Types, potency, and impotency: Why nonlinearity and amnesia make a type system work

ACM SIGPLAN Notices

Volumn 39, Issue 9, 2004, Pages 138-149

  Neergaard, Peter Møller ^a   Mairson, Harry G ^a  

^a BRANDEIS UNIVERSITY   (United States)

Author keywords

Complexity; Idempotence; Intersection types; Normalization; Proofnet; Type inference

Indexed keywords

ACCIDENT PREVENTION; ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER PROGRAMMING LANGUAGES; CONSTRAINT THEORY; FUNCTIONS; GRANULAR MATERIALS; MATHEMATICAL MODELS;

COMPLEXITY; IDEMPOTENCE; INTERSECTION TYPES; NORMALIZATION; PROOFNET; TYPE INFERENCES;

CONTROL NONLINEARITIES;

EID: 9744230066     PISSN: 03621340     EISSN: None     Source Type: Journal    
DOI: 10.1145/1016848.1016871     Document Type: Conference Paper

References (48)

1. H. Abelson and G. J. Sussman. Structure and Interpretation of Computer Programs. MIT Press, 1985.
2. R. Amadio and P.-L. Curien. Domains and Lambda Calculi, volume 46 of Cambridge tracts in theoretical computer science. Cambridge University Press, 1998.
3. A. Asperti and S. Guerrini. The Optimal Implementation of Functional Programming Languages. Cambridge University Press, 1998.
4. A. Banerjee. A modular, polyvariant, and type-based closure analysis. In Proc. 1997 Int'l Conf. Functional Programming. ACM Press, 1997.
5. H. P. Barendregt. The Lambda Calculus: Its Syntax and Semantics. North-Holland, revised edition, 1984.
6. S. Carlier, J. Polakow, J. B. Wells, and A. J. Kfoury. System E: Expansion variables for flexible typing with linear and non-linear types and intersection types. In Programming Languages & Systems, 13th European Symp. Programming, volume 2986 of LNCS, pages 294-309. Springer-Verlag, 2004.
7. S. Carlier and J. B. Wells. Type inference with expansion variables and intersection types in System E and an exact correspondence with β-reduction. Technical Report HW-MACS-TR-0012, Heriot-Watt Univ., School of Math. & Comput. Sci., Jan. 2004.
8. M. Coppo, F. Damiani, and P. Giannini. Strictness, totality, and non-standard type inference. Theoret. Comput. Sci., 272(1-2):69-111, Feb. 2002.
9. M. Coppo, M. Dezani-Ciancaglini, and B. Venneri. Functional characters of solvable terms. Z. Math. Logik Grundlag. Math., 27(1):45-58, 1981.
10. F. Damiani. A conjunctive type system for useless-code elimination. Math. Structures Comput. Sci., 13:157-197, 2003.
11. F. Damiani. Rank 2 intersection types for local definitions and conditional expressions. ACM Trans. on Prog. Langs. & Systs., 25(4):401-451, 2003.
12. F. Damiani. Rank 2 intersection types for modules. In Proc. 5th Int'l Conf. Principles & Practice Declarative Programming, pages 67-78, 2003.
13. F. Damiani and P. Giannini. Automatic useless-code detection and elimination for HOT functional programs. J. Funct. Programming, pages 509-559, 2000.
14. V. Danos and L. Regnier. The structure of multiplicatives. Arch. Math. Logic, 26, 1989.
15. G. Gonthier, M. Abadi, and J.-J. Lévy. The geometry of op timal lambda reduction. In Conf. Rec. 19th Ann. ACM Symp. Princ. of Prog. Langs., pages 15-26, 1992.
16. G. Gonthier, M. Abadi, and J.-J. Lévy. Linear logic without boxes. In Proc. 7th Ann. IEEE Symp. Logic in Comput. Sci., pages 223-34. IEEE Comput. Soc. Press, 1992.
17. F. Henglein and H. G. Mairson. The complexity of type inference for higher-order typed lambda calculi. J. Funct. Programming, 4(4):435-478, Oct. 1994.
18. J. R. Hindley. The principal type scheme of an object in combinatory logic. Trans. American Mathematical Society, 146:29-60, Dec. 1969.
19. J. R. Hindley and J. P. Seldin, editors. To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism. Academic Press, 1980.
20. T. Jensen. Inference of polymorphic and conditional strictness properties. In Conf. Rec. POPL '98: 25th ACM Symp. Princ. of Prog. Langs., 1998.
21. T. Jim. What are principal typings and what are they good for? In Conf. Rec. POPL '96: 23rd ACM Symp. Princ. of Prog. Langs., 1996.
22. P. Kanellakis, H. Mairson, and J. C. Mitchell. Unification and ML type reconstruction. In J.-L. Lassez and G. Plotkin, editors, Computational Logic: Essays in Honor of Alan Robinson. MIT Press, 1991.
23. A. J. Kfoury. A linearization of the lambda-calculus. J. Logic Comput., 10(3), 2000.
24. A. J. Kfoury, H. G. Mairson, F. A. Turbak, and J. B. Wells. Relating typability and expressibility in finite-rank intersection type systems. In Proc. 1999 Int'l Conf. Functional Programming, pages 90-101. ACM Press, 1999.
25. A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. ML typability is DEXPTIME complete. In 15th Colloq. Trees in Algebra and Programming, volume 431 of LNCS, pages 206-220. Springer-Verlag, 1990.
26. A. J. Kfoury, G. Washburn, and J. B. Wells. Implementing compositional analysis using intersection types with expansion variables. In Proceedings of the 2nd Workshop on Intersection Types and Related Systems, 2002.
27. A. J. Kfoury and J. B. Wells. Principality and decidable type inference for finite-rank intersection types. In Conf. Rec. POPL '99: 26th ACM Symp. Princ. of Prog. Langs., pages 161-174, 1999.
28. A. J. Kfoury and J. B. Wells. Principality and type inference for intersection types using expansion variables. Theoret. Comput. Sci., 311(1-3):1-70, 2004.
29. Y. Lafont. From proof-nets to interaction nets. In J.-Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, Proceedings of the 1993 Workshop on Linear Logic, London Math. Soc. Lecture Note Series 222, pages 225-247. Cambridge University Press, 1995.
30. J. Lamping. An algorithm for optimal lambda-calculus reductions. In POPL '90 [38], pages 16-30.
31. J.-J. Lévy. Optimal reductions in the lambda-calculus. In Hindley and Seldin [19], pages 159-191.
32. H. G. Mairson. Deciding ML typability is complete for deterministic exponential time. In POPL '90 [38], pages 382-401.
33. H. G. Mairson. Outline of a proof theory of parametricity. In FPCA '91, Conf. Funct. Program. Lang. Comput. Arch., volume 523 of LNCS, pages 313-327, Cambridge, MA. U.S.A., 1991. Springer-Verlag.
34. nd Conference on Foundations of Software Technology and Theoretical Computer Science, 2002.
35. R. Milner. A theory of type polymorphism in programming. J. Comput. System Sci., 17:348-375, 1978.
36. J. C. Mitchell. Type systems for programming languages. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 365-458. North-Holland, 1990.
37. C. Mossin. Exact flow analysis. Math. Structures Comput. Sci., 13:125-156, 2003.
38. Conf. Rec. 17th Ann. ACM Symp. Princ. of Prog. Langs., 1990.
39. L. Regnier. Lambda calcul et réseaux. PhD thesis, University Paris 7, 1992.
40. S. Ronchi Della Rocca. Principal type schemes and unification for intersection type discipline. Theoret. Comput. Sci., 59(1-2): 181-209, Mar. 1988.
41. S. Ronchi Della Rocca and B. Venneri. Principal type schemes for an extended type theory. Theoret. Comput. Sci., 28(12): 151-169, Jan. 1984.
42. É. Sayag and M. Mauny. A new presentation of the intersection type discipline through principal typings of normal forms. Technical Report RR-2998, INRIA, Oct. 16, 1996.
43. R. Statman. The typed lambda-calculus is not elementary recursive. Theoret. Comput. Sci., 9(1):73-81, July 1979.
44. S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
45. P. Wadler. Theorems for free! In Proceedings 4th Int. Conf. on Funct. Program. Languages and Computer Architecture, pages 347-359. ACM, 1989.
46. G. Washburn, A. Kfoury, J. Wells, B. Alan, B. Yates, O. Schwartz, and S. Carlier. System I experimentation tool, http ://types.bu.edu/modular/ compositional/experimentation-tool/.
47. J. B. Wells. Typability and type checking in System F are equivalent and undecidable. Ann. Pure Appl. Logic, 98(13): 111-156, 1999.
48. J. B. Wells, A. Dimock, R. Muller, and F. Turbak. A calculus with polymorphic and polyvariant flow types. J. Funct. Programming, 12(3): 183-227, May 2002.