A bisimulation for type abstraction and recursion

Journal of the ACM

Volumn 54, Issue 5, 2007, Pages

  Sumii, Eijiro ^a   Pierce, Benjamin C ^b,c  

^a TOHOKU UNIVERSITY   (Japan)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Bisimulations; Contextual equivalence; Existential types; Lambda calculus; Logical relations; Recursive types

Indexed keywords

BISIMULATIONS; CONTEXTUAL EQUIVALENCE; EXISTENTIAL TYPES; LAMBDA-CALCULUS; LOGICAL RELATIONS; RECURSIVE TYPES;

ABSTRACTING; CALCULATIONS; RECURSIVE FUNCTIONS; SEMANTICS; SYNTACTICS;

COMPUTER SIMULATION;

EID: 35348948557     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/1284320.1284325     Document Type: Article

References (50)

1. ABADI, M., AND FOURNET, C. 2001. Mobile values, new names, and secure communication. In Proceedings of the 28th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, New York, 104-115.
2. ABADI, M., AND GORDON, A. D. 1998. A bisimulation method for cryptographic protocols. Nordic Journal of Computing 5, 267-303.
3. (Preliminary version appeared in Proceedings of the 7th European Symposium on Programming. Lecture Notes in Computer Science, vol. 1381, Springer-Verlag, New York, pp. 12-26, 1998).
4. ABADI, M., AND GORDON, A. D. 1999. A calculus for cryptographic protocols: The spi calculus. Information and Computation 148, 1, 1-70.
5. (Preliminary version appeared in Proceedings of the 4th ACM Conference on Computer and Communications Security, ACM, New York, pp. 36-47, 1997).
6. ABRAMSKY, S. 1990. The lazy lambda calculus. In Research Topics in Functional Programming, D. A. Turner, Ed. Addison-Wesley, Reading, MA, 65-117.
7. AHMED, A. 2006. Step-indexed syntactic logical relations for recursive and quantified types. In Proceedings of the 15th European Symposium on Programming. 69-83.
8. AHMED, A., APPEL, A. W., AND VIRGA, R. 2003. An indexed model, of impredicative polymorphism and mutable references. http://www.cs.princeton.edu/~amal/papers/impred.pdf.
9. APPEL, A. W., AND MCALLESTER, D. 2001. An indexed model of recursive types for foundational proof-carrying code. ACM Trans. Prog. Lang. Syst. 23, 5, 657-683.
10. BERGER, M., HONDA, K., AND YOSHIDA, N. 2003. Genericity and the pi-calculus. In Proceedings of the Foundations of Software Science and Computation Structures. Lecture Notes in Computer Science, vol. 2620. Springer-Verlag, New York, 103-119.
11. BIERMAN, G. M., PITTS, A. M., AND RUSSO, C. V. 2000. Operational properties of Lily, a polymorphic linear lambda calculus with recursion. In Higher Order Operational Techniques in Semantics. Electronic Notes in Theoretical Computer Science, vol. 41. Elsevier Science, Amsterdam, The Netherlands.
12. BIRKEDAL, L., AND HARPER, R. 1999. Relational interpretations of recursive types in an operational setting. Info. Comput. 155, 1-2, 3-63.
13. (Summary appeared in Theoretical Aspects of Computer Software, Lecture Notes in Computer Science, vol. 1281, Springer-Verlag, New York, pp. 458-490, 1997).
14. BOREALE, M., DE NICOLA, R., AND PUGLIESE, R. 2002. Proof techniques for cryptographic processes. SIAM J. Comput. 31, 3, 947-986.
15. (Preliminary version appeared in. Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science, pp. 157-166, 1999).
16. BORGSTRÖM, J., AND NESTMANN, U. 2002. On bisimulations for the spi calculus. In Proceedings of the 9th International Conference on Algebraic Methodology and Software Technology. Lecture Notes in Computer Science, vol. 2422. Springer-Verlag, New York, 287-303.
17. BRUCE, K. B., CARDELLI, L., AND PIERCE, B. C. 1999. Comparing object encodings. Info. Comput. 155, 1-2, 108-133.
18. (Extended abstract appeared in Theoretical Aspects of Computer Software, vol. 1281, Springer-Verlag, New York, pp. 415-338, 1997).
19. CRARY, K., AND HARPER, R. 2007. Syntactic logical relations for polymorphic and recursive types. In Computation, Meaning, and Logic: Articles Dedicated to Gordon Plotkin. Electronic Notes in Theoretical Computer Science, vol. 172. Elsevier Science, Amsterdam, The Netherlands, 259-299.
20. GORDON, A. D. 1995a. Bisimilarity as a theory of functional programming, mini-course. http://research.microsoft.com/~adg/Publications/BRICS- NS-95-3.dvi.gz.
21. GORDON, A. D. 1995b. Operational equivalences for untyped and polymorphic object calculi. In Higher Order Operational Techniques in Semantics, Cambridge University Press, Cambridge, UK, 9-54.
22. GORDON, A. D., AND REES, G. D. 1995. Bisimilarity for F<:. Draft.
23. GORDON, A. D., AND REES, G. D. 1996. Bisimilarity for a first-order calculus of objects with subtyping. In Proceedings of the 23rd ACM SIGPLAN-SIGACT Symposium on Principles ofProgramming Languages. ACM, New York, 386-395.
24. HEINTZE, N., AND RIECKE, J. G. 1998. The SLam calculus: Programming with secrecy and integrity. In Proceedings of the 25 th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, New York.
25. HOWE, D. J. 1996. Proving congruence of bisimulation in functional programming languages. Info. Comput. 124, 2, 103-112.
26. HUGHES, D. J. 1997. Games and definability for System F. In Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 76-86.
27. KOUTAVAS, V., AND WAND, M. 2006a. Bisimulations for untyped imperative objects. In Proceedings of the 15th European Symposium on Programming. 146-161.
28. KOUTAVAS, V., AND WAND, M. 2006b. Small bisimulations for reasoning about higher-order imperative programs. In Proceedings of the 33rd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, New York, 141-152.
29. KOUTAVAS, V., AND WAND, M. 2007. Reasoning about class behavior. In Proceedings of the 2007 International Workshop on Foundations and Developments of Object-Oriented Languages. http://foolwood07.cs.uchicago.edu/program/koutavas.pdf.
30. MELLIÉS, P.-A., AND VOUILLON, J. 2005. Recursive polymorphic types and parametricity in an operational framework. In Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Pres, Los Alamitos, CA, 82-91.
31. MEYER, A. R., AND SIEBER, K. 1988. Towards fully abstract semantics for local variables: Preliminary report. In Proceedings of the 15th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, New York, 191-203.
32. MILNER, R. 1980. A Calculus of Communicating Systems. Number 92 in Lecture Notes in Computer Science. Springer-Verlag, New York.
33. MILNER, R. 1989. Communication and Concurrency. Prentice Hall, Englewood Cliffs, NJ.
34. MILNER, R. 1999. Communicating and Mobile Systems: The π-Calculus. Cambridge University Press, Cambridge, MA.
35. MITCHELL, J. C. 1996. Foundations for Programming Languages. MIT Press, Cambridge, MA.
36. MOGGI, E. 1991. Notions of computation and monads. Info. Comput. 93, 1, 55-92.
37. MORRIS, JR., J. H. 1973a. Protection in programming languages. Commun. ACM 16, 1, 15-21.
38. MORRIS, JR., J. H. 1973b. Types are not sets. In Proceedings ofthe 1st Annual ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, ACM, New York, 120-124.
39. PIERCE, B. C., AND SANGIORGI, D. 2000. Behavioral equivalence in the polymorphic pi-calculus. J. ACM 47, 3, 531-586.
40. (Extended abstract appeared in Proceedings of the 24th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, 1997, pp. 531-584).
41. PITTS, A. 2005. Typed operational reasoning. In Advanced Topics in Types and Programming Languages, B. C. Pierce, Ed. MIT Press, Cambridge, MA, Chapter 7, 245-289.
42. (Preliminary version appeared as Existential Types: Logical Relations and Operational Equivalence in Automata, Languages and Programming, Lecture Notes in Computer Science, vol. 1443, Springer-Verlag, pp. 309-326, 1998).
43. PITTS, A. M. 2000. Parametric polymorphism and operational equivalence. Math. Struct. Comput. Sci. 10, 321-359.
44. (Preliminary version appeared in HOOTS II Second Workshop on Higher-Order Operational Techniques in Semantics, Electronic Notes in Theoretical Computer Science, vol. 10, 1998).
45. PITTS, A. M., AND STARK, I. 1993. Observable properties of higher order functions that dynamically create local names, or: What's new? In Proceedings of the Symposium on Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 711. Springer-Verlag, New York, 122-141.
46. PITTS, A. M., AND STARK, I. 1998. Operational reasoning for functions with local state. In Higher Order Operational Techniques in Semantics. Cambridge University Press, Cambridge, MA, 227-273.
47. SANGIORGI, D. 1992. Expressing mobility in process algebras: First-order and higher-order paradigm. Ph.D. dissertation, University of Edinburgh, Edinburgh, Scotland.
48. SANGIORGI, D., KOBAYASHI, N., AND SUMII, E. 2007. Environmental bisimulations for higher-order languages. In Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Almitos, CA, To appear. (Draft available at http://www.kb.ecei.tohoku.ac.jp/~sumii/pub/infohide6.pdf).
49. SUMU, E., AND PIERCE, B. C. 2004. A bisimulation for dynamic sealing. In Proceedings of the 31st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, New York, 161-172.
50. WADLER, P. 1989. Theorems for free! In Proceedings of the 4th International Conference on Functional Programming Languages and Computer Architecture. ACM, New York, 347-359.