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arXiv · 1409.3316

Confluence for classical logic through the distinction between values and computations

José Espírito Santo·Ralph Matthes·Koji Nakazawa·Luís Pinto
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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.

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José Espírito Santo, Ralph Matthes, Koji Nakazawa, Luís Pinto. 2014-09-11. Confluence for classical logic through the distinction between values and computations. https://doi.org/10.4204/eptcs.164.5

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