Category-theoretic models of linear Abadi & Plotkin logic

Theory and Applications of Categories

Volumn 20, Issue , 2008, Pages 116-151

  Birkedal, Lars ^a   Møgelberg, Rasmus E ^a   Petersen, Rasmus L ^b  

^a IT UNIVERSITY OF COPENHAGEN   (Denmark)

^b QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Axiomatic domain theory; Categorical semantics; Fibrations; Parametric polymorphism; Recursive types

Indexed keywords

EID: 42949142051     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. Barber, A. (1997). Linear Type Theories, Semantics and Action Calculi. PhD thesis, Edinburgh University.
2. Benton, P. (1995). A mixed linear and non-linear logic: Proofs, terms and models (preliminary report). Technical report, University of Cambridge.
3. Bierman, G. M., Pitts, A. M., and Russo, C. V. (2000). Operational properties of Lily, a polymorphic linear lambda calculus with recursion. In Fourth International Workshop on Higher Order Operational Techniques in Semantics, Montréal, volume 41 of Electronic Notes in Theoretical Computer Science. Elsevier.
4. Birkedal, L. and Møgelberg, R. E. (2005). Categorical models of Abadi-Plotkin's logic for parametricity. Mathematical Structures in Computer Science, 15(4):709-772.
5. Birkedal, L., Møgelberg, R. E., and Petersen, R. L. (2006). Linear Abadi & Plotkin logic. Logical Methods in Computer Science, 2.
6. Birkedal, L., Møgelberg, R. E., and Petersen, R. L. (2007). Domain-theoretical models of parametric polymorphism. Theor. Comput. Sci, 388(1-3):152-172.
7. Freyd, P. (1990a). Algebraically complete categories. In Carboni, A., Pedicchio, M. C., and Rosolini, G., editors, Category Theory. Proceedings, Como 1990, volume 1488 of Lecture Notes in Mathematics, pages 95-104. Springer-Verlag.
8. Freyd, P. (1990b). Recursive types reduced to inductive types. In Proceedings of the fifth IEEE Conference on Logic in Computer Science, pages 498-507.
9. Freyd, P. (1991). Remarks on algebraically compact categories. In Fourman, M. P., Johnstone, P., and Pitts, A. M., editors, Applications of Categories in Computer Science. Proceedings of the LMS Symposium, Durham 1991, volume 177 of London Mathematical Society Lecture Note Series, pages 95-106. Cambridge University Press.
10. Huwig, H. and Poigné, A. (1990). A note on inconsistencies caused by fixpoints in a cartesian closed category. Theoretical Computer Science, 73:101-112.
11. Jacobs, B. (1993). Comprehension categories and the semantics of type dependency. Theoretical Computer Science, 107:169-207.
12. Jacobs, B. (1999). Categorical Logic and Type Theory, volume 141 of Studies in Logic and the Foundations of Mathematics. Elsevier Science Publishers B.V.
13. Ma, Q. and Reynolds, J. (1992). Types, abstraction, and parametric polymorphism, part 2. In Brookes, S., Main, M., Melton, A., Mislove, M., and Schmidt, D., editors, Mathematical Foundations of Programming Semantics, volume 598 of Lecture Notes in Computer Science, pages 1-40. Springer-Verlag.
14. Maietti, M. E., Maneggia, P., de Paiva, V., and Ritter, E. (2005). Relating categorical semantics for intuitionistic linear logic. Applied Categorical Structures, 13(1):1-36.
15. Maneggia, P. (2004). Models of linear polymorphism. PhD thesis, University of Birmingham.
16. Møgelberg, R. E. (2005a). Category theoretic and domain theoretic models of parametric polymorphism. PhD thesis, IT University of Copenhagen.
17. Møgelberg, R. E. (2005b). Parametric completion for models of polymorphic intuitionistic / linear lambda calculus. Technical Report TR-2005-60, IT University of Copenhagen.
18. Møgelberg, R. E., Birkedal, L., and Petersen, R. L. (2005). Categorical models of PILL. Technical Report TR-2005-58, IT University of Copenhagen.
19. O'Hearn, P. W. and Tennent, R. D. (1995). Parametricity and local variables. Journal of the ACM, 42(3):658-709.
20. Pitts, A. M. (2000). Parametric polymorphism and operational equivalence. Mathematical Structures in computer Science, 10:321-359.
21. Plotkin, G. (1993a). Second order type theory and recursion. Notes for a talk at the Scott Fest.
22. Plotkin, G. and Abadi, M. (1993). A logic for parametric polymorphism. In Typed lambda calculi and applications (Utrecht, 1993), volume 664 of Lecture Notes in Comput. Sci., pages 361-375. Springer, Berlin.
23. Plotkin, G. D. (1993b). Type theory and recursion (extended abstract). In Proceedings, Eighth Annual IEEE Symposium on Logic in Computer Science, page 374, Montreal, Canada. IEEE Computer Society Press.
24. Reynolds, J. (1983). Types, abstraction, and parametric polymorphism. Information Processing, 83:513-523.
25. Robinson, E. and Rosolini, G. (1994). Reflexive graphs and parametric polymorphism. In Abramsky, S., editor, Proc. 9th Symposium in Logic in Computer Science, pages 364-371, Paris. I.E.E.E. Computer Society.
26. Rosolini, G. and Simpson, A. (2004). Using synthetic domain theory to prove operational properties of a polymorphic programming language based on strictness. Manuscript.
27. Tse, S. and Zdancewic, S. (2004). Translating dependency into parametricity. In ICFP '04: Proceedings of the ninth ACM SIGPLAN international conference on Functional programming, pages 115-125. ACM Press.