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Communication Dans Un Congrès Année : 2014

Confluence for classical logic through the distinction between values and computations

Résumé

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.

Dates et versions

hal-03252258 , version 1 (07-06-2021)

Identifiants

Citer

José Espirito Santo, Ralph Matthes, Koji Nakazawa, Luis Pinto. Confluence for classical logic through the distinction between values and computations. 5th International Workshop on Classical Logic and Computation (CL&C 2014), Jul 2014, Vienne, Austria. pp.63--77, ⟨10.4204/EPTCS.164.5⟩. ⟨hal-03252258⟩
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