A characterisation of lambda definability with sums via TT-closure operators

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5213 LNCS, Issue , 2008, Pages 278-292

  Katsumata, Shin Ya ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; DIFFERENTIATION (CALCULUS); FUNCTIONS; TECHNICAL PRESENTATIONS;

CARTESIANS; CHARACTERISATION; CLOSED CATEGORIES; CLOSURE OPERATORS; CO PRODUCTS; DEFINABILITY; MORPHISMS; TYPED LAMBDA CALCULUSES;

COMPUTERS;

EID: 57849163198     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-87531-421     Document Type: Conference Paper

References (26)

1. Alimohamed, M.: A characterization of lambda definability in categorical models of implicit polymorphism. Theor. Comput. Sci. 146(1&2), 5-23 (1995)
2. Altenkirch, T., Dybjer, P., Hofmann, M., Scott, P.: Normalization by evaluation for typed lambda calculus with coproducts. In: LICS, pp. 303-310 (2001)
3. Balat, V., Di Cosmo, R., Fiore, M.: Extensional normalisation and type-directed partial evaluation for typed lambda calculus with sums. In: Jones, N., Leroy, X. (eds.) POPL, pp. 64-76. ACM, New York (2004)
4. Barr, M., Wells, C.: Toposes, Triples and Theories. Springer, Heidelberg (1998)
5. Benton, N.: A typed, compositional logic for a stack-based abstract machine. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 364-380. Springer, Heidelberg (2005)
6. Borceux, F.: Handbook of Categorical Algebra 1. Encyclopedia of Mathematics and Its Applications, vol. 50. Cambridge University Press, Cambridge (1994)
7. Cockett, J.: Introduction to distributive categories. Mathematical Structures in Computer Science 3(3), 277-307 (1993)
8. Day, B. : A reflection theorem for closed categories. Journal of pure and applied algebra 2( 1), 1-11 (1972)
9. Dougherty, D., Subrahmanyam, R.: Equality between functional in the presence of coproducts. In: LICS, pp. 282-291. IEEE Computer Society, Los Alamitos (1995)
10. Fiore, M., Di Cosmo, R., Balat, V: Remarks on isomorphisms in typed lambda calculi with empty and sum types. In: LICS, pp. 147-157. IEEE Computer Society, Los Alamitos (2002)
11. Fiore, M., Simpson, A.: Lambda definability with sums via grothendieck logical relations. In: Girard, J.-Y. (ed.) TLCA 1999. LNCS, vol. 1581, pp. 147-161. Springer, Heidelberg (1999)
12. Ghani, N.: βη-equality for coproducts. In: Dezani-Ciancaglini, M., Plotkin, G.D. (eds.) TLCA 1995. LNCS, vol. 902, pp. .171-185. Springer, Heidelberg (1995)
13. Girard, J.-Y: Linear logic. Theor. Comp. Sci. 50, 1-102 (1987)
14. Jacobs, B.: Categorical Logic and Type Theory. Elsevier, Amsterdam (1999)
15. Jung, A., Tiuryn, J.: A new characterization of lambda definability. In: Bezem, M., Groote, J.F. (eds.) TLCA 1993. LNCS, vol. 664, pp. 245-257. Springer, Heidelberg (1993)
16. Katsumata, S.: A semantic formulation of TT-lifting and logical predicates for computational metalanguage. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 87-102. Springer, Heidelberg (2005)
17. Lafont, Y.: Logiques, Categories et Machines. PhD thesis, Universit"e Paris VII (1988)
18. Lambek, J., Scott, PJ.: Introduction to Higher Order Categorical Logic. In: Cambridge studies in advanced mathematics. CUP (1986)
19. Lindley, S.: Normalisation by Evaluation in the Compilation of Typed Functional Programming Languages. PhD thesis, University of Edinburgh (2004)
20. Lindley, S., Stark, I.: Reducibility and TT-lifting for computation types. In: Urzyczyn, P. (ed.) TLCA 2005. LNCS, vol. 3461, pp. 262-277. Springer, Heidelberg (2005)
21. Melliès, P-A., Vouillon, J.: Recursive polymorphic types and parametricky in an operational framework. In: Proc. LICS 2005, pp. 82-91. IEEE Computer Society, Los Alamitos (2005)
22. Mitchell, J.: Representation independence and data abstraction. In: Proc. POPL 1986, pp. 263-276 (1986)
23. Parigot, M.: Proofs of strong normalisation for second order classical natural deduction. Journal of Symbolic Logic 62(4), 1461-1479 (1997)
24. Pitts, A.: Parametric polymorphism and operational equivalence. Mathematical Structures in Computer Science 10(3), 321-359 (2000)
25. Pitts, A., Stark, I.: Operational reasoning for functions with local state. In: Gordon, A.D., Pitts, A.M. (eds.) Higher Order Operational Techniques in Semantics. Publications of the Newton Institute, pp. 227-273. Cambridge University Press, Cambridge (1998)
26. Walters, R.F.C.: Categories and Computer Science. Cambridge Computer Science Texts. Cambridge University Press, Cambridge (1992)