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Focused Linear Logic and the λ-calculus

Taus Brock-Nannestad 1 Nicolas Guenot 2
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : Linear logic enjoys strong symmetries inherited from classical logic while providing a constructive framework comparable to intuitionistic logic. However, the computational interpretation of sequent calculus presentations of linear logic remains problematic, mostly because of the many rule permutations allowed in the sequent calculus. We address this problem by providing a simple interpretation of focused proofs, a complete subclass of linear sequent proofs known to have a much stronger structure than the standard sequent calculus for linear logic. Despite the classical setting, the interpretation relates proofs to a refined linear λ-calculus, and we investigate its properties and relation to other calculi, such as the usual λ-calculus, the λµ-calculus, and their variants based on sequent calculi.
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https://hal.inria.fr/hal-01249220
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Taus Brock-Nannestad, Nicolas Guenot. Focused Linear Logic and the λ-calculus. Mathematical Foundations of Programming Semantics XXXI, Jun 2015, Nijmegen, Netherlands. ⟨10.1016/j.entcs.2015.12.008⟩. ⟨hal-01249220⟩

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