Classical linear logic of implications

Mathematical Structures in Computer Science

Volumn 15, Issue 2, 2005, Pages 323-342

  Hasegawa, Masahito ^a,b  

^a KYOTO UNIVERSITY   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749395084     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129504004621     Document Type: Article

References (38)

1. Barber, A. (1997) Linear Type Theories, Semantics and Action Calculi, Ph.D. Thesis, ECS-LFCS-97-371, University of Edinburgh.
2. Barber, A. and Plotkin, G. (1997) Dual intuitionistic linear logic. Manuscript. (An earlier version is available as Technical Report ECS-LFCS-96-347, Laboratory for Foundations of Computer Science, University of Edinburgh.)
3. Barr, M. (1979) *-Autonomous Categories. Springer-Verlag Lecture Notes in Mathematics 752.
4. Barr, M. (1991) *-autonomous categories and linear logic. Mathematical Structures in Computer Science 1 159-178.
5. Benton, P. N. (1995) A mixed linear and non-linear logic: proofs, terms and models (extended abstract). In: Computer Science Logic (CSL'94). Springer-Verlag Lecture Notes in Computer Science 933 121-135.
6. Berdine, J., O'Hearn, P. W., Reddy, U. S. and Thielecke, H. (2001) Linearly used continuations. In: Proc. ACM SIGPLAN Workshop on Continuations (CW'01). Technical Report No. 545, Computer Science Department, Indiana University, 47-54.
7. Berdine, J., O'Hearn, P. W., Reddy, U. S. and Thielecke, H. (2002) Linear continuation-passing. Higher-Order and Symbolic Computation 15 (2/3) 181-203.
8. Bierman, G. M. (1995) What is a categorical model of intuitionistic linear logic? In: Proc. Typed Lambda Calculi and Applications (TLCA'95). Springer-Verlag Lecture Notes in Computer Science 902 78-93.
9. Bierman, G. M. (1999) A classical linear lambda-calculus. Theoret. Comp. Sci. 227 (1-2) 43-78.
10. Bierman, G. M., Pitts, A. M. and Russo, C. V. (2000) Operational properties of Lily, a polymorphic linear lambda calculus with recursion. In: Proc. Higher Order Operational Techniques in Semantics (HOOTS 2000). Electronic Notes in Theoretical Computer Science 41.
11. Blute, R. F., Cockett, J. R. B., Seely, R. A. G. and Trimble, T. H. (1996) Natural deduction and coherence for weakly distributive categories. J. Pure Appl. Algebra 113 (3) 229-296.
12. Blute, R. F., Cockett, J. R. B. and Seely, R. A. G. (1997) Categories for computation in context and unified logic. J. Pure Appl. Algebra 116 49-98.
13. Cockett, J. R. B., Hasegawa, M. and Seely. R. A. G. (2003) Coherence of the double involution on *-autonomous categories. (Submitted for publication.)
14. Felleisen, M., Friedman, D. P., Kohlbecker, E. E. and Duba, B. F. (1987) A syntactic theory of sequential control. Theor. Comput. Sci. 52 205-237.
15. Filinski, A. (1992) Linear continuations. In: Proc. Principles of Programming Languages (POPL'92) 27-38.
16. Führmann, C. and Thielecke, H. (2004) On the call-by-value CPS transform and its semantics. Inform. and Compt. 188 241-283.
17. Girard, J.-Y. (1987) Linear logic. Theoret. Comp. Sci. 50 1-102.
18. Hasegawa, M. (1999) Logical predicates for intuitionistic linear type theories. In: Proc. Typed Lambda Calculi and Applications (TLCA'99). Springer-Verlag Lecture Notes in Computer Science 1581 198-213.
19. Hasegawa, M. (2000) Girard translation and logical predicates. J. Funct. Programming 10 (1) 77-89.
20. Hasegawa, M. (2002) Linearly used effects: monadic and CPS transformations into the linear lambda calculus. In: Proc. Functional and Logic Programming (FLOPS2002). Springer-Verlag Lecture Notes in Computer Science 2441 67-182.
21. Hasegawa, M. (2002) Classical linear logic of implications. In: Proc. Computer Science Logic (CSL'02). Springer-Verlag Lecture Notes in Computer Science 2471 458-472.
22. Hasegawa, M. (2004) Semantics of linear continuation-passing in call-by-name. In: Proc. Functional and Logic Programming (FLOPS2004). Springer-Verlag Lecture Notes in Computer Science 2998 229-243.
23. Hodas, J. S. and Miller, D. (1994) Logic programming in a fragment of intuitionistic linear logic. Inform. and Comput. 110 (2) 327-365.
24. Hyland, M. (2002) Proof theory in the abstract. Ann. Pure Appl. Logic 114 43-78.
25. Hyland, M. and Schalk, A. (2003) Glueing and orthogonality for models of linear logic. Theoret. Comp. Sci. 294 (1/2) 183-231.
26. Kelly, G. M. and Mac Lane, S. (1971) Coherence in closed categories. J. Pure Appl. Algebra 1 (1) 97-140.
27. Koh, T. W. and Ong, C.-H. L. (1999) Explicit substitution internal languages for autonomous and *-autonomous categories. In: Proc. Category Theory and Computer Science (CTCS'99). Electronic Notes in Theoretical Computer Science 29.
28. Lambek, J. (1989) Multicategories revisited. In: Categories in Computer Science. AMS Contemporary Mathematics 92 217-239.
29. Maietti, M. E., de Paiva, V. and Ritter, E. (2000) Categorical models for intuitionistic and linear type theory. In: Foundations of Software Science and Computation Structure (FoSSaCS 2000). Springer-Verlag Lecture Notes in Computer Science 1784 223-237.
30. Murawski, A. S. and Ong, C.-H. L. (1999) Exhausting strategies, Joker games and IMLL with units. In: Proc. Category Theory and Computer Science (CTCS'99). Electronic Notes in Theoretical Computer Science 29.
31. Nishizaki, S. (1993) Programs with continuations and linear logic. Science of Computer Programming 21 (2) 165-190.
32. Parigot, M. (1992) λμ-calculus: an algorithmic interpretation of classical natural deduction. In: Proc. Logic Programming and Automated Reasoning. Springer-Verlag Lecture Notes in Computer Science 624 190-201.
33. Plotkin, G. (1993) Type theory and recursion (extended abstract). In: Proc. Logic in Computer Science (LICS'93) 374.
34. Seely, R. A. G. (1989) Linear logic, *-autonomous categories and cofree coalgebras. In: Categories in Computer Science. AMS Contemporary Mathematics 92 371-389.
35. Streicher, T. (1999) Denotational completeness revisited. In: Proc. Category Theory and Computer Science (CTCS'99). Electronic Notes in Theoretical Computer Science 29.
36. Szabo, M. E. (1975) Polycategories. Comm. Algebra 3 663-689.
37. Wadler, P. (1990) Linear types can change the world! In: Proc. Programming Concepts and Methods, North-Holland 561-581.
38. Wadler, P. (1993) A syntax for linear logic. In: Proc. Mathematical Foundations of Programming Semantics (MFPS'93). Springer-Verlag Lecture Notes in Computer Science 802 513-529.