## Explicit Substitutions and Reducibility (2001)

Venue: | Journal of Logic and Computation |

Citations: | 7 - 1 self |

### BibTeX

@ARTICLE{Herbelin01explicitsubstitutions,

author = {Hugo Herbelin},

title = {Explicit Substitutions and Reducibility},

journal = {Journal of Logic and Computation},

year = {2001},

volume = {11},

pages = {2001}

}

### OpenURL

### Abstract

. We consider reducibility sets dened not by induction on types but by induction on sequents as a tool to prove strong normalization of systems with explicit substitution. To illustrate this point, we give a proof of strong normalization (SN) for simply-typed call-by-name ~-calculus enriched with operators of explicit unary substitutions. The ~-calculus, dened by Curien & Herbelin, is a variant of -calculus with a let operator that exhibits symmetries such as terms/contexts and call-byname /call-by-value reduction. The ~-calculus embeds various standard -calculi (and Gentzen's style sequent calculi too) and as an application we derive the strong normalization of Parigot's simply-typed -calculus with explicit substitution. Introduction Explicit substitution in -calculus The traditional theory of -calculus relies on -reduction, that is the capture by a function of its argument followed by the process of substituting this argument to the places where it is used. The ...