An abstract factorization theorem for explicit substitutions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2012

An abstract factorization theorem for explicit substitutions


We study a simple form of standardization, here called factorization, for explicit substitutions calculi, i.e. lambda-calculi where beta-reduction is decomposed in various rules. These calculi, despite being non-terminating and non-orthogonal, have a key feature: each rule terminates when considered separately. It is well-known that the study of rewriting properties simplifies in presence of termination (e.g. confluence reduces to local confluence). This remark is exploited to develop an abstract theorem deducing factorization from some axioms on local diagrams. The axioms are simple and easy to check, in particular they do not mention residuals. The abstract theorem is then applied to some explicit substitution calculi related to Proof-Nets. We show how to recover standardization by levels, we model both call-by-name and call-by-value calculi and we characterize linear head reduction via a factorization theorem for a linear calculus of substitutions.
Fichier principal
Vignette du fichier
RTA2012-1.pdf (560.41 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00780344 , version 1 (23-01-2013)


  • HAL Id : hal-00780344 , version 1


Beniamino Accattoli. An abstract factorization theorem for explicit substitutions. 23rd International Conference on Rewriting Techniques and Applications (RTA'12), May 2012, Nagoya, Japan. ⟨hal-00780344⟩
370 View
133 Download


Gmail Facebook X LinkedIn More