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arXiv · 1102.3730

Swapping: a natural bridge between named and indexed explicit substitution calculi

Ariel Mendelzon·Alejandro Ríos·Beta Ziliani
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Abstract

This article is devoted to the presentation of lambda_rex, an explicit substitution calculus with de Bruijn indexes and a simple notation. By being isomorphic to lambda_ex - a recent formalism with variable names -, lambda_rex accomplishes simulation of beta-reduction (Sim), preservation of beta-strong normalization (PSN) and meta-confluence (MC), among other desirable properties. Our calculus is based on a novel presentation of lambda_dB, using a swap notion that was originally devised by de Bruijn. Besides lambda_rex, two other indexed calculi isomorphic to lambda_x and lambda_xgc are presented, demonstrating the potential of our technique when applied to the design of indexed versions of known named calculi.

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Ariel Mendelzon, Alejandro Ríos, Beta Ziliani. 2011-02-18. Swapping: a natural bridge between named and indexed explicit substitution calculi. https://doi.org/10.4204/eptcs.49.1

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