Syntactic Logical Relations for Polymorphic and Recursive Types

Electronic Notes in Theoretical Computer Science

Volumn 172, Issue , 2007, Pages 259-299

  Crary, Karl ^a   Harper, Robert ^a  

^a Carnegie Mellon University ^*  (United States)

Author keywords

data abstraction; lambda calculus and related systems; logics of programs; Operational semantics; polymorphism; type structure

Indexed keywords

DATA STRUCTURES; FORMAL LANGUAGES; SEMANTICS;

CONTEXTUAL EQUIVALENCES; DATA ABSTRACTION; LAMBDA CALCULUS; OPERATIONAL SEMANTICS;

RECURSIVE FUNCTIONS;

EID: 33847630863     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2007.02.010     Document Type: Article

References (36)

1. Abadi, M. and G.D. Plotkin, A per model of polymorphism and recursive types, in: LICS [13], pp. 355-365
2. Ahmed, A., Step-indexed syntactic logical relations for recursive and quantified types, in: Fifteenth European Symposium on Programming, Vienna, Austria, 2006, pp. 69-83
3. Appel A.W., and McAllester D.A. An indexed model of recursive types for foundational proof-carrying code. ACM Trans. Program. Lang. Syst. 23 (2001) 657-683
4. Birkedal L., and Harper R. Relational interpretations of recursive types in an operational setting. Information and Computation 155 (1999) 3-63
5. Filinski, A., On the relations between monadic semantics, in: John Reynolds Festschrift, 2007 To appear
6. Freyd, P.J., Recursive types reduced to inductive types, in: LICS [13], pp. 498-507
7. Girard, J.-Y., "Interprétation Fonctionnelle et Élimination des Coupures dans l'Arithmétique d'Ordre Supérieure," Ph.D. thesis, Université Paris VII (1972)
8. Girard J.-Y., Lafont Y., and Taylor P. Proofs and Types. Cambridge Tracts in Theoretical Computer Science 7 (1989), Cambridge University Press, Cambridge, England
9. Ho, W.K., An operational domain-theoretic treatment of recursive types, in: Twenty-Second Mathematical Foundations of Programming Semantics, 2006
10. Hoare C.A.R. Proof of correctness of data representation. Artificial Intelligence 1 (1972) 271-281
11. Howe, D.J., Equality in lazy computation systems, in: Proceedings of the Fourth Annual Symposium on Logic in Computer Science (1989), pp. 198-203 URL citeseer.ist.psu.edu/howe89equality.html
12. Howe D.J. Proving congruence of bisimulation in functional programming languages. Inf. Comput. 124 (1996) 103-112
13. Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, 4-7 June 1990, Philadelphia, Pennsylvania, USA (1990), IEEE Computer Society
14. Mason I.A., Smith S.F., and Talcott C.L. From operational semantics to domain theory. Information and Computation 128 (1996) 26-47
15. Mitchell, J.C., Representation independence and data abstraction, in: Thirteenth ACM SIGACT/SIGPLAN Symposium on Principles of Programming Languages, 1986, pp. 263-276
16. Mitchell J.C., and Plotkin G.D. Abstract types have existential type. ACM Trans. Program. Lang. Syst. 10 (1988) 470-502
17. Pitts A. Typed operational reasoning. In: Pierce B.C. (Ed). Advanced Topics in Types and Programming Languages (2005), mit-press 245-289
18. Pitts A.M. Operationally-based theories of program equivalence. In: Dybjer P. (Ed). Semantics and Logics of Computation (1995), Cambridge University Press 241-283. URL citeseer.ist.psu.edu/113777.html
19. Pitts A.M. Relational properties of domains. Information and Computation 127 (1996) 66-90
20. Pitts A.M. Existential types: Logical relations and operational equivalence. In: Larsen K.G., Skyu S., and Winskel G. (Eds). ICALP. Lecture Notes in Computer Science vol. 1443 (1998) 309-326
21. Pitts A.M. Parametric polymorphism and operational equivalence. Mathematical Structures in Computer Science 10 (2000) 321-359
22. Plotkin G.D. LCF considered as a programming language. Theor. Comput. Sci. 5 (1977) 225-255
23. Plotkin, G.D., Domain theory (1983), unpublished Notes. URL http://homepages.inf.ed.ac.uk/gdp/publications/Domains.ps
24. Plotkin G.D. The origins of structural operational semantics. J. Log. Algebr. Program. 60-61 (2004) 3-15
25. Plotkin G.D. A structural approach to operational semantics. J. Log. Algebr. Program. 60-61 (2004) 17-139
26. Plotkin G.D., and Abadi M. A logic for parametric polymorphism. In: Bezem M., and Groote J.F. (Eds). TLCA. Lecture Notes in Computer Science 664 (1993) 361-375
27. Reynolds J.C. On the relation between direct and continuation semantics. Second Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science vol. 14 (1974) 141-156
28. Reynolds J.C. Towards a theory of type structure. Colloq. sur la Programmation. Lecture Notes in Computer Science vol. 19 (1974) 408-423
29. Reynolds, J.C., Types, abstraction, and parametric polymorphism, in: R.E.A. Mason, editor, Information Processing '83 (1983), pp. 513-523
30. Riecke, J.G. and R. Subrahmanyam, Semantic orthogonality of type disciplines (1997), (Unpublished manuscript.). URL citeseer.ist.psu.edu/riecke97semantic.html
31. Smyth M.B., and Plotkin G.D. The category-theoretic solution of recursive domain equations. SIAM J. Comput. 11 (1982) 761-783
32. Statman R. Logical relations and the typed λ-calculus. Information and Control 65 (1985) 85-97
33. Sumii, E. and B.C. Pierce, A bisimulation for type abstraction and recursion, in: POPL '05: Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages (2005), pp. 63-74
34. Vouillon, J. and P.-A. Melliès, Semantic types: A fresh look at the ideal model for types, in: Thirty-First ACM Symposium on Principles of Programming Languages, Venice, Italy, 2004, pp. 52-63
35. Wadler, P., Theorems for free!, in: FPCA '89: Proceedings of the fourth international conference on Functional programming languages and computer architecture (1989), pp. 347-359
36. Wadler, P., Theorems for free!, in: Fourth Conference on Functional Programming Languages and Computer Architecture, London, 1989