for the alternative and the original embeddings. The investigation of preservation of proof-reduction steps by the alternative embedding enables the analysis of generation of “administrative” redexes. These are the key, on the one hand, to understand the difference between the two embeddings; on the other hand, to understand whether the final word on the embedding of IPC into atomic system F has been said.

2019Journal article

Open access