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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: | Santo, J.E. (2002). An Isomorphism between a Fragment of Sequent Calculus and an Extension of Natural Deduction. In: Baaz, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2002. Lecture Notes in Computer Science(), vol 2514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36078-6_24 |
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: | 978-3-540-00010-5 |
e-ISBN: | 978-3-540-36078-0 |
DOI: | 10.1007/3-540-36078-6_24 |
ISSN: | 0302-9743 |
Versão da editora: | https://link.springer.com/chapter/10.1007/3-540-36078-6_24 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
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