Unique decomposition categories, Geometry of Interaction and combinatory logic

Mathematical Structures in Computer Science

Volumn 10, Issue 2, 2000, Pages 205-230

  Haghverdi, Esfandiar ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14544279370     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129599003035     Document Type: Article

References (29)

1. Abramsky, S. (1996) Retracing Some Paths in Process Algebra. In: CONCUR 96. Springer-Verlag Lecture Notes in Computer Science 1119 1–17.
2. Abramsky, S. (1997) Interaction, Combinators and Complexity. Lecture Notes, Siena, Italy.
3. Abramsky, S., Blute, R. and Panangaden, P. (1997) Nuclear and Traced Ideals in Tensored *-categories. (To appear in J. Pure and Applied Algebra.)
4. Abramsky, S., Haghverdi, E. and Scott, P. J. (1999) Geometry of Interaction and Linear Combinatory Algebras. (To appear.)
5. Abramsky, S. and Jagadeesan, R. (1994) New Foundations for the Geometry of Interaction. Information and Computation 111 (1) 53–119.
6. Asperti, A., Danos, V., Laneve, C. and Regnier, L. (1994) Paths in the 2-calculus: Three years of communication without understanding. In: Proc. Ninth LICS, IEEE Press 426–436.
7. Asperti, A. and Mairson, H. G. (1998) Parallel beta reduction is not elementary recursive. In: Proc. ACM Symposium on the Principles of Programming Languages.
8. Barr, M. (1992) Algebraically Compact Functors. J. Pure and Applied Algebra 82 211–231.
9. Bourbaki, N. (1996) General Topology, Part 1, Addison-Wesley. Danos, V. (1990) La logique lineaire appliquee a l'etude de divers processus de normalisation et principalement du λ-calcul, Ph. D. thesis, Universite Paris VII.
10. Danos, V. and Regnier, L. (1993) Local and Asynchronous beta-reduction (An Analysis of Girard’s Execution Formula). In: Proc. Eighth LICS, IEEE Press 296–306.
11. Danos, V. and Regnier, L. (1994) Proof-nets and Hilbert Spaces. In: Girard, J-Y. et al. (eds.) Advances in Linear Logic, London Math. Soc. LNS 222 307–328.
12. Girard, J.-Y. (1987) Linear Logic. Theoretical Computer Science 50 (1) 1–102.
13. Girard, J.-Y. (1988) Geometry of Interaction II: Deadlock-free Algorithms. In: Proc. of COLOG’88. Springer-Verlag Lecture Notes in Computer Science 417 76–93.
14. Girard, J.-Y. (1989) Towards a Geometry of Interaction. Contemp. Math. 92 69–108.
15. Girard, J.-Y. (1989a) Geometry of Interaction I: Interpretation of System F. In Proc. Logic Collo-quium 88, North Holland 221–260.
16. Girard, J.-Y. (1995) Geometry of Interaction III: Accommodating the Additives. Advances in Linear Logic, London Math. Soc. LNS 222 329–389.
17. Gonthier, G., Abadi, M. and Levy, J.-J. (1992) The geometry of optimal lambda reduction. In: Proc. Ninth ACM Symposium on Principles of Programming Languages 15–26.
18. Haghverdi, E. (1999) Forthcoming Ph. D. Thesis, University of Ottawa.
19. Higgs, D. (1980) Axiomatic Infinite Sums - An Algebraic Approach to Integration Theory. Contemp. Math. 2 205–213.
20. Joyal, A., Street, R. and Verity, D. (1996) Traced Monoidal Categories. Math. Proc. Comb. Phil. Soc. 119 447–468.
21. Kadison, R. V. and Ringrose, J. R. (1983) Fundamentals of the Theory of Operator Algebras, Volume 1, Academic Press.
22. Kuroš, A. G. (1963) Direct Decomposition in Algebraic Categories. Amer. Math. Soc. Transl. Ser. 2, 27 231–255.
23. Mackie, I. (1994) The Geometry of Implementation, Ph. D. Thesis, University of London, Imperial College of Science, Technology and Medicine.
24. Malacaria, P. and Regnier. L. (1991) Some Results on the Interpretation of 2-calculus in Operator Algebras. In: Proc. of Sixth LICS, IEEE Computer Society Press 63–72.
25. Manes, E. G. and Arbib, M.A. (1986) Algebraic Approaches to Program Semantics, Springer-Verlag.
26. Manes E. G. and Benson, D. B. (1985) The Inverse Semigroup of a Sum-Ordered Semiring. Semigroup Forum 31 129–152.
27. Moggi, E. (1991) Notions of Computation and Monads. Infor. and Comput. 93 55–93.
28. Panangaden, P. (1997) Stochastic Techniques in Concurrency. Lecture Notes, BRICS, Aarhus, Denmark.
29. Regnier, L. (1992) Lambda-calcul et Reseaux, Ph. D. Thesis, Universite Paris VII.