Confluence properties of extensional and non-extensional λ-calculi with explicit substitutions

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

Volumn 1103, Issue , 1996, Pages 184-199

  Kesner, Delia ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

PATHOLOGY;

CONFLUENCE PROPERTY; EXPLICIT SUBSTITUTIONS; EXTENSIONALITY; LAMBDA-CALCULI;

BIOMINERALIZATION;

EID: 84957637612     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61464-8_52     Document Type: Conference Paper

References (38)

1. M. Abadi, L. Cardelii, P-L. Curien, and J-J. Lévy. Explicit substitutions. JFP, 4(1):375-416,1991.
2. Y. Akama. On mints' reductions for ccc-calculus. In TLCA, LNCS 664, 1993.
3. H. Barendregt. The Lambda Calculus; Its syntax and Semantics (revised edition). North Holland, 1984.
4. v a calculus of explicit substitutions which preserves strong normalisation. Available from http: //www. loria. fr/ lescanne/publications.html. 1995.
5. D. Briaud. An explicit eta rewrite rule. In TLCA, LNCS 902,1995.
6. P-L. Curien and R. Di Cosmo. A confluent reduction system for the λ-calculus with suijective pairing and terminal object. In 1C ALP, LNCS 510,1991.
7. P-L. Curien, T. Hardin, and J-J. Lévy. Confluence properties of weak and strong calculi of explicit substitutions. Technical Report 1617, INR1A Rocquencourt, 1992.
8. P-L. Curien, T. Hardin, and A. Rios. Strong normalisation of substitutions. In MFCS'92, LNCS 629,1992.
9. N. de Bruijn. Lambda-calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the church-rosser theorem. Indag. Mat., 5(35):381-392, 1972.
10. N. de Bruijn. Lambda-calculus notation with namefree formulas involving symbols that represent reference transforming mappings. Indag. Mat., (40):384-356, 1978.
11. Roberto Di Cosmo and Delia Kesner. A confluent reduction for the extensional typed λ-calculus with pairs, sums, recursion and terminal object. In ICALP, LNCS 700,1993.
12. Roberto Di Cosmo and Delia Kesner. Combining first order algebraic rewriting systems, recursion and extensional typed lambda calculi. In ICALP, LNCS 820,1994.
13. R. Di Cosmo and D. Kesner. Rewriting with extensional polymorphic λ-calculus. In CSL, 1995.
14. R. Di Cosmo and A. Piperno. Expanding extensional polymorphism. In TLCA, LNCS 902, 1995.
15. D. Dougherty. Some lambda calculi with categorical sums and products. In RTA, LNCS 690,1993.
16. Thomas Ehrhard. Une sémantique catégorique des types dependants. Application au calcul des constructions. Thèse de doctoral, Université de Paris VII, 1988.
17. J-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types. Cambridge University Press, 1990.
18. T. Hardin. Résuhats de confluence pour les regies fortes de la logique combinatoire catégorique et liens avec les lambda-calculs. Thèse de doctorat, Université de Paris VII, 1987.
19. T. Hardin, η-reduction for explicit substitutions. In ALP'92, LNCS 632,1992.
20. T. Hardin. Eta-conversion for the languages of explicit substitutions. AAECC, 5:317-341, 1994.
21. T. Hardin and A. Laville. Proof of termination of the rewriting system subst on c.c.l. TCS, 1986.
22. T. Hardin and J-J. Lévy. A confluent calculus of substitutions. In France-Japan Art. Int. and Comp. Sci. Symp., 1989.
23. G. Huet. Résolution d'equations dans les langages d'ordre 1, 2,…, ω. Thèse de doctorat d'état, Université Paris VII, 1976.
24. C. Barry Jay and N. Ghani. The virtues of eta-expansion. JFP, 5(2): 135-154, 1995.
25. D. Kesner. Confluence properties of extensional and non-extensional λ-calculi with explicit substitutions, 1995. Available as ftp: / /ftp. lri. f r/LRI/art icles/kesner/explicit.ps. gz.
26. e-calculus via a generalized interpretation method, 1995. Draft.
27. F. Kamareddine and A. Rios. A λ-calculus à la de bruijn with explicit substitutions. In PULP, LNCS 982,1995.
28. P. Lescanne. Personal Communication.
29. υ, a journey through calculi of explicit substitutions. In POPL, pages 60-69. ACM, 1994.
30. υ Technical Report, INRIA, Lorraine, 1994.
31. C. Marché. Réécriture modulo une théorie presentee par un système convergent et décidabilité des problèmes du mot dans certains classes de theories équationnelles. PhD thesis, Université Paris-Sud, Orsay, 1993.
32. P-A. Mellies. Typed λ-calculi with explicit substitutions may not terminate. In TLCA, LNCS 902,1995.
33. G. Mints. Closed categories and the theory of proofs. Zap. Nauch. Semin. Leningradskogo, 68:83-114, 1977.
34. G. Mints. Teorija categorii i teoria dokazatelstv.I. Aktualnye pmblemy logiki i metodologii nauky, pages 252-278, 1979.
35. G. Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Jour, of Formal Logic, 22(3):264-268, 1981.
36. D. Prawitz. Ideas and results in proof theory. Proceedings of the 2nd Scandinavian Logic Symposium, pages 235-307, 1971.
37. A. Rios. Contribution à l'étude des λ-calculus avec substitutions explicites. Thèse de doctorat, Université de Paris VII, 1993.
38. V. van Oostrom and F. van Raamsdonk. Weak orthogonality implies confluence: the higher-order case. In UCS, 1994