Structural cut elimination: I. Intuitionistic and classical logic

Information and Computation

Volumn 157, Issue 1-2, 2000, Pages 84-141

  Pfenning, Frank ^a  

^a Carnegie Mellon University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; LOGIC PROGRAMMING; THEOREM PROVING;

STRUCTURAL CUT ELIMINATION;

FORMAL LOGIC;

EID: 0034711981     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1006/inco.1999.2832     Document Type: Article

References (31)

1. Abramsky, S. (1993), Computational interpretations of linear logic, Theoret. Comput. Sci. 111, 3-57.
2. Breazu-Tannen, V., Kesner, D., and Puel, L. (1993), A typed pattern calculus, in "Proceedings of the Eight Annual IEEE Symposium on Logic in Computer Science, Montreal, Canada" (Moshe Y. Vardi, Ed.), pp. 262-274.
3. Dowek, G., Felty, A., Herbelin, H., Huet, G., Murthy, C., Parent, C., Paulin-Mohring, Ch., and Werner, B. (1993), "The Coq proof assistant user's guide," Rapport Techniques 154, INRIA, Rocquencourt, France. [Version 5.8].
4. Despeyroux, J, Felty, A, and Hirschowitz, A (1995), Higher-order abstract syntax in Coq, in "Proceedings of the International Conference on Typed Lambda Calculi and Applications, Edinburgh, Scotland" (M. Dezani-Ciancaglini and G. Plotkin, Eds.), Lecture Notes in Computer Science, Vol. 902, pp. 124-138, Springer-Verlag, Berlin/New Nork.
5. Despeyroux, J., and Hirschowitz, A. (1994), Higher-order abstract syntax with induction in Coq, in "Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning, Kiev, Ukraine" (Frank Pfenning, Ed.), Lecture Notes in Artificial Intelligence, Vol. 822, pp. 159-173, Springer-Verlag, Berlin/New York.
6. Dragalin, A. G. (1987), "Mathematical Intuitionism: Introduction to Proof Theory," Translations of Mathematical Monographs, Vol. 67, Amer. Math. Soc., Providence, RI.
7. Felty, A. (1989), "Specifying and Implementing Theorem Provers in a Higher-Order Logic Programming Language," Ph.D. thesis, University of Pennsylvania. [Available as Technical Report MS-CIS-89-53]
8. Gallier, J. (1993), Constructive logics. A tutorial on proof systems and typed λ-calculi, Theoret. Comput. Sci. 110, 249-339.
9. Gentzen, G. (1935), Untersuchungen über das logische Schließen, Math. Z. 39, 176-210, 405-431;
10. English translation in Szabo, M. E., Ed. (1969), "The Collected Papers of Gerhard Gentzen," pp. 68-131, North-Holland, Amsterdam.
11. Girard, J.-Y. (1987), Linear logic, Theoret. Comput. Sci. 50, 1-102.
12. Girard, J.-Y. (1993), On the unity of logic, Ann. Pure Appl. Logic 59, 201-217.
13. Herbelin, H. (1995), "Séquents qu'on Calcule," Ph.D. thesis, Université Paris 7.
14. Harper, R., Honsell, F., and Plotkin, G. (1993), A framework for defining logics, J. Assoc. Comput. Mach. 40(1), 143-184.
15. Kleene, S. C. (1952), "Introduction to Metamathematics," North-Holland, Amsterdam.
16. 0, in "What is a Logical System?" (Dov Gabbay and Franz Guenthner, Ed.), Oxford Univ. Press, London.
17. Miller, D. (1994), A multiple-conclusion meta-logic, in "Ninth Annual IEEE Symposium on Logic in Computer Science, Paris, France" (S. Abramsky, Ed.), pp. 272-281.
18. Martin-Löf, P. (1968), "Notes on Constructive Mathematics," Almqvist & Wiksell, Stockholm.
19. Miller, D., Nadathur, G., Pfenning, F., and Scedrov, A. (1991), Uniform proofs as a foundation for logic programming, Ann. Pure Appl. Logic 51, 125-157.
20. Michaylov, S., and Pfenning, F. (1991), Natural semantics and some of its meta-theory in Elf, in "Proceedings of the Second International Workshop on Extensions of Logic Programming, Stockholm, Sweden" (L.-H. Eriksson, L. Hallnäs, and P. Schroeder-Heister, Eds.), Lecture Notes in Artificial Intelligence, Vol. 596, pp. 299-344, Springer-Verlag, Berlin/New York.
21. Nipkow, T. (1991), Higher-order critical pairs, in "Sixth Annual IEEE Symposium on Logic in Computer Science, Amsterdam, The Netherlands" (G. Kahn, Ed.), pp. 342-349.
22. Parigot, M. (1992), λμ-calculus: An algorithmic interpretation of classical natural deduction, in "Proceedings of the International Conference on Logic Programming and Automated Reasoning, St. Petersburg, Russia" (A. Voronkov, Ed.), Lecture Notes in Computer Science, Vol. 624, pp. 190-201, Springer-Verlag, Berlin/New York.
23. Pfenning, F., Structural cut elimination. II. Linear logic, in preparation.
24. Pfenning, F. (1991), Logic programming in the LF logical framework, in "Logical Frameworks" (Gérard Huet and Gordon Plotkin, Eds.), pp. 149-181, Cambridge Univ. Press, Cambridge, UK.
25. Pfenning, F. (1994), "Structural Cut Elimination in Linear Logic," Technical Report CMU-CS-94-222, Department of Computer Science, Carnegie Mellon University.
26. Pfenning, F. (1995), Structural cut elimination, in "Proceedings of the Tenth Annual Symposium on Logic in Computer Science, San Diego, California" (D. Kozen, Ed.), IEEE Comput. Soc., Los Alamitos, CA.
27. Rohwedder, E. (1994), "Verifying the Meta-theory of Deductive Systems," thesis proposal.
28. Schwichtenberg, H. (1977), Proof theory: Some applications of cut-elimination, in "Handbook of Mathematical Logic," pp. 867-895, North-Holland, Amsterdam.
29. Virga, R. (1995), "Higher-order superposition for dependent types," Technical Report CMU-CS-95-150, Carnegie Mellon University.
30. Wallen L. A. (1990), "Automated Deduction in Non-Classical Logics," MIT Press, Cambridge, MA.
31. Zucker, J. (1974), The correspondence between cut-elimination and normalization, I, Ann. Math. Logic 7, 1-112.