Bounded quantification is undecidable

Information and Computation

Volumn 112, Issue 1, 1994, Pages 131-165

  Pierce, Benjamin C ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003102688     PISSN: 08905401     EISSN: 10902651     Source Type: Journal    
DOI: 10.1006/inco.1994.1055     Document Type: Article

References (46)

1. Breazu-Tannen, V., Coquand, T., Gunter, C., and Scedrov, A. (1991), Inheritance as implicit coercion, Inform, and Comput. 93, 172-221.
2. Bruce, K. B., and Longo, G. (1990), A modest model of records, inheritance, and bounded quantification, Inform, and Comput. 87, 196-240.
3. Bruce, K. B., and Longo, G., To appear in (Gunter and Mitchell, 1994). An earlier version appeared in the Proceedings of the IEEE Symposium on Logic in Computer Science, 1988.
4. Bruce, K., and Mitchell, J. (1992), PER models of subtyping, recursive types and higher- order polymorphism, in "Proceedings of the Nineteenth ACM Symposium on Principles of Programming Languages, Albequerque, NM."
5. Bruce, K. B. (1991), The equivalence of two semantic definitions for inheritance in object- oriented languages, in "Proceedings of Mathematical Foundations of Programming Semantics, Pittsburgh, PA."
6. Bruce, K. B. (1992), "A Paradigmatic Object-Oriented Language: Design, Static Typing and Semantics," Technical Report CS-92-01, WIIIiams College.
7. Bruce, K. B. (1993), Safe type checking in a statically typed object-oriented programming language, in "Proceedings of the Twentieth ACM Symposium on Principles of Programming Languages."
8. Canning, P., Cook, W., WIII, W., and Olthoff, W. (1989a), Interfaces for strongly-typed object-oriented programming, in "Object Oriented Programming: Systems, Languages, and Applications (Conference Proceedings)," pp. 457-467.
9. Canning, P., Cook, W., WIII, W., and Olthoff, W. (1989b), F-bounded quantification for object-oriented programming, in "Fourth International Conference on Functional Programming Languages and Computer Architecture," pp. 273-280.
10. Cardelli, L., and Longo, G. (1991), A semantic basis for Quest, J. Functional Programming 1 (4), 417-458.
11. Cardelli, L., and Longo, G., Preliminary version in "ACM Conference on Lisp and Functional Programming," June 1990. Also available as DEC SRC Research Report 55, Feb. 1990.
12. Cardelli, L., and Mitchell, J. (1991), Operations on records, Math. Structures Comput. Sci. 1, 3-48. To appear in (Gunter and Mitchell, 1994); also available as DEC Systems Research Center Research Report #48, August, 1989, and in the proceedings of MFPS '89, Springer LNCS volume 442.
13. Cardelli, L., and Wegner, P. (1985), On understanding types, data abstraction, and polymorphism, Comput. Surv. 17 (4).
14. Cardelli, L., Martini, S., Mitchell, J. C., and Scedrov, A. (1991), An extension of system F with subtyping, in Ito and Meyer (1991, pp. 750-770).
15. Cardelli, L. (1988a), A semantics of multiple inheritance, Inform, and Comput. 76, 138-164. Preliminary version in "Semantics of Data Types" (Kahn, MacQueen, and Plotkin, Eds.), Lecture Notes in Computer Science, Vol. 173, Springer-Verlag, Berlin/New York.
16. Cardelli, L. (1988b), Structural subtyping and the notion of power type, in "Proceedings of the 15th ACM Symposium on Principles of Programming Languages, San Diego," pp. 70-79.
17. Cardelli, L. (1991a), F-sub, the system, unpublished manuscript.
18. Cardelli, L. (1991b), Typeful programming, in "Formal Description of Programming Concepts" (E. J. Neuhold and M. Paul, Eds.), Springer-Verlag, Berlin/New York. An earlier version appeared as DEC Systems Research Center Research Report 45, 1989.
19. Cardelli, L. (1992), "Extensible Records in a Pure Calculus of Subtyping," Research Report 81, DEC Systems Research Center. To appear in (Gunter and Mitchell, 1994).
20. Cardone, F. (1989), Relational semantics for recursive types and bounded quantification, in "Proceedings of the Sixteenth International Colloquium on Automata, Languages, and Programming, Stresa, Italy," pp. 164-178, Lecture Notes in Computer Science, Vol. 372, Springer-Verlag, Berlin/New York.
21. Cook, W. R., HIII, W. L., and Canning, P. S. (1990), Inheritance is not subtyping, in "Seventeenth Annual ACM Symposium on Principles of Programming Languages, San Francisco," pp. 125-135. To appear in (Gunter and Mitchell, 1994).
22. Coppo, M., Dezani-Ciancaglini, M., and Venneri, B. (1980), Principal type schemes and lambda calculus semantics, in "To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism," pp. 535-560, Academic Press, New York.
23. Curien, P.-L., and Ghelli, G. (1991), Subtyping + extensionality: Confluence of β-reductions in F ≤, in Ito and Meyer (1991, pp. 731-749).
24. Curien, P.-L., and Ghelli, G. (1992), Coherence of subsumption: Minimum typing and type-checking in F≤, Math. Structures Comput. Sci. 2, 55-91. To appear in (Gunter and Mitchell, 1994).
25. de Brujjn, N. G. (1972), Lambda-calculus notation with nameless dummies: A tool for automatic formula manipulation with application to the Church-Rosser theorem, Indag. Math. 34 (5), 381-392.
26. Ghelli, G., and Pierce, B. (1992), "Bounded Existentials and Minimal Typing," Draft technical report.
27. Ghelli, G. (1990), "Proof Theoretic Studies about a Minimal Type System Integrating Inclusion and Parametric Polymorphism," Ph.D. Thesis, Universita di Pisa; Technical Report TD-6-90, Dipartimento di Informatica, Universita di Pisa.
28. Ghelli, G. (1991), Modelling features of object-oriented languages in second-order functional languages with subtypes, in "Foundations of Object-Oriented Programming" (J. W. de Bakker, W. P. de Roever, and G. Rozenberg, Eds.), pp. 311-340, Lecture Notes in Computer Science, Vol. 489, Springer-Verlag, Berlin/New York.
29. Ghelli, G. (1992), Divergence of F≤ type checking, Theoret. Comput. Sci., to appear.
30. Ghelli, G. (1993), Recursive types are not conservative over F≤, in "Typed Lambda Calculus and Applications."
31. Girard, J. Y. (1972), "Interpretation fonctionelle et elimination des coupures de l'arithmetique d'ordre superieur," Ph.D. Thesis, Universite de Paris VII.
32. Gunter, C. A., and Mitchell, J. C., Eds. (1994), "Theoretical Aspects de Object- Oriented Programming: Types, Semantics, and Language Design," MIT Press, Cambridge, MA.
33. Hofmann, M., and Pierce, B. (1992), "An Abstract View of Objects and Subtyping (Preliminary Report)," Technical Report ECS-LFCS-92-226, University of Edinburgh.
34. Hopcroft, J. E., and Ullman, J. D. (1979), "Introduction to Automata Theory, Languages, and Computation," Addison-Wesley, Reading, MA.
35. Ito, T., and Meyer, A. R., Eds. (1991), "Theoretical Aspects of Computer Software, Sendai, Japan," Lecture Notes in Computer Science, No. 526, Springer-Verlag, Berlin/New York.
36. Katiyar, D., and Sankar, S. (1992), Completely bounded quantification is decidable, in "Proceedings of the ACM SIGPLAN Workshop on ML and its Applications."
37. Martini, S. (1988), Bounded quantifiers have interval models, in "Proceedings of the ACM Conference on Lisp and Functional Programming, Snowbird, UT," pp. 174-183, Assoc. Com put. Mach.
38. Mitchell, J., and Plotkin, G. (1988), Abstract types have existential type, ACM Trans. Programming Languages Systems 10 (3).
39. Mitchell, J., Meldal, S., and Madhav, N. (1991), An extension of Standard ML modules with subtyping and inheritance, in "Proceedings of the Eighteenth ACM Symposium on Principles of Programming Languages, Orlando, FL," pp. 270-278.
40. Mitchell, J. C. (1988), Polymorphic type inference and containment, Inform, and Comput. 76, 211-249
41. Pierce, B. C., and Turner, D. N. (1994), Simple type-theoretic foundations for object- oriented programming, J. Functional Programming, to appear.
42. Pierce, B. C., and Turner, D. N. A preliminary version appeared in "Principles of Programming Languages" (1993) and as University of Edinburgh Technical Report ECS-LFCS-92-225, under the title "Object-Oriented Programming Without Recursive Types."
43. Pierce, B. C. (1991), "Programming with Intersection Types and Bounded Polymorphism," Ph.D. Thesis, Carnegie-Mellon University. Available as School of Computer Science Technical Report CMU-CS-91-205.
44. Pierce, B. C. (1993), Intersection types and bounded polymorphism, in "Conference on Typed Lambda Calculi and Applications," to appear. Preliminary version available as University of Edinburgh Technical Report ECS-LFCS-92-200.
45. Reynolds, J. (1974), Towards a theory of type structure, in "Proc. Colloque sur la Programmation, New York," pp. 408-425, Lecture Notes in Computer Science, Vol. 19, Springer-Verlag, Berlin/New York.
46. Reynolds, J. C. (1988), "Preliminary Design of the Programming Language Forsythe," Technical Report CMU-CS-88-159, Carnegie-Mellon University.