## Bridging de Bruijn indices and variable names in explicit substitutions calculi (1996)

Venue: | Logic Journal of the Interest Group of Pure and Applied Logic (IGPL |

Citations: | 9 - 6 self |

### BibTeX

@INPROCEEDINGS{Kamareddine96bridgingde,

author = {Fairouz Kamareddine and Alejandro Ríos},

title = {Bridging de Bruijn indices and variable names in explicit substitutions calculi},

booktitle = {Logic Journal of the Interest Group of Pure and Applied Logic (IGPL},

year = {1996},

pages = {6--6}

}

### OpenURL

### Abstract

Calculi of explicit substitutions have almost always been presented using de Bruijn indices with the aim of avoiding ff-conversion and being as close to machines as possible. De Bruijn indices however, though very suitable for the machine, are difficult to human users. This is the reason for a renewed interest in systems of explicit substitutions using variable names. Formal systems of explicit substitutions using variable names is a new area however and we believe, it should not develop without being well-tied to existing work on explicit substitutions. The aim of this paper is to establish a bridge between explicit substitutions using de Bruijn indices and using variable names. In our aim to do so, we provide the t-calculus: a -calculus `a la de Bruijn which can be translated into a -calculus with explicit substitutions written with variables names. We present explicitly this translation and use it to obtain preservation of strong normalisation for t. Moreover, we show several prope...