2014/09/11 by José Espírito Santo, Ralph Matthes, Koji Nakazawa +1
Computer Science · #cs.LO
paper · pdf · doi:10.4204/eptcs.164.5
published as EPTCS 164, 2014, pp. 63-77 · In Proceedings CL&C 2014, arXiv:1409.2593
arxiv created 2014/09/11 · arxiv updated 2014/09/12
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.