Weak and strong beta normalisations in typed λ-calculi

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

Volumn 1210, Issue , 1997, Pages 390-404

  Xi, Hongwei ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PATHOLOGY;

CURRY-TYPING; LAMBDA TERMS; LAMBDA-CALCULI; PURE TYPE SYSTEMS;

BIOMINERALIZATION;

EID: 84922983928     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-62688-3_48     Document Type: Conference Paper

References (35)

1. H.P. Barendregt (1984), The Lambda Calculus: Its Syntax and Semantics, North-Holland Publishing Company, Amsterdam.
2. H.P. Barendregt (1992), Lambda calculi with types, in Handbook of Logic in Computer Science Vol. P, edited by S. Abramsky, D. M. Gabbay and T.S.E. Maibanm, Clarendon Press, Oxford, pp. 117-309.
3. J.A. Bergstra and J.W. Klop (1982), Strong normalization and perpetual reductions in the lambda calculus, J. Inform. Process. Cybernet. 18, pp. 403-417.
4. A. Church, (1941), The Calculi of Lambda Conversion, Princeton University Press, Princeton.
5. Th. Coquand and G. Huèt (1988), The calculus of constructions, Information and Computation vol. 76, pp. 95-120.
6. M. Coppo and M. Dezani-Ciancaglini (1980), An extension of basic functionality theory for the lambda-calculus, Notre Dame Journal of Formal Logic 21 (4), pp. 685-693.
7. M. Coppo, M. Dezani-Ciancaglini and B. Venneri (1981), Functional characters of solvable terms, Zeit. Math. Logik und Grundlagen der Math. 27 (1), pp. 45-58.
8. P. de Croote (1993), The conservation theorem revisited, Typed Lambda Calculi and Applications: TLCA '93, LNCS vol. 664, Springer, pp. 163-178.
9. R.O. Gandy (1980), An early proof of normalisation by A.M. Turing, in To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, pp. 453-456.
10. R.O. Gandy (1980), Proofs of strong normalisation, in To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, pp. 457-478.
11. J.-Y. Girard (1972), Interprdtation Fonctionnelle et Elimination des Coupures de l'Arithmdtique d'Ordre Supdrieur, Thèse de Doctorat d'Etat, Universitè Paris VII.
12. H. Geuvers and M.J. Nederhof (1991), A modular proof of strong normalisation for the calculus of constructions, J. Functional Programming 1,155-189.
13. R. Harper, F. Honsell and G. Plotkin (1987), A framework for defining logics. In Proc. Second Annual Symposium on Logic in Computer Science, I.E.E.E., Ithaca, N.Y., pages 194-204.
14. R. Harper and M. Lillibridge (1993), Explicit polymorphism and CPS conversion, In Proceedings of the Twentieth A CM Symposium on Principles of Programming Languages, pp. 206-209
15. R. Harper and M. Lillibridge (1993), Polymorphic type assignment and CPS conversion, LISP and Symbolic Computation, vol. 6, 3(4), pp. 361-380.
16. Stefan Kahrs (1995), Towards a Domain Theory for Termination Proofs, Laboratory for Foundation of Computer Science, Report 95-314, Department of Computer Science, The University of Edinburgh.
17. M. Karr (1985), "Delayability" in proofs of strong normalisabilities in the typed lambda-calculus, in Mathematical Foundation of Computer Software, edited by H. Ehrig, C. Floyd, M. N'ivat and J. Thatcher, LNCS vol. 185, Springer, pp. 208-222.
18. J.W. Klop (1980), Combinatory Reduction Systems, Ph.D. thesis, CWI, Amsterdam, Mathematical Center Tracts, No. 127.
19. J.W. Klop, (1992), Term rewriting systems, in Handbook of Logic in Computer Science Vol.2, edited by S. Abramsky, D. M. Gabbay and T.S.E. Maibaum, Clarendon Press, Oxford, pp. 1-116.
20. J.L. Krivine (1990), Lambda-calcul, Types et ModUles, Masson, Paris.
21. A.J. Kfoury and J.B. Wells (1994), New notions of reduction and nonsemantic proofs of β-strong normalisation in typed A-calculi, Tech. Rep. 94-104, Computer Science Department, Boston University.
22. R.P. Nederpelt (1973), Strong normalization in a typed lambda calculus with lambda structured types, Ph.D. thesis, Technische Hogeschool Eindhoven.
23. G. Plotkin (1975), Call-by-name, call-by-value, and the lambda calculus, Theoretical Computer Science, vol 1, pp. 125-159.
24. J. van de Pol (1994), Termination proofs for higher-order rewrite systems, in Higher Order Algebra, Logic and Term Rewriting, edited by J. Heering, K. Meinke, B. Möller and T. Nipkow, LNCS vol. 816, Springer, pp. 305-325.
25. J. van de Pol and H. Schwichtenberg (1995), Strict functionals for termination proofs, Typed lambda calculi and applications: TLCA '95, LNCS vol. 902, Springer, pp. 350-364.
26. D. Prawitz (1965), Natural Deduction: A proof theoretical study, Almquist & Wiksell publishing company, Stockholm.
27. D. Prawitz (1971), Ideas and results of proof theory, in Proceedings of the 2nd Scandinavian Logic Symposium, edited by J.E. Fenstad, North-Holland Publishing Company, Amsterdam.
28. J. Reynolds (1974), Towards a theory of type structure, Colloquium sur la Programmation, LNCS vol. 19, Springer, pp. 408-423.
29. H. Schwichtenberg (1991), An upper bound for reduction sequences in the typed lambda-calculus, Archive for Mathematical Logic, 30, 405-408.
30. M.H. Sørensen (1996), Strong Normalization from Weak Normalization by A-Translation in Typed lambda-Calculi, Manuscript announced on the types mailing list, February.
31. J. Springintveld (1993), Lower and upper bounds for reductions of types in λω and λP, in Typed lambda calculi and applications: TLCA '93, LNCS vol. 664, Springer, pp. 391-405.
32. P. Urzyczyn (1995), Positive recursive type assignment, in Mathematical Foundations of Computer Science, LNCS vol. 969, Springer, pp. 382-391.
33. H. Xi (1996), On weak and strong normalisations, Research Report 96-187, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh.
34. H. Xi (1996), Upper bounds for standardisations and an application, Research Report 96-189, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh.
35. H. Xi (1996), An induction measure on λ-terms and its applications, Research Report 96-192, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh.