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https://hdl.handle.net/1822/3863
Título: | An isomorphism between a fragment of sequent calculus and an extension of natural deduction |
Autor(es): | Espírito Santo, José |
Palavras-chave: | Cut-elimination Normalisation $\lambda$-calculus |
Data: | 2002 |
Editora: | Springer |
Revista: | Lecture Notes in Computer Science |
Citação: | BAAZ, Matthias ; VORONKOV, Andrei, ed. – “Logic for programming, artificial intelligence, and reasoning : 9th International Conference, LPAR 2002, Tbilisi, Georgia, October 14-18, 2002 : proceedings”. Berlin [etc.] : Springer, cop. 2002. ISBN 3-540-00010-0. p. 352-366. |
Resumo(s): | Variants of Herbelin's $\lambda$-calculus, here collectively named Herbelin calculi, have proved useful both in foundational studies and as internal languages for the efficient representation of $\lambda$-terms. An obvious requirement of both these two kinds of applications is a clear understanding of the relationship between cut-elimination in Herbelin calculi and normalisation in the $\lambda$-calculus. However, this understanding is not complete so far. Our previous work showed that $\lambda$ is isomorphic to a Herbelin calculus, here named lambda-P, only admitting cuts that are both left- and right-permuted. In this paper we consider a generalisation lambda-Ph admitting any kind of right-permuted cut. We show that there is a natural deduction system lambda-Nh which conservatively extends $\lambda$ and is isomorphic to lambda-Ph. The idea is to build in the natural deduction system a distinction between applicative term and application, together with a distinction between head and tail application. This is suggested by examining how natural deduction proofs are mapped to sequent calculus derivations according to a translation due to Prawitz. In addition to $\beta$, lambda-Nh includes a reduction rule that mirrors left permutation of cuts, but without performing any append of lists/spines. |
Tipo: | Artigo em ata de conferência |
URI: | https://hdl.handle.net/1822/3863 |
ISBN: | 3540000100 |
ISSN: | 0302-9743 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
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