  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.
