Axiomatic rewriting theory VI: Residual theory revisited

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

Volumn 2378, Issue , 2002, Pages 24-50

  Melli È S, Paul André ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS;

ALGEBRAIC THEORIES; ASSOCIATIVITY; CHURCH-ROSSER PROPERTY; EXTRACTION PROCEDURE; LAMBDA CALCULUS; OPTIMALITY THEORIES; REWRITING SYSTEMS; REWRITING THEORY;

DIFFERENTIATION (CALCULUS);

EID: 84893451590     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45610-4_4     Document Type: Conference Paper

References (48)

1. E. Artin. Theory ofbraids. Annals of Mathematics. 48(1):101–126, 1947.
2. M. Abadi, L. Cardelli, P.-L. Curien, J.-J. Lévy. “Explicit substitutions”. Journal of Functional Programming, 1(4):375–416, 1991.
3. A. Asperti, C. Laneve. Interaction Systems I: the theory ofoptimal reductions. In Mathematical Structures in Computer Science, Volume 4(4), pp. 457-504, 1995.
4. H. Barendregt. The Lambda Calculus: Its Syntax and Semantics. North Holland, 1985.
5. J. Birman, K.H. Ko and S.J. Lee. A new approach to the word problem in the braid groups. Advances in Math. vol 139-2, pp. 322-353. 1998.
6. G. Boudol. Computational semantics ofterm rewriting systems. In Maurice Nivat and John C. Reynolds (eds), Algebraic methods in Semantics. Cambridge University Press, 1985.
7. M. Bezem, V. van Oostrom and J. W. Klop. Diagram Techniques for Confluence. Information and Computation, Volume 141, No. 2, pp. 172-204, March 15, 1998.
8. P.-L. Curien. An abstract framework for environment machines. Theoretical Computer Science, 82(2):389-402, 31 May 1991.
9. H.B. Curry, R. Feys. Combinatory Logic I. North Holland, 1958.
10. P. Dehornoy. On completeness ofw ord reversing. Discrete Math. 225 pp 93–119, 2000.
11. P. Dehornoy. Complete positive group presentations. Preprint. Université de Caen, 2001.
12. P. Dehornoy, Y. Lafont. Homology of gaussian groups. Preprint. Université de Caen, 2001.
13. F. A. Garside. The braid grup and other groups. Quarterly Journal of Mathematic 20:235–254, 1969.
14. B. Gramlich. Confluence without Termination via Parallel Critical Pairs. Proc. 21st Int. Coll. on Trees in Algebra and Programming (CAAP’96), ed. H. Kirchner. LNCS 1059, pp. 211-225, 1996.
15. G. Gonthier, J.-J. Lévy, P.-A. Melliès. An abstract standardization theorem. Proceedings of the 7th Annual IEEE Symposium on Logic In Computer Science, Santa Cruz, 1992.
16. J.R. Hindley. An abstract form of the Church-Rosser theorem. Journal of Symbolic Logic, vol 34, 1969.
17. G. Huet. Confluent reductions: abstract properties and applications to term rewriting systems. Journal of the ACM, 27(4):797–821, 1980.
18. G. Huet, J.-J. Lévy. Computations in orthogonal rewriting systems. In J.- L. Lassez and G. D. Plotkin, editors, Computational Logic; Essays in Honor of Alan Robinson, pages 394–443. MIT Press, 1991.
19. J.M.E. Hyland. A simple proofofthe Church-Rosser theorem. Manuscript, 1973.
20. J.W. Klop. Combinatory Reduction Systems. Volume 127 of Mathematical Centre Tracts, CWI, Amsterdam, 1980. PhD thesis.
21. J.W. Klop. Term Rewriting Systems. In S. Abramsky, D. Gabbay, T. Maibaum, eds. Handbook of Logic in Computer Science, vol. 2, pp. 2–117. Clarendon Press, Oxford, 1992.
22. J.W. Klop, V. van Oostrom and R. de Vrijer. Course notes on braids. University of Utrec ht and CWI. Draft, 45 pages, July 1998.
23. J.W. Klop, V. van Oostrom and R. de Vrijer. A geometric proofofconfluence by decreasing diagrams Journal of Logic and Computation, Volume 10, No. 3, pp. 437-460, June 2000
24. D. E. Knuth, P.B. Bendix. Simple word problems in universal algebras. In J. Leech (ed) Computational Problems in Abstract Algebra. Pergamon Press, Oxford, 1970. Reprinted in Automation of Reasoning 2. Springer Verlag, 1983.
25. J. Lamping. An algorithm for optimal lambda-calculus reductions. In proceedings of Principles of Programming Languages, 1990.
26. J.-J. Lévy. Réductions correctes et optimales dans le λ-calcul. Thèse de Doctorat d’Etat, Université Paris VII, 1978.
27. J.-J. Lévy. Optimal reductions in the lambda-calculus. In J.P. Seldin and J.R. Hindley, editors, To H.B. Curry,essays on Combinatory Logic,L ambda Calculus, and Formalisms, pp. 159–191.Academic Press, 1980.
28. L. Maranget. Optimal Derivations inWeak Lambda-calculi and in Orthogonal Term Rewriting Systems. Proceedings POPL’91.
29. S. Mac Lane. Categories for the working mathematician. Springer Verlag, 1971.
30. P.-A. Melliès. Description abstraite des systèmes de récriture. Thèse de l’Université Paris VII, December 1996.
31. P.-A. Melliès. Axiomatic Rewriting Theory I: A diagrammatic standardization theorem. 2001. Submitted.
32. P.-A. Melliès. Axiomatic Rewriting Theory IV: A stability theorem in Rewriting Theory. Proceedings of the 14th Annual Symposium on Logic in Computer Science. Indianapolis, 1998.
33. P.-A. Melliès. Braids as a conflict-free rewriting system. Manuscript. Amsterdam, 1995.
34. P.-A. Melliès. Mac Lane’s coherence theorem expressed as a word problem. Manuscript. Paris, 2001.
35. R. Mayr, T. Nipkow. Higher-Order Rewrite Systems and their Confluence. Theoretical Computer Science, 192:3-29, 1998.
36. M. H. A. Newman. On theories with a combinatorial definition of“equiv alence”. Annals of Math. 43(2):223-243, 1942.
37. T. Nipkow. Higher-order critical pairs. In Proceedings of Logic in Computer Science, 1991.
38. V. van Oostrom. Confluence for Abstract and Higher-Order Rewriting. PhD thesis, Vrije Universiteit, Amsterdam, 1994.
39. V. van Oostrom. Confluence by decreasing diagrams. Theoretical Computer Science, 121:259–280, 1994.
40. V. van Oostrom. Higher-order family. In Rewriting Techniques and Applications 96, Lecture Notes in Computer Science 1103, Springer Verlag, 1996.
41. V. van Oostrom. Finite family developments. In Rewriting Techniques and Applications 97, Lecture Notes in Computer Science 1232, Springer Verlag, 1997.
42. V. van Oostrom. Developing developments. Theoretical Computer Science, Volume 175, No. 1, pp. 159-181, March 30, 1997
43. V. van Oostrom and F. van Raamsdonk. Weak orthogonality implies confluence: the higher-order case. In Logical Foundations of Computer Science 94, Lecture Notes in Computer Science 813, Springer Verlag, 1994.
44. V. van Oostrom and R. de Vrijer. Equivalence ofreductions, and Strategies. Chapter 8 of Term Rewriting Systems, a book by TeReSe group. To appear this summer 2002.
45. G.D. Plotkin, Church-Rosser categories. Unpublished manuscript. 1978.
46. F. van Raamsdonk. Confluence and Normalisation for Higher-Order Rewriting. PhD thesis, Vrije Universiteit van Amsterdam, 1996.
47. E.W. Stark. Concurrent transition systems. Theoretical Computer Science 64. May 1989.
48. Y. Toyama. Commutativity ofterm rewriting systems. In K. Fuchi and L. Kott (eds) Programming of Future Generation Computer, vol II, pp. 393–407. North-Holland, 1988.