The girard-reynolds isomorphism

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

Volumn 2215, Issue , 2001, Pages 468-491

  Wadler, Philip ^a  

^a AVAYA LABS RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; COMPUTER SOFTWARE; DIFFERENTIATION (CALCULUS);

INDUCTIVE DEFINITIONS; INTUITIONISTIC PROPOSITIONAL LOGIC; LOGICAL RELATIONS; NATURAL NUMBER; PARAMETRICITY; POLYMORPHIC LAMBDA CALCULUS; REPRESENTATION THEOREM; SECOND ORDERS;

FORMAL LOGIC;

EID: 84978946106     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45500-0_24     Document Type: Conference Paper

References (38)

1. [ACC93] M. Abadi, L. Cardelli, and P.-L. Curien, Formal Parametric Polymorphism, Theoretical Computer Science 121(1-2): 9-58, December 1993. (Part of A Collection of Contributions in Honour of Corrado Boehm on the Occasion of his 70th Birthday.) Also appeared as SRC Research Report 109.
2. [Bar91] H. Barendregt, Introduction to generalized types systems, Journal of Functional Programming, 1(2): 125-154, April 1991.
3. [BFSS90] E. S. Bainbridge, P. J. Freyd, A. Scedrov, and P. J. Scott, Functorial polymorphism, in G. Huet, editor, Logical Foundations of Functional Programming, pp. 315-330, Addison-Wesley, 1990.
4. [BB85] C. Böhm and A. Berarducci, Automatic synthesis of typed Λ-programs on term algebras, Theoretical Computer Science 39(2-3): 135-154, August 1985.
5. [BC88] V. Breazu-Tannen and T. Coquand, Extensional models for polymorphism, Theoretical Computer Science, 59: 85-114, 1988.
6. [CF58] H. B. Curry and R. Feys, Combinatory Logic, North Holland, 1958.
7. [CH88] T. Coquand and G. Huet, The calculus of constructions, Information and Computation, 76: 95-120, 1988.
8. [Con86] R. Constable, et al., Implementing mathematics with the Nuprl proof development system, Prentice-Hall, 1986.
9. [deB70] N. G. de Bruijn, The mathematical language of AUTOMATH, its usage and some of its extensions, Proceedings of the Symposium on Automatic Demonstration, LNCS 125, Springer-Verlag, 1970.
10. [DM82] L. Damas and R. Milner, Principal type schemes for functional programs, 9th Annual Symposium on Principles of Programming Languages, Albuquerque, N. M., January 1982.
11. [Fre79] Gottlob Frege. Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought (1879). In Jan van Heijenoort, editor, From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard University Press, 1967.
12. [Gir72] J.-Y. Girard, Interprétation functionelle et élimination des coupures dans l'arithmétique d'ordre supérieure, Ph. D. thesis, Université Paris VII, 1972.
13. [GLT89] J.-Y. Girard, Y. Lafont, and P. Taylor, Proofs and Types, Cambridge University Press, 1989.
14. [Has94] R. Hasegawa, Categorical data types in parametric polymorphism, Mathematical Structures in Computer Science, 4: 71-109, (1994).
15. [Hin69] R. Hindley, The principal type scheme of an object in combinatory logic, Trans. Am. Math. Soc., 146: 29-60, December 1969.
16. [How80] W. A. Howard, The formulae-as-types notion of construction, in J. P. Seldin and J. R. Hindley, editors, To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism, Academic Press, 1980. (The original version was circulated privately in 1969.).
17. [KP90] J.-L. Krivine and M. Parigot, Programming with proofs, J. Inf. Process. Cybern. (EIK), 26(3): 149-167, 1990. Revised version of a lecture presented at the 6th International Symposium on Computation Theory, (SCT '87), Wednisch-Rietz, GDR, 30 November-4 December 1987.
18. [Lei83] D. Leivant, Reasoningab out functional programs and complexity classes associated with type disciplines, 24th Symposium on Foundations of Computer Science, Washington D. C., IEEE, 460-469.
19. [Lei90] D. Leivant, Contractingpro ofs to programs, in P. Odifreddi, editor, Logic and Computer Science, Academic Press, 1990.
20. [Mai91] H. Mairson, Outline of a proof theory of parametricity, in J. Hughes, editor, 5th International Conference on Functional Programming Languages and Computer Architecture, Springer-Verlag LNCS 523, Cambridge, Massachusetts, August 1991.
21. [Mar82] P. Martin-Löf, Constructive mathematics and computer programming, 6th International Congress for Logic, Methodology, and Philosophy of Science, North Holland, pp. 153-175, 1982.
22. [Mil78] R. Milner, A theory of type polymorphism in programming, Journal of Computers and Systems Science, 17: 348-375, 1978.
23. [Mog86] E. Moggi, Communication to the Types electronic forum, 10 February 1986.
24. [MR91] Q. Ma and J. C. Reynolds, Types, abstraction, and parametric polymorphism, part 2, in S. Brookes et al. editors, Mathematical Foundations of Programming Semantics, Springer Verlag LNCS, 1991.
25. [Pit87] A. M. Pitts, Polymorphism Is Set Theoretic, Constructively, in D. H. Pitt and A. Poigné and D. E. Rydeheard, editors, Category Theory and Computer Science, pages 12-39, Edinburgh 1987.
26. [Pit89] A. M. Pitts, Non-trivial power types can't be subtypes of polymorphic types, in 4th Annual Symposium on Logic in Computer Science, pages 6-13, IEEE Computer Society Press, Washington 1989.
27. [Pit98] A. M. Pitts, Parametric polymorphism and operational equivalence, technical report 453, Cambridge University Computer Laboratory, 1998.
28. [PA93] G. Plotkin and M. Abadi, A logic for parametric polymorphism, in M. Bezem and J. F. Groote, editors, Typed Lambda Calculi and Applications, LNCS 664, Springer-Verlag, pp. 361-375, March 1993.
29. [PAC94] G. Plotkin, M. Abadi, and L. Cardelli, Subtypingand parametricity, 9th Annual Symposium on Logic in Computer Science, pp. 310-319, July 1994.
30. [Rey74] J. C. Reynolds, Towards a theory of type structure, in B. Robinet, editor, Colloque sur la Programmation, LNCS 19, Springer-Verlag.
31. [Rey83] J. C. Reynolds, Types, abstraction, and parametric polymorphism, in R. E. A. Mason, editor, Information Processing 83, pp. 513-523, North-Holland, Amsterdam, 1983.
32. [Rey84] J. C. Reynolds, Polymorphism is not set theoretic, in Kahn, MacQueen, and Plotkin, editors, Semantics of Data Types, Sophia-Antipolis, France, pp. 145-156, LNCS 173, Springer-Verlag, 1984.
33. [Rey90] J. C. Reynolds, Introduction to Part II: Polymorphic Lambda Calculus, in G. Huet, editor, Logical Foundations of Functional Programming, Addison-Wesley, 1990.
34. [RP90] J. C. Reynolds and G. D. Plotkin, On Functors Expressible in the polymorphic typed lambda calculus, in G. Huet, editor, Logical Foundations of Functional Programming, pp. 127-152, Addison-Wesley, 1990.
35. [Str67] C. Strachey, Fundamental concepts in programming languages, Lecture notes, International Summer School in Computer Programming, Copenhagen, August 1967. Reprinted in Higher-Order and Symbolic Computation 13(1/2): 11-49, May 2000.
36. [Tak98] Izumi Takeuiti, An axiomatic system of parametricity, Fundamenta Informaticae, 33: 397-432, IOS Press, 1998.
37. [Wad89] P. Wadler, Theorems for free!, 4th International Conference on Functional Programming Languages and Computer Architecture, ACM Press, London, September 1989.
38. [Wad91] P. Wadler, Recursive types for free!, manuscript, 1991.