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Call-by-value, call-by-name, and strong normalization for the classical sequent calculus

Abstract : We present a typed calculus LambdaXi isomorphic to the implicational fragment of the classical sequent calculus LK. Reductions in LK eliminate the cut-rule by local rewriting steps, which correspond to the evaluation of explicit substitutions in the calculus. This bridges the gap between Curien and Herbelin's LambdaBarMuMu~-calculus and Urban's rewriting system for proofs. Encodings of one into the other are defined, and from one of them we derive the strong normalization of LambdaBarMuMu~. Identifying two reduction strategies CBV and CBN in Urban's rewriting system enables us to derive two corresponding semantics of continuations from those of LambdaBarMuMu~, via the other encoding.
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https://hal.archives-ouvertes.fr/hal-00150290
Contributor : Stéphane Graham-Lengrand <>
Submitted on : Wednesday, May 30, 2007 - 2:46:31 AM
Last modification on : Saturday, March 28, 2020 - 2:08:23 AM

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  • HAL Id : hal-00150290, version 1

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Stéphane Lengrand. Call-by-value, call-by-name, and strong normalization for the classical sequent calculus. Nov 2003, pp.714-730. ⟨hal-00150290⟩

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