Descendants and origins in term rewriting

Information and Computation

Volumn 159, Issue 1-2, 2000, Pages 59-124

  Bethke, Inge ^a   Klop, Jan Willem ^b,c,d   De Vrijer, Roel ^c  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^c VU UNIVERSITY AMSTERDAM   (Netherlands)

^d CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

INFORMATION ANALYSIS; THEOREM PROVING;

REWRITING;

COMPUTATIONAL METHODS;

EID: 0034713208     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1006/inco.2000.2876     Document Type: Article

References (72)

1. Abramsky, S., and Ong, C.-H. L. (1993), Full abstraction in the lazy lambda calculus, Inform. and Comput. 105, 159-267.
2. Aczel, P. (1978), "A General Church-Rosser Theorem," Technical report, University of Manchester, July.
3. Baader, F., and Nipkow, T. (1998), "Term Rewriting and All That," Cambridge Univ. Press, Cambridge, UK.
4. Barendregt, H. P. (1971), "Some Extensional Term Models for Combinatory Logics and λ-calculi," Ph.D. thesis, University of Utrecht.
5. Barendregt, H. P. (1984), "The Lambda Calculus, its Syntax and Semantics," Studies in Logic and the Foundations of Mathematics, Vol. 103, revised ed., North-Holland, Amsterdam.
6. Barendregt, H. P., Bergstra, J. A., Klop, J. W., and Volken, H. (1976), Degrees, reductions and representability in the lambda calculus, Preprint 22, Department of Mathematics, Utrecht University.
7. Barendregt, H. P., Kennaway, J. R., Klop, J. W., and Sleep, M. R. (1987), Needed reduction and spine strategies for the lambda calculus, Inform. and Comput. 75, 191-231.
8. Berarducci, A., and Intrigua, B. (1996), Church-Rosser λ-theories, infinite λ-terms and consistency problems, in "Logic: From Foundations to Applications; European Logic Colloquium 93, Keele, Staffordshire, England" (C. Steinhorn, W. Hodges, M. Hyland, and J. Truss, Eds.), pp. 33-58, Oxford University Press, Oxford.
9. Berry, G. (1978), Séquentialité de l'évaluation formelle des lambda-expressions, in "Transformations de Programmes; 3e Colloque International sur la Programmation, Paris, France" (B. Robinet, Ed.), pp. 66-80, Dunod, Paris.
10. Berry, G. (1979), "Modèles complètement adéquats et stables des λ-calculs typés," Ph.D. thesis, University of Paris 7.
11. Bertot, Y. (1992), Origin functions in λ-calculus and term rewriting systems, in "17th Colloquium on Trees in Algebra and Programming, CAAP'92, Rennes, France, February 26-28, 1992" (J.-C. Raoult, Ed.), Lecture Notes in Computer Science, Vol. 581, pp. 49-65, Springer-Verlag, Berlin.
12. Boudol, G. (1985), Computational semantics of term rewriting systems, in "Algebraic Methods in Semantics (Fontainebleau, 1982)" (M. Nivat and J. C. Reynolds, Eds.), pp. 169-236, Cambridge Univ. Press, Cambridge, UK.
13. Church, A. (1941), "The Calculi of Lambda Conversion," Princeton University Press, Princeton.
14. Church, A., and Rosser, J. B. (1936), Some properties of conversion, Trans. Amer. Math. Soc. 39, 472-482.
15. Curien, P.-L. (1993), "Categorical Combinatorics, Sequential Algorithms and Functional Programming," second ed., Birkhäuser, Boston.
16. Curry, H. B., and Feys, R. (1958), "Combinatory Logic," Vol. I, North-Holland, Amsterdam.
17. Dershowitz, N., and Jouannaud, J.-P. (1990), Rewrite systems, in "Formal Methods and Semantics, Handbook of Theoretical Computer Science" (J. van Leeuwen, Ed.), Vol. B, Chap. 6, pp. 243-320, MIT Press, Cambridge, MA.
18. Derschowitz, N., Kaplan, S., and Plaisted, D. A. (1989), Infinite normal forms, in "ICALP'89," Lecture Notes in Computer Science, Vol. 372, pp. 249-262.
19. Farmer, W. M., and Watro, R. J. (1989), "Redex Capturing in Term Graph Rewriting," Technical report, M89-59, MITRE.
20. Field, J., and Tip, F. (1994), Dynamic dependence in term rewriting systems and its application to program slicing, in "Proceedings of the Sixth International Symposium on Programming Language Implementation and Logic Programming, PLILP'94" (M. Hermenegildo and J. Penjam, Eds.), Lecture Notes in Computer Science, Vol. 844, pp. 415-431, Springer-Verlag, Berlin.
21. Glauert, J., and Khasidashvili, Z. (1994), Relative normalization in orthogonal expression reduction systems, in "Workshop on Conditional (and Typed) Term Rewriting Systems, CTRS'94" (N. Dershowitz and N. Lindenstrauss, Eds.), Lecture Notes in Computer Science, Vol. 968, pp. 144-165, Springer-Verlag, Berlin.
22. Glauert, J., and Khasidashvili, Z. (1996), Relative normalization in deterministic residual structures, in "Proceedings of the 19th International Colloquium on Trees in Algebra and Programming, CAAP '96" (H. Kirchner, Ed.), Lecture Notes in Computer Science, Vol. 1059, pp. 180-195, Springer-Verlag, Berlin.
23. Gonthier, G., Lévy, J.-J., and Melliès, P.-A. (1992), An abstract standardisation theorem, in "Proceedings of 7th Annual Symposium on Logic in Computer Science, LICS '92, Santa Cruz, CA," pp. 72-81, IEEE Computer Society Press, Los Alamitos, CA.
24. Hindley, J. R. (1969), An abstract form of the Church-Rosser theorem, I, J. Symbolic Logic 34, 545-560.
25. Hindley, J. R. (1974), An abstract Church-Rosser theorem, II, applications, J. Symbolic Logic 39, 1-22.
26. Hindley, R. (1977), The equivalence of complete reductions, Trans. Amer. Math. Soc. 229, 227-248.
27. Huet, G., and Levy, J.-J. (1991), Computations in orthogonal rewriting systems, in "Computational Logic: Essays in honor of Alan Robinson" (J.-J. Lassez and G. Plotkin, Eds.), pp. 395-443, The MIT Press, Cambridge, MA.
28. Hudak, P. (1988), Report on the functional programming language Haskell, Draft proposed standard.
29. Kennaway, J. R., Klop, J. W., Sleep, M. R., and de Vries, F. J. (1993), An infinitary Church-Rosser property for non-collapsing orthogonal term rewriting systems, in "Term Graph Rewriting - Theory and Practice" (M. R. Sleep, M. J. Plasmeijer, and M. C. J. D. van Eekelen, Eds.), pp. 47-59, Wiley, New York.
30. Kennaway, J. R., Klop, J. W., Sleep, M. R., and de Vries, F. J. (1995), Infinitary lambda calculus and Böhm models, in "Proceedings of the Conference on Rewriting Techniques and Applications, RTA95, Kaiserslautern," Lecture Notes in Computer Science, Vol. 914, pp. 257-270, Springer-Verlag, Berlin.
31. Kennaway, J. R., Klop, J. W., Sleep, M. R., and de Vries, F. J. (1995), Transfinite reductions in orthogonal term rewriting systems, Inform. and Comput. 119, 18-38.
32. Kennaway, J. R., Klop, J. W., Sleep, M. R., and de Vries, F. J. (1997), Infinitary lambda calculus, Theoret. Comput. Sci. 175, 93-125.
33. Kennaway, J. R., van Oostrom, V., and de Vries, F. J. (1999), Meaningless terms in rewriting, J. Funct. Logic Progr. 1999, February, http://www.cs.tu-berlin.de/journal/jflp/.
34. Khasidashvili, Z. O. (1990), β-reductions and β-developments of λ-terms with the least number of steps, in "COLOG-88 (Tallinn, 1988)," pp. 105-111, Springer-Verlag, Berlin.
35. Khasidashvili, Z. (1993), Optimal normalization in orthogonal term rewriting systems, in "Rewriting Techniques and Applications (Montreal, 1993)," pp. 243-258, Springer-Verlag, Berlin.
36. Khasidashvili, Z., and Glauert, J. (1996), Discrete normalization in deterministic residual structures, in "Proceedings of the 5th International Conference on Algebraic and Logic Programming, ALP '96" (M. Hanus and M. Rodriguez-Artalejo, Eds.), Lecture Notes in Computer Science, Vol. 1139, pp. 135-149, Springer-Verlag, Berlin.
37. Khasidashvili, Z., and Glauert, J. (1997), The geometry of orthogonal reduction spaces, in "Proceedings of the 24th International Colloquium on Automata, Languages, and Programming, ICALP '97" (P. Degano, R. Gorrieri, and A. Marchetti-Spaccamela, Eds.), Lecture Notes in Computer Science, Vol. 1256, pp. 649-659, Springer-Verlag, Berlin.
38. Khasidashvili, Z., and van Oostrom, V. (1995), Context-sensitive conditional expression reduction systems, in "Electronic Notes in Theoretical Computer Science, SEGRAGRA '95, Joint COMPUGRAPH/SEMAGRAPH Workshop on Graph Rewriting and Computation, Volterra," pp. 141-150.
39. Klop, J. W. (1980), "Combinatory Reduction Systems," Mathematical Centre Tracts Number 127, Ph.D. thesis, CWI, Amsterdam.
40. Klop, J. W. (1990), "Term Rewriting Systems," Report CS-R9073, Centre for Mathematics and Computer Science, December.
41. Klop, J. W. (1992), Term rewriting systems, in "Handbook of Logic in Computer Science" (S. Abramsky, D. Gabbay, and T. Maibaum, Eds.), Vol. II, Oxford University Press, Oxford.
42. Klop, J. W., van Oostrom, V., and van Raamsdonk, F. (1993), Combinatory reduction systems, introduction and survey, Theoret. Comput. Sci. 121, 279-308.
43. Klop, J. W., and de Vrijer, R. C. (1991), Extended rewriting systems, in "Proceedings of the Workshop on Conditional an Typed Rewriting Systems, Montreal" (S. Kaplan and M. Okada, Eds.), Lecture Notes in Computer Science, Vol. 516, pp. 26-50, Springer-Verlag, Berlin.
44. Krivine, J. L. (1993), "Lambda-calculus, Types and Models," Massan, Paris.
45. Kuper, J. (1994), "Partiality in Logic and Computation," Ph.D. thesis, University of Twente.
46. Lévy, J.-J. (1975), An algebraic interpretation of λ-calculus and a labelled λ-calculus, in "λ-calculus and Computer Science" (C. Böhm, Ed.), Lecture Notes in Computer Science, Vol. 37, pp. 147-165, Springer-Verlag, Berlin.
47. Lévy, J.-J. (1978), "Réductions correctes et optimales dans le lambda-calcul," Ph.D. thesis, Université de Paris VII.
48. Maranget, L. (1992), "La stratégie paresseuse," Ph.D. thesis, L'Université Paris VII.
49. Melliès, P.-A. (1997), Axiomatic rewriting theory III: A factorisation theorem in rewriting theory, in "Proceedings of the 7th Conference on Category Theory and Computer Science, CTCS '97, Santa Margherita Ligure," Lecture Notes in Computer Science, Vol. 1290, pp. 46-68, Springer-Verlag, Berlin.
50. Melliès, P.-A. (1998), Axiomatic rewriting theory IV: A stability theorem in rewriting theory, in "Proceedings of the 14th Annual Symposium on Logic in Computer Science, LICS '98, Indianapolis," pp. 287-298, IEEE Computer Society Press, Los Alamitos, CA.
51. Middeldorp, A. (1997), Call by need computations to root-stable form, in "Proceedings of the 24th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL'97," pp. 94-105.
52. Newman, M. H. A. (1942), On theories with a combinatorial definition of "equivalence," Ann. of Math. 43, 223-243.
53. Nederpelt, R. P., Geuvers, J. H., and de Vrijer, R. C. (1994), "Selected Papers on Automath," Studies in Logic and the Foundations of Mathematics, Vol. 133, North-Holland, Amsterdam.
54. Nipkow, T. (1991), Higher-order critical pairs, in "Proceedings of the sixth annual IEEE Symposium on Logic in Computer Science," pp. 342-349, IEEE Computer Society Press, Los Alamitos, CA.
55. Nipkow, T. (1993), Orthogonal higher-order rewrite systems are confluent, in "Proceedings of the International Conference on Typed Lambda Calculi and Application," pp. 306-317.
56. O'Donnell, M. J. (1977), "Computing in Systems Described by Equations," Lecture Notes in Computer Science, Vol. 58, Springer-Verlag, Berlin.
57. van Oostrom, V. (1994), "Confluence for Abstract and Higher-Order Rewriting," Ph.D. thesis, Vrije Universiteit, Amsterdam, March.
58. van Oostrom, V. (1996), "Take Five," Technical report IR-406, Vrije Universiteit, Amsterdam.
59. van Oostrom, V. (1997), Developing developments, Theoret. Comput. Sci. 175, 159-181.
60. van Oostrom, V. (1997), Finite family developments, in "Rewriting Techniques and Applications. 8th International Conference, RTA 97" (H. Comon, Ed.), Lecture Notes in Computer Science, Vol. 1232, pp. 308-322, Springer-Verlag, Berlin.
61. van Oostrom, V. (1999), Normalisation in weakly orthogonal rewriting, in "10th International Conference on Rewriting Techniques and Applications, RTA '99, Trento, June" (P. Narendran and M. Rusinowitch, Eds.), Lecture Notes in Computer Science, Vol. 1631, pp. 60-74, Springer-Verlag, Berlin.
62. van Oostrom, V., and van Raamsdonk, F. (1994), Weak orthogonality implies confluence: The higher-order case, in "Proceedings of the Third International Symposium on Logical Foundations of Computer Science" (A. Nerode and Yu. V. Matiyasevich, Eds.), Lecture Notes in Computer Science, Vol. 813, pp. 379-392, Springer-Verlag, Berlin.
63. Plasmeijer, M. J., and van Eekelen, M. C. J. D. (1993), "Functional Programming and Parallel Graph Rewriting," Addison-Wesley, Reading, MA.
64. Plotkin, G. (1978), Church-Rosser categories, manuscript.
65. van Raamsdonk, F. (1993), Confluence and superdevelopments, in "Proceedings of the 5th International Conference on Rewriting Techniques and Applications (RTA 93)" (C. Kirchner, Ed.), Lecture Notes in Computer Science, Vol. 690, pp. 168-182, Springer-Verlag, Berlin.
66. van Raamsdonk, F. (1996), "Confluence and Normalisation for Higher-Order Rewriting," Ph.D. thesis, Vrije Universiteit Amsterdam.
67. Takahashi, M. (1995), Parallel reductions in λ-calculus, Inform. and Comput. 118, 120-127.
68. Tip, F. (1995), "Generation of Program Analysis Tools," Ph.D. thesis, Universiteit van Amsterdam.
69. Turner, D. A. (1985), Miranda: a non-strict functional language with polymorphic types, in "Proceedings of the ACM Conference on Functional Programming Languages and Computer Architecture" (J.-P. Jouannaud, Ed.), Lecture Notes in Computer Science, Vol. 201, pp. 1-16, Springer-Verlag, Berlin.
70. de Vrijer, R. C. (1985), A direct proof of the finite development theorem, J. Symbolic Logic 50, 339-343.
71. de Vrijer, R. C. (1987), "Surjective Pairing and Strong Normalization: Two Themes in Lambda Calculus," Ph.D. thesis, University of Amsterdam.
72. de Vrijer, R. C. (1989), Extending the lambda calculus with surjective pairing is conservative, in "Proceedings of the 4th IEEE Symposium on Logic in Computer Science, Asilomar, CA," pp. 204-215.