Arithmetical proofs of strong normalization results for symmetric lambda calculi

René David; Karim Nour

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arXiv · 0905.0762

Arithmetical proofs of strong normalization results for symmetric lambda calculi

René David·Karim Nour

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Abstract

We give arithmetical proofs of the strong normalization of two symmetric $λ$-calculi corresponding to classical logic. The first one is the $\barλμ\tildeμ$-calculus introduced by Curien & Herbelin. It is derived via the Curry-Howard correspondence from Gentzen's classical sequent calculus LK in order to have a symmetry on one side between "program" and "context" and on other side between "call-by-name" and "call-by-value". The second one is the symmetric $λμ$-calculus. It is the $λμ$-calculus introduced by Parigot in which the reduction rule $μ'$, which is the symmetric of $μ$, is added. These results were already known but the previous proofs use candidates of reducibility where the interpretation of a type is defined as the fix point of some increasing operator and thus, are highly non arithmetical.

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BibTeX RIS

René David, Karim Nour. 2009-05-06. Arithmetical proofs of strong normalization results for symmetric lambda calculi. https://arxiv.org/abs/0905.0762

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