Confluence for classical logic through the distinction between values and computations
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 fr...
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| Published in: | Electronic proceedings in theoretical computer science Vol. 164; no. Proc. CL&C 2014; pp. 63 - 77 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Open Publishing Association
09.09.2014
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| ISSN: | 2075-2180, 2075-2180 |
| Online Access: | Get full text |
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| Summary: | 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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| ISSN: | 2075-2180 2075-2180 |
| DOI: | 10.4204/EPTCS.164.5 |