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

By Ariel Mendelzon, Alejandro Ríos and Beta Ziliani

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.Comment: In Proceedings HOR 2010, arXiv:1102.346

Topics: Computer Science - Logic in Computer Science, Computer Science - Programming Languages
Year: 2011
DOI identifier: 10.4204/EPTCS.49.1
OAI identifier: oai:arXiv.org:1102.3730
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