Induction and Co-induction in Sequent Calculus

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

Volumn 3085, Issue , 2004, Pages 293-308

  Momigliano, Alberto ^a,d   Tiu, Alwen ^b,c  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b UNIVERSITY OF MILAN   (Italy)

^c ÉCOLE POLYTECHNIQUE   (France)

^d PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DIFFERENTIATION (CALCULUS); HYBRID SYSTEMS; LOGIC PROGRAMMING; PROLOG (PROGRAMMING LANGUAGE); SYNTACTICS;

COMPUTATION SYSTEMS; CUT ELIMINATION; HIGHER-ORDER ABSTRACT SYNTAX; LAMBDA CALCULUS; LOGIC PROGRAMS; PROOF-THEORETIC NOTIONS; PROTOTYPE IMPLEMENTATIONS; SEQUENT CALCULUS;

CALCULATIONS;

EID: 35048859203     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24849-1_19     Document Type: Article

References (31)

1. A. Abel and T. Altenkirch. A predicative strong normalisation proof for a λ-calculus with interleaving inductive types. In T. Coquand, P. Dybjer, B. Nordström, and J. Smith, editors, Types for Proof and Programs, International Workshop, TYPES '99, vol 1956 of Lecture Notes in Computer Science, pp 21-40. Springer-Verlag, 2000.
2. P. Aczel. An introduction to inductive definitions. In J. Barwise, editor, Handbook of Mathematical Logic, vol 90 of Studies in Logic and the Foundations of Mathematics, pp 739-782. North-Holland, Amsterdam, 1977.
3. S. Ambler, R. Croie, and A. Momigliano. Combining higher order abstract syntax with tactical theorem proving and (co)induction. In V. A. Carreño, editor, Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics, Hampton, VA, 1-3 August 2002, vol 2342 of LNCS. Springer Verlag, 2002.
4. C. Bohm and A. Berarducci. Automatic synthesis of typed lambda programs on term algebras. Theoretical Computer Science, 39(2-3):135-153, Aug. 1985.
5. R. L. Croie. Lectures on [Co]Induction and [Co]Algebras. Technical Report 1998/12, Department of Mathematics and Computer Science, University of Leicester, 1998.
6. N. de Bruijn. A plea for weaker frameworks. In G. Huet and G. Plotkin, editors, Logical Frameworks, pp 40-67. Cambridge University Press, 1991.
7. J. Despeyroux and A. Hirschowitz. Higher-order abstract syntax with induction in Coq. In Fifth Conference on Logic Programming and Automated Reasoning, pp 159-173, 1994.
8. H. Geuvers. Inductive and coinductive types with iteration and recursion. In B. Nordström, K. Pettersson, and G. Plotkin, editors, Informal Proceedings Workshop on Types for Proofs and Programs, Båstad, Sweden, 8-12 June 1992, pp 193-217. Dept. of Computing Science, Chalmers Univ. of Technology and Göteborg Univ., 1992.
9. E. Giménez. Un Calcul de Constructions Infinies et son Application a la Verification des Systemes Communicants. PhD thesis PhD 96-11, Laboratoire de l'Informatique du Parallélisme, Ecole Normale Supérieure de Lyon, Dec. 1996.
10. J.-Y. Girard. A fixpoint theorem in linear logic. Email to the linear@cs.stanford.edu mailing list, February 1992.
11. R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. Journal of the ACM, 40(1):143-184, 1993.
12. F. Honsell, M. Miculan, and I. Scagnetto. An axiomatic approach to metareasoning on systems in higher-order abstract syntax. In Proc. ICALP'01, number 2076 in LNCS, pp 963-978. Springer-Verlag, 2001.
13. P. Martin-Löf. Hauptsatz for the intuitionistic theory of iterated inductive definitions. In J. Fenstad, editor, Proceedings of the Second Scandinavian Logic Symposium, vol 63 of Studies in Logic and the Foundations of Mathematics, pp 179-216. North-Holland, 1971.
14. R. McDowell and D. Miller. Cut-elimination for a logic with definitions and induction. Theoretical Computer Science, 232:91-119, 2000.
15. R. McDowell and D. Miller. Reasoning with higher-order abstract syntax in a logical framework. ACM Transactions on Computational Logic, 3(1):80-136, January 2002.
16. R. McDowell, D. Miller, and C. Palamidessi. Encoding transition systems in sequent calculus. TCS, 294(3):411-437, 2003.
17. N. P. Mendier. Inductive types and type constraints in the second order lambda calculus. Annals of Pure and Applied Logic, 51(1):159-172, 1991.
18. D. Miller and A. Tiu. A proof theory for generic judgments: An extended abstract. Proceedings of LICS'03, January 2003.
19. A. Momigliano and S. Ambler. Multi-level meta-reasoning with higher order abstract syntax. In A. Gordon, editor, FOSSACS'03, vol 2620 of LNCS, pp 375-392. Springer, 2003.
20. C. Paulin-Mohring. Inductive definitions in the system Coq: Rules and properties. In M. Bezem and J. Groote, editors, Proc. of the International Conference on Typed Lambda Calculi and Applications, pp 328-345, Utrecht, Mar. 1993. Springer-Verlag LNCS 664.
21. L. C. Paulson. Mechanizing coinduction and corecursion in higher-order logic. Journal of Logic and Computation, 7(2):175-204, Mar. 1997.
22. F. Pfenning. Logical frameworks. In Handbook of Automated Reasoning, pp 1063-1147. MIT Press, 2001.
23. E. Rohwedder and F. Pfenning. Mode and termination analysis for higher-order logic programs. In Proc. of the European Symposium on Programming, pp 296-310, April 1996.
24. L. Santocanale. A calculus of circular proofs and its categorical semantics. In M. Nielsen and U. Engberg editors, Proc. of 5th Int. Conf. on Foundations of Software Science and Computation Structures, FoSSaCS 2002, pp 357-371, Grenoble, Apr. 2002, Springer-Verlag LNCS 2303.
25. P. Schroeder-Heister. Cut-elimination in logics with definitional reflection. In D. Pearce and H. Wansing, editors, Nonclassical Logics and Information Processing, vol 619 of LNCS, pp 146-171. Springer, 1992.
26. P. Schroeder-Heister. Definitional reflection and the completion. In R. Dyckhoff, editor, Proceedings of the 4th International Workshop on Extensions of Logic Programming, pp 333-347. Springer-Verlag LNAI 798, 1993.
27. P. Schroeder-Heister. Rules of definitional reflection. In M. Vardi, editor, Eighth Annual Symposium on Logic in Computer Science, pp 222-232. IEEE Press, June 1993.
28. C. Schürmann. Automating the Meta-Theory of Deductive Systems. PhD thesis, Carnegie-Mellon University, 2000. CMU-CS-00-146.
29. A. K. Simpson. Compositionality via cut-elimination: Hennessy-Milner logic for an arbitrary GSOS. In D. Kozen, editor, Proceedings of LICS'95, pp 420-430, San Diego, California, June 1995. IEEE Computer Society Press.
30. C. Spenger and M. Dams. On the structure of inductive reasoning: Circular and tree-shaped proofs in the μ-calculus. In A. Gordon, editor, FOSSACS'03, vol 2620 of LNCS, pp 425-440, Springer Verlag, 2003.
31. A. Tiu. Cut-elimination for a logic with induction and co-induction. Draft, available via http://www.cse.psu.edu/tiu/lce.pdf, Sept. 2003.