Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/11161
Título: | Towards a canonical classical natural deduction system |
Autor(es): | Espírito Santo, José |
Data: | 2010 |
Editora: | Springer |
Revista: | Lecture Notes in Computer Science |
Citação: | DAWAR, Anuj ; VEITH , Helmut, ed. lit. – “Computer science logic : proceedings of the Annual Conference of the EACSL, 19, Brno, Czech Republic, 2010”. Berlin : Springer, cop. 2010. ISBN 978-3-642-15204-7. p. 290-304. |
Resumo(s): | This paper studies a new classical natural deduction system, presented as a typed calculus named $\lml$. It is designed to be isomorphic to Curien-Herbelin's calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's $\lambda\mu$-calculus with the idea of ``coercion calculus'' due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction system for classical logic. $\lml$ is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics of Curien-Herbelin's calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by $\lml$. The third problem is the lack of a robust process of ``read-back'' into natural deduction syntax of calculi in the sequent calculus format, that affects mainly the recent proof-theoretic efforts of derivation of $\lambda$-calculi for call-by-value. An isomorphic counterpart to the $Q$-subsystem of Curien-Herbelin's-calculus is derived, obtaining a new $\lambda$-calculus for call-by-value, combining control and let-expressions. |
Tipo: | Artigo em ata de conferência |
URI: | https://hdl.handle.net/1822/11161 |
ISBN: | 9783642152047 |
DOI: | 10.1007/978-3-642-15205-4_24 |
ISSN: | 0302-9743 |
Versão da editora: | www.springerlink.com |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
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Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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TowardsClassicalNatDed.pdf | 232,13 kB | Adobe PDF | Ver/Abrir |