Confluence for classical logic through the distinction between values and computations

• Main Authors: José Espírito Santo, Ralph Matthes, Koji Nakazawa, Luís Pinto
• Format: Article
• Language: English
• Published: Open Publishing Association 2014-09-01
• Series: Electronic Proceedings in Theoretical Computer Science
• Online Access: http://arxiv.org/pdf/1409.3316v1

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.