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This article is devoted to the presentation of lambda_rex, an explicitsubstitution calculus with de Bruijn indexes and a simple notation. By beingisomorphic to lambda_ex - a recent formalism with variable names -, lambda_rexaccomplishes simulation of beta-reduction (Sim), preservation of beta-strongnormalization (PSN) and meta-confluence (MC), among other desirable properties.Our calculus is based on a novel presentation of lambda_dB, using a swap notionthat was originally devised by de Bruijn. Besides lambda_rex, two other indexedcalculi isomorphic to lambda_x and lambda_xgc are presented, demonstrating thepotential of our technique when applied to the design of indexed versions ofknown named calculi.

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