Since it was realized that the Curry-Howard isomorphism can be extended to the case of classical logic as well, several calculi have appeared as candidates for the encodings of proofs in classical logic. One of the most extensively studied among them is the $\lambda\mu$-calculus of Parigot. In this paper, based on the result of Xi presented for the $\lambda$-calculus Xi, we give an upper bound for the lengths of the reduction sequences in the $\lambda\mu$-calculus extended with the $\rho$- and $\theta$-rules. Surprisingly, our results show that the new terms and the new rules do not add to the computational complexity of the calculus despite the fact that $\mu$-abstraction is able to consume an unbounded number of arguments by virtue of the $\mu$-rule.

Source : oai:arXiv.org:1703.05930

DOI : 10.23638/LMCS-14(2:17)2018

Volume: Volume 14, Issue 2

Published on: June 22, 2018

Submitted on: March 20, 2017

Keywords: Mathematics - Logic

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