In this paper we give an arithmetical proof of the strong normalization of lambda-Sym-Prop of Berardi and Barbanera [1], which can be considered as a formulae-as-types translation of classical propositional logic in natural deduction style. Then we give a translation between the lambda-Sym-Prop-calculus and the lambda-bar-mu-mu-tilde-star-calculus, which is the implicational part of the lambda-bar-mu-mu-tilde-calculus invented by Curien and Herbelin [3] extended with negation. In this paper we adapt the method of David and Nour [4] for proving strong normalization. The novelty in our proof is the notion of zoom-in sequences of redexes, which leads us directly to the proof of the main theorem.

Source : oai:arXiv.org:1706.07246

DOI : 10.23638/LMCS-13(3:34)2017

Volume: Volume 13, Issue 3

Published on: September 28, 2017

Submitted on: September 28, 2017

Keywords: Mathematics - Logic

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