Domain-theoretical models of parametric polymorphism

Theoretical Computer Science

Volumn 388, Issue 1-3, 2007, Pages 152-172

  Birkedal, L ^a   Mogelberg R E ^b   Petersen, R L ^a  

^a IT UNIVERSITY OF COPENHAGEN   (Denmark)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

Domain theory; Parametric polymorphism; Realizability models

Indexed keywords

COMPUTER PROGRAMMING; MATHEMATICAL MODELS; SEMANTICS;

DOMAIN THEORY; PARAMETRIC POLYMORPHISM; PLOTKIN'S LOGIC; REALIZABILITY MODELS;

POLYMORPHISM;

EID: 35748932653     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2007.06.016     Document Type: Article

References (26)

1. Abadi M., and Plotkin G.D. A per model of polymorphism and recursive types. 5th Annual IEEE Symposium on Logic in Computer Science (1990), IEEE Computer Society Press 355-365
2. Amadio R.M., and Curien P.-L. Domains and Lambda-Calculi. Cambridge Tracts in Theoretical Computer Science vol. 46 (1998), Cambridge University Press, Cambridge
3. A. Barber, Linear Type Theories, Semantics and Action Calculi, Ph.D. Thesis, Edinburgh University, 1997
4. Bierman G.M., Pitts A.M., and Russo C.V. Operational properties of Lily, a polymorphic linear lambda calculus with recursion. Fourth International Workshop on Higher Order Operational Techniques in Semantics, Montréal. Electronic Notes in Theoretical Computer Science vol. 41 (September 2000), Elsevier
5. L. Birkedal, R.E. Møgelberg, R.L. Petersen, Category theoretic models of linear Abadi & Plotkin logic, 2006 (submitted for publication)
6. Birkedal L., Møgelberg R.E., and Petersen R.L. Linear Abadi & Plotkin logic. Logical Methods in Computer Science 2 5:1 (2006) 1-33
7. L. Birkedal, R.E. Møgelberg, R.L. Petersen, Parametric domain-theoretic models of polymorphic intuitionistic/linear lambda calculus, in: M. Escardó, A. Jung, M. Mislove (Eds.), Proceedings of Mathematical Foundations of Programming Semantics 2005, vol. 155, 2005, pp. 191-217
8. Fiore M. Axiomatic Domain Theory in Categories of Partial Maps. Distinguished Dissertations in Computer Science (1996), Cambridge University Press
9. J.-Y. Girard, Interprétation fonctionelle et élimination des coupures de l'arithmétique d'ordre supérieur, Thèse d'Etat, Université Paris VII, 1972
10. Hasegawa M. Logical predicates for intuitionistic linear type theories. Proc. 4th International Conference on Typed Lambda Calculi and Applications. TLCA'99. Lecture Notes in Computer Science vol. 1581 (1999), Springer 198-213
11. Huwig H., and Poigné A. A note on inconsistencies caused by fixpoints in a cartesian closed category. Theoretical Computer Science 73 (1990) 101-112
12. Jacobs B. Semantics of weakening and contraction. Annals of Pure and Applied Logic 69 (1994) 73-106
13. Jacobs B. Categorical Logic and Type Theory. Studies in Logic and the Foundations of Mathematics vol. 141 (1999), Elsevier Science Publishers B.V.
14. R.E. Møgelberg, Category theoretic and domain theoretic models of parametric polymorphism, Ph.D. Thesis, IT University of Copenhagen, 2005
15. Møgelberg R.E. Interpreting polymorphic FPC into domain theoretic models of parametric polymorphism. Automata, Languages and Programming 33rd International Colloquium, ICALP 2006, Venice, Italy, July 10-14, 2006, Proceedings, Part II. Lecture Notes in Computer Science vol. 4052 (2006), Springer, Berlin, Heidelberg 372-383
16. R.E. Møgelberg, L. Birkedal, R.L. Petersen, Categorical models of PILL, Technical Report TR-2005-58, IT University of Copenhagen, February 2005
17. Pierce B.C. Types and Programming Languages (2002), MIT Press
18. Pitts A.M. Parametric polymorphism and operational equivalence. Mathematical Structures in computer Science 10 (2000) 321-359
19. G.D. Plotkin, Lectures on predomains and partial functions. Notes for a course given at the Center for the Study of Language and Information, Stanford, 1985
20. G.D. Plotkin, Second order type theory and recursion, Notes for a talk at the Scott Fest, February 1993
21. Plotkin G., and Abadi M. A logic for parametric polymorphism. Typed lambda calculi and applications (Utrecht, 1993). Lecture Notes in Comput. Sci. vol. 664 (1993), Springer, Berlin 361-375
22. Reynolds J.C. Towards a theory of type structure. Colloquium sur La Programmation. Lecture Notes in Computer Science vol. 19 (1974), Springer-Verlag 408-423
23. Reynolds J.C. Types, abstraction, and parametric polymorphism. Information Processing 83 (1983) 513-523
24. J.C. Reynolds, Private communication, June 2000
25. Robinson E.P., and Rosolini G. Reflexive graphs and parametric polymorphism. In: Abramsky S. (Ed). Proc. 9th Symposium in Logic in Computer Science (1994), I.E.E.E. Computer Society, Paris 364-371
26. G. Rosolini, A. Simpson, Using synthetic domain theory to prove operational properties of a polymorphic programming language based on strictness. Manuscript, 2004