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Conference Papers Year : 2021

An Anti-Locally-Nameless Approach to Formalizing Quantifiers

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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Dates and versions

hal-03096253 , version 1 (04-01-2021)

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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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