λυ, a calculus of explicit substitutions which preserves strong normalisation

Journal of Functional Programming

Volumn 6, Issue 5, 1996, Pages 699-722

  Benaissa, Zine El Abidine ^a   Briaud, Daniel ^a   Lescanne, Pierre ^a   Rouyer Degli, Jocelyne ^a  

^a LORIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030371868     PISSN: 09567968     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0956796800001945     Document Type: Article

References (28)

1. Abadi, M., Cardelli, L., Curien, P.-L. and Lévy, J.-J. (1990) Explicit substitutions. Tech. rept. 54, Digital Systems Research Center. Preliminary version in Proc. of the 17th POPL conference, Orlando, FL, USA.
2. Abadi, M., Cardelli, L., Curien, P.-L. and Lévy, J.-J. (1991) Explicit substitutions. J. Functional Programming, 1(4): 375-416.
3. Barendregt, H. P. (1984) The Lambda-Calculus, its syntax and semantics. Studies in Logic and the Foundation of Mathematics. Elsevier.
4. ie.
5. Briaud, D. (1995) An explicit Eta rewrite rule. In: Dezani, M., editor, Int. Conf. on Typed Lambda Calculus and Applications.
6. Curien, P.-L. (1983) Combinateurs catégoriques, algorithms séquentiels et programmation applicative. Thèse de Doctorat d'Etat, Université Paris 7.
7. Curien, P.-L. (1986a) Categorical combinators. Information and Control, 69: 188-254.
8. Curien, P.-L. (1986b) Categorical Combinators, Sequential Algorithms and Functional Programming. Pitman.
9. Curien, P.-L. (1991) An abstract framework for environment machines. Theoretical Computer Science, 82: 389-402.
10. Curien, P.-L., Hardin, Th. and Lévy, J.-J. (1992) Confluence properties of weak and strong calculi of explicit substitutions. RR 1617. INRIA, Rocquencourt.
11. Curry, H. B. and Feys (1958) Combinatory Logic. Vol. 1. Elsevier.
12. de Bruijn, N. G. (1972) Lambda calculus with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Proc. koninkl. nederl. akademie van wetenschappen, 75(5): 381-392.
13. de Bruijn, N. G. (1978) A namefree lambda calculus with facilities for internal definition of expressions and segments. TH-Report 78-WSK-03. Technological University Eindhoven, Netherlands, Department of Mathematics.
14. Dershowitz, N. and Jouannaud, J.-P. (1990) Rewrite Systems. In: van Leeuwen, J., editor, Handbook of Theoretical Computer Science, Chapter 6, pp. 244-320. Elsevier.
15. Ehrhrard, T. (1988) Une sémantique catégorique des types dépendants. Application au calcul des constructions. Thèse de Doctorat d'Université, Universite Paris VII.
16. Field, J. (1990) On laziness and optimality in lambda interpreters: Tools for specification and analysis. Proc. 17th annual ACM symposium on Principles Of Programming Languages, Orlando, FL, USA. ACM.
17. Hardin, T. (1992) Eta-conversion for the languages of explicit substitutions. In Kirchner, H. and Levi, G., editors, Proceedings 3rd International Conference on Algebraic and Logic Programming, Volterra, Italy). Lecture Notes in Computer Science 632, pp. 306-321. Springer-Verlag.
18. Hardin, Th. (1987) Résultats de confluence pour les règles fortes de la logique combinatoire catégorique et liens avec les lambda-calculs. Thèse de Doctorat d'Etat, Université Paris 7.
19. Hardin, Th. (1989) Confluence results for the pure strong categorical combinatory logic CCL: λ-calculi as subsystems of CCL. Theoretical Computer Science, 65: 291-342.
20. Hardin, Th. and Lévy, J.-J. (1989) A confluent calculus of substitutions. France-Japan Artificial Intelligence and Computer Science Symposium.
21. Kamareddine, F. and Ríos, A. (1995) A λ-calculus à la de Bruijn with explicit substitutions. PLILP'95: Lecture Notes in Computer Science. Springer-Verlag.
22. Kamereddine, F. and Nederpelt, R. P. (1993) On stepwise explicit substitutions. Int. J. Foundations of Computer Science, 4(3): 197-240.
23. Lescanne, P. (1992) Termination of rewrite systems by elementary interpretations. In: Kirchner, H. and Levi, G., editors, Proceedings 3rd International Conference on Algebraic and Logic Programming: Lecture Notes in Computer Science 632, Volterra, Italy. Springer-Verlag.
24. Lescanne, P. (1994) From λσ to λυ, a journey through calculi of explicit substitutions. In: Boehm, H., editor, Proceedings of the 21st Annual ACM Symposium on Principles Of Programming Languages, pp. 60-69. Portland, OR, USA. ACM.
25. Lescanne, P. and Rouyer-Degli, J. (1994) The calculus of explicit substitutions λυ. Tech. rept. RR-2222, INRIA-Lorraine.
26. Melliès, P.-A. (1995) Typed λ-calculi with explicit substitutions may not terminate. In: Dezani, M., editor, Int. Conf. on Typed Lambda Calculus and Applications.
27. Ríos, A. (1993) Contributions à l'étude des λ-calculs avec des substitutions explicites. Thèse de Doctorat d'Université, Universite Paris VII.
28. Rose, K. and Bloo, R. (1995) Deriving requirements for preservation of strong normalisation in lambda calculi with explicit substitution. Available as ftp://ftp.diku.dk/diku/users/ kris/Explicit-PSN.ps.