Confluence for classical logic through the distinction between values and computations
Abstract
We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus we obtain comprehends the call-by-name and call-by-value fragments of Curien-Herbelin's lambda-bar-mu-mu-tilde-calculus without losing confluence, and is based on a distinction of "modes" in the proof expressions and "mode" annotations in types. Modes resemble colors and polarities, but are quite different: we give meaning to them in terms of a monadic meta-language where the distinction between values and computations is fully explored. This meta-language is a refinement of the classical monadic language previously introduced by the authors, and is also developed in the paper.
Keywords
Cite
@article{arxiv.1409.3316,
title = {Confluence for classical logic through the distinction between values and computations},
author = {José Espírito Santo and Ralph Matthes and Koji Nakazawa and Luís Pinto},
journal= {arXiv preprint arXiv:1409.3316},
year = {2014}
}
Comments
In Proceedings CL&C 2014, arXiv:1409.2593