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An Anti-Locally-Nameless Approach to Formalizing Quantifiers

Olivier Laurent 1, 2
2 PLUME - Preuves et Langages
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We investigate the possibility of formalizing quantifiers in proof theory while avoiding, as far as possible, the use of true binding structures, α-equivalence or variable renamings. We propose a solution with two kinds of variables in terms and formulas, as originally done by Gentzen. In this way formulas are first-order structures, and we are able to avoid capture problems in substitutions. However at the level of proofs and proof manipulations, some binding structure seems unavoidable. We give a representation with de Bruijn indices for proof rules which does not impact the formula representation and keeps the whole set of definitions firstorder.
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https://hal.archives-ouvertes.fr/hal-03096253
Contributor : Olivier Laurent Connect in order to contact the contributor
Submitted on : Monday, January 4, 2021 - 9:33:19 PM
Last modification on : Saturday, September 11, 2021 - 3:19:42 AM
Long-term archiving on: : Monday, April 5, 2021 - 9:51:22 PM

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Olivier Laurent. An Anti-Locally-Nameless Approach to Formalizing Quantifiers. Certified Programs and Proofs, Jan 2021, virtual, Denmark. pp.300-312, ⟨10.1145/3437992.3439926⟩. ⟨hal-03096253⟩

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