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Strong normalization of lambda-bar-mu-mu-tilde-calculus with explicit substitutions

Abstract : The lambda-bar-mu-mu-tilde-calculus, defined by Curien and Herbelin, is a variant of the lambda-mu-calculus that exhibits symmetries such as terms/contexts and call-by-name/call-by-value. Since it is a symmetric, and hence a non-deterministic calculus, usual proof techniques of normalization needs some adjustments to work in this setting. Here we prove the strong normalization (SN) of simply typed lambda-bar-mu-mu-tilde-calculus with explicit substitutions. For that purpose, we first prove SN of simply typed lambda-bar-mu-mu-tilde-calculus (by a variant of the reducibility technique from Barbanera and Berardi), then we formalize a proof technique of SN via PSN (preservation of strong normalization), and we prove PSN by the perpetuality technique, as formalized by Bonelli.
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Contributor : Emmanuel Polonowski <>
Submitted on : Tuesday, February 22, 2005 - 1:56:22 PM
Last modification on : Saturday, March 28, 2020 - 2:20:09 AM
Long-term archiving on: : Thursday, April 1, 2010 - 8:39:51 PM


  • HAL Id : hal-00004321, version 1



Emmanuel Polonovski. Strong normalization of lambda-bar-mu-mu-tilde-calculus with explicit substitutions. FOSSACS, 2004, Barcelona, Spain. pp.423-437. ⟨hal-00004321⟩



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