Revisiting the correspondence between cut elimination and normalisation

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1853, Issue , 2000, Pages 600-611

  Espìrito Santo, Josè ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; COMPUTER CIRCUITS; DIFFERENTIATION (CALCULUS);

BETA-REDUCTION; CLASSICAL LOGIC; CUT ELIMINATION; CUT-ELIMINATION PROCEDURE; INTUITIONISTIC LOGIC; NATURAL DEDUCTION; NATURAL DEDUCTION PROOFS; SEQUENT CALCULUS;

CALCULATIONS;

EID: 84974530584     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45022-x_51     Document Type: Conference Paper

References (15)

1. V. Danos, J-B. Joinet, and H. Schellinx. A new deconstructive logic: linear logic. The Journal of Symbolic Logic, 62(2):755-807, 1997.
2. R. Dyckhoff and L. Pinto. Cut-elimination and a permutation-free sequent calculus for intuitionistic logic. Studia Logica, 60:107-118, 1998.
3. R. Dyckhoff and L. Pinto. Permutability of proofs in intuitionistic sequent calculi. Theoretical Computer Science, 212:141-155, 1999.
4. J. Espìrito Santo, 2000. PhD Thesis (in preparation).
5. J. Gallier. Constructive logics. Part I. Theoretical Computer Science, 110:248-339, 1993.
6. H. Herbelin. A λ-calculus structure isomorphic to a Gentzen-style sequent calculus structure. In L. Pacholski and J. Tiuryn, editors, Proceedings of CSL’94, volume 933 of Lecture Notes in Computer Science, pages 61-75. Springer-Verlag, 1995.
7. H. Herbelin. Sequents qu’on calcule, 1995. PhD Thesis, Universitè Paris VII.
8. M. Parigot. λμ-calculus: an algorithmic interpretation of classic natural deduction. In Int. Conf. Logic Prog. Automated Reasoning, volume 624 of Lecture Notes in Computer Science. Springer Verlag, 1992.
9. G. Pottinger. Normalization as a homomorphic image of cut-elimination. Annals of Mathematical Logic, 12:323-357, 1977.
10. D. Prawitz. Natural Deduction. A Proof-Theoretical Study. Almquist and Wiksell, Stockholm, 1965.
11. A.M. Ungar. Normalization, Cut-eliminations and the Theory of Proofs. Number 28 in CSLI Lecture Notes. 1992.
12. C. Urban and G. Bierman. Strong normalisation of cut-elimination in classical logic. In Proceedings of TLCA’99, Lecture Notes in Computer Science. Springer- Verlag, 1999.
13. R. Vestergaard and J. Wells. Cut rules and explicit substitutions. In Second International Workshop on Explicit Substitutions, 1999.
14. P. Wadler. A Curry-Howard isomorphism for sequent calculus, 1993. Manuscript.
15. J. Zucker. The correspondence between cut-elimination and normalization. Annals of Mathematical Logic, 7:1-112, 1974.