Skip to Main content Skip to Navigation
Journal articles

A lambda-calculus with explicit weakening and explicit substitution

René David 1 Bruno Guillaume 2
2 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Since Melliès has shown that lambda-sigma (a calculus of explicit substitutions) does not preserve the strong normalization of the beta-reduction, it became a challenge to find a calculus satisfying the following properties: step by step simulation of the beta-reduction, confluence on terms with metavariables, strong normalization of the calculus of substitutions and preservation of the strong normalization of the lambda-calculus. We present here such a calculus. The main novelty of the calculus (given with de Bruijn indices) is the use of labels that represent updating functions and correspond to explicit weakening. A typed version is also presented.
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download
Contributor : René David <>
Submitted on : Friday, May 15, 2009 - 4:05:48 PM
Last modification on : Thursday, January 11, 2018 - 6:19:48 AM
Document(s) archivé(s) le : Thursday, June 10, 2010 - 11:15:23 PM


Files produced by the author(s)


  • HAL Id : hal-00384683, version 1



René David, Bruno Guillaume. A lambda-calculus with explicit weakening and explicit substitution. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2001, 11 (1), pp.169-206. ⟨hal-00384683⟩



Record views


Files downloads