On the semantics of classical disjunction

Journal of Pure and Applied Algebra

Volumn 159, Issue 2-3, 2001, Pages 315-338

  Pym, David ^a   Ritter, Eike ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

03B05; 03B40; 03F03; 03G30; 68Q55

Indexed keywords

EID: 0042694623     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(00)00161-4     Document Type: Article

References (28)

1. Dummett M. Elements of Intuitionism. 1980;Oxford University Press, Oxford.
2. Felleisen M., Friedman D.P. Control operators, the SECD-machine and the. λ -calculus Wirsing M. Formal Descriptions for Programming Concepts III. 1996;193-217 North-Holland, Amsterdam.
3. M. Felleisen, The calculi of lambda-v-CS conversion: a syntactic theory of control and state in imperative higher-order programming languages, Ph.D. Dissertation, Department of Computer Science, Indiana University, IN, 1987.
4. M. Felleisen, R. Hieb, The revised report on the syntactic theories of sequential control and state, Theoret. Comput. Sci. 103(2) 235-271.
5. G. Gentzen, Untersuchungen über das logische Schliessen, Math. Zeit. (1934) 176-210, 405-431.
6. Girard J.-Y. On the unity of logic. Ann. Pure Appl. Logic. 59:1993;201-217.
7. Girard J.-Y., Taylor P., Lafont Y. Proofs and Types. 1989;Cambridge University Press, Cambridge.
8. N. Ghani, βη -equality for coproducts, in: Proceedings of TLCA '95, Lecture Notes in Computer Science, vol. 902, Springer, Berlin, 1995, pp. 171-185.
9. Jay C.B., Ghani N. The virtues of eta-expansion. J. Funct. Programming. 5(2):1995;135-154.
10. Haynes C.T. Logic Continuations. J. Logic Programming. 4:1987;157-176.
11. M. Hofmann, Sound and complete axiomatizations of call-by-value control operators, Math. Struct. Comput. Sci. 5 (1995) 461-482.
12. M. Hofmann, T. Streicher, Continuation models are universal for λμ -calculus, Proceedings of LICS '97, Warsaw, IEEE Press, New York, 1997, pp. 387-397.
13. Hyland J.M.E., Pitts A.M. The theory of constructions: Categorical semantics and topos theoretic models. Contemp. Math. 92:1989;137-198.
14. B. Jacobs, Categorical type theory, Doctoral Thesis, Katholieke Universiteit Nijmegen, 1991.
15. Klop J.W. Term rewriting systems. Abramsky S., M. Gabbay Dov, Maibaum T.S.E. Handbook of Logic in Computer Science, vol. 2. 1992;1-116 Oxford Science Publications, Oxford.
16. Lambek J., Scott P. Introduction to Higher-Order Cateogrical Logic. 1986;Cambridge University Press, Cambridge.
17. L. Ong, A semantic view of classical proofs, Proceedings of LICS 96, IEEE Computer Society Press, New York, 1996, pp. 230-241.
18. M. Parigot, λμ -calculus: an algorithmic interpretation of classical natural deduction, in: Proceedings of LPAR '92, Lecture Notes in Computer Science, vol. 624, Springer, Berlin, 1992, pp. 190-201.
19. M. Parigot, Church-Rosser property in classical free deduction, in: Logical Environments, G. Huet, G. Plotkin (Eds.), Cambridge University Press, Cambridge, 1993.
20. M. Parigot, Strong normalization for second order classical natural deduction, in: Proceedings of LICS 93, IEEE Computer Society Press, New York, 1993, pp. 39-47.
21. Plotkin G. Call-by-name, call-by-value and the. λ -calculus Theoret. Comput. Sci. 1:1975;125-159.
22. G. Plotkin, The category of complete partial orders: a tool for making meanings, Proceedings of the Summer School on the Foundations of Artifical Intelligence and Computer Science, Instituto di Scienze dell'Informazione, Università di Pisa, June 1978 ("Pisa Notes"), Available at: http: // www.dcs.ed.ac.uk / home / gdp / , June 1999.
23. Ritter E., Pym D., Wallen L. On the intuitionistic force of classical search (extended abstract). Miglioli P., Moscato U., Mundici D., Ornaghi M. Proceedings of Tableaux '96. Lecture Notes in Computer Science. vol. 1071:1996;295-311 Springer, Berlin.
24. Ritter E., Pym D., Wallen L. On the intuitionistic force of classical search. Theoret. Comput. Sci. 232:2000;299-333.
25. Ritter E., Pym D., Wallen L. Proof-terms for classical and intuitionistic resolution (extended abstract), Proceedings of CADE-13. McRobbie M., Slaney J. Lecture Notes in Computer Science. vol, 1104:1996;17-31 Springer, Berlin.
26. Reynolds J.C. The Discoveries of Continuations. Lisp Symbolic Comput. 6:1993;233-247.
27. Schmidt D. Denotational Semantics. 1986;Allyn & Bacon, Newton, MA.
28. Seely R. Hyperdoctrines, natural deduction and the Beck condition. Z. Math. Logik Grundlag. Math. 29:1983;505-542.