## Explicit Substitutions for Control Operators (1997)

Citations: | 1 - 0 self |

### BibTeX

@TECHREPORT{Barthe97explicitsubstitutions,

author = {Gilles Barthe and Fairouz Kamareddine and Alejandro Ríos},

title = {Explicit Substitutions for Control Operators},

institution = {},

year = {1997}

}

### OpenURL

### Abstract

. The \Delta-calculus is a -calculus with a local operator closely related to normalisation procedures in classical logic and control operators in functional programming. We introduce \Deltaexp, an explicit substitution calculus for \Delta, show it preserves strong normalisation and that its simply typed version is strongly normalising. Interestingly, \Deltaexp is the first example for which the decency method of showing preservation of strong normalisation (PSN) works whereas the structure preserving method which is based on the decency method does not. In particular, \Deltaexp is a very simple calculus yet is not structure preserving. This shows that the structure preserving notion intended to give a general description of calculi of explicit substitution that satisfy PSN, is restrictive. To our knowledge, \Deltaexp is the first calculus of explicit substitution that is not structure preserving. 5 1 Introduction Explicit substitutions were introduced in [1] as a bridge between -cal...