Quotient types: A modular approach

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

Volumn 2410, Issue , 2002, Pages 263-280

  Nogin, Aleksey ^a  

^a School of Operations Research and Information Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FORMAL LOGIC;

AXIOMATIZING; MODULAR APPROACH; NEW APPROACHES; PRIMITIVE OPERATIONS; RULE SET; SET OF RULES; TYPE THEORY;

THEOREM PROVING;

EID: 84945314444     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45685-6_18     Document Type: Conference Paper

References (28)

1. Stuart F. Allen. A Non-Type-Theoretic Semantics for Type-Theoretic Language. PhD thesis, Cornell University, 1987.
2. Stuart F. Allen. A Non-type-theoretic Definition of Martin-Lof's Types. In Proceedings of the Second Symposium on Logic in Computer Science, pages 215-224. IEEE, June 1987.
3. Roland Backhouse. A note of subtypes in Martin-Lof's theory of types. Technical Report CSM-90, University of Essex, November 1984.
4. Roland Backhouse. On the meaning andconstruction of the rules in Martin-Loof's theory of types. In A. Avron, editor, Workshop on General Logic, Edinburgh, February 1987, number ECS-LFCS-88-52. Department of Computer Science, University of Edinburgh, May 1988.
5. Roland C. Backhouse, Paul Chisholm, Grant Malcolm, andErik Saaman. Do-it-yourself type theory. Formal Aspects of Computing, 1:19-84, 1989.
6. Ken Birman, Robert Constable, Mark Hayden, Jason J. Hickey, Christoph Kreitz, Robbert van Renesse, Ohad Rodeh, and Werner Vogels. The Horus andEnsemble projects: Accomplishments andlimitations. In DARPA Information Survivability Conference and Exposition (DISCEX 2000), pages 149-161. IEEE, 2000.
7. Robert L. Constable. Mathematics as programming. In Proceedings of the Workshop on Programming and Logics, Lectures Notes in Computer Science 164, pages 116-128. Springer-Verlag, 1983.
8. Robert L. Constable. Types in logic, mathematics, andprogramming. In S. R. Buss, editor, Handbook of Proof Theory, chapter X, pages 683-786. Elsevier Science B.V., 1998.
9. Robert L. Constable, Stuart F. Allen, H.M. Bromley, W.R. Cleaveland, J.F. Cremer, R.W. Harper, Douglas J. Howe, T.B. Knoblock, N.P. Mendler, P. Panangaden, James T. Sasaki, and Scott F. Smith. Implementing Mathematics with the NuPRL Development System. Prentice-Hall, NJ, 1986.
10. Pierre Courtieu. Normalizedtypes. In L. Fribourg, editor, Computer Science Logic, Proceedings of the 10th Annual Conference of the EACSL, volume 2142 of Lecture Notes in Computer Science, pages 554-569. Springer-Verlag, 2001. http://link.springer-ny.com/link/service/series/0558/tocs/t2142.htm.
11. Jason J. Hickey. NuPRL-Light: An implementation framework for higer-order logics. In William McCune, editor, Proceedings of the 14th International Conference on Automated Deduction, volume 1249 of Lecture Notes on Artificial Intelligence, pages 395-399, Berlin, July 13-17 1997. Springer. CADE'97. An extended version of the paper can be found at http://www.cs.caltech.edu/~jyh/papers/cade14_nl/default.html.
12. Jason J. Hickey. The MetaPRL Logical Programming Environment. PhD thesis, Cornell University, Ithaca, NY, January 2001.
13. Jason J. Hickey, Brian Aydemir, Yegor Bryukhov, Alexei Kopylov, Aleksey Nogin, and Xin Yu. A listing of MetaPRL theories. http://metaprl.org/theories.pdf.
14. Jason J. Hickey, Aleksey Nogin, Alexei Kopylov, et al. MetaPRL home page. http://metaprl.org/.
15. Martin Hofmann. Extensional concepts in intensional Type theory. PhDthesis, University of Edinburgh, Laboratory for Foundations of Computer Science, July 1995.
16. Martin Hofmann. A simple model for quotient types. In TypedLambdaCalculus and Applications, volume 902 of Lecture Notes in Computer Science, pages 216-234, 1995.
17. Douglas J. Howe. Semantic foundations for embedding HOL in NuPRL. In Martin Wirsing andMaurice Nivat, editors, Algebraic Methodology and Software Technology, volume 1101 of Lecture Notes in Computer Science, pages 85-101. Springer-Verlag, Berlin, 1996.
18. Alexei Kopylov and Aleksey Nogin. Markov's principle for propositional type theory. In L. Fribourg, editor, Computer Science Logic, Proceedings of the 10th Annual Conference of the EACSL, volume 2142 of Lecture Notes in Computer Science, pages 570-584. Springer-Verlag, 2001. http://link.springer-ny.com/link/service/series/0558/tocs/t2142.htm.
19. Xiaoming Liu, Christoph Kreitz, Robbert van Renesse, Jason J. Hickey, Mark Hay-den, Kenneth Birman, and Robert Constable. Building reliable, high-performance communication systems from components. In 17th ACM Symposium on Operating Systems Principles, December 1999.
20. Per Martin-Loof. Constructive mathematics andcomputer programming. In Proceedings ofthe Sixth International Congress for Logic, Methodology, and Philosophy ofScience, pages 153-175, Amsterdam, 1982. North Holland.
21. J. McCarthy. A basis for a mathematical theory of computation. In P. Braffort andD. Hirschberg, editors, Computer Programming and Formal Systems, pages 33-70. Amsterdam:North-Holland, 1963.
22. Aleksey Nogin. Quotient types — A modular approach. Department of Computer Science http://cs-tr.cs.cornell.edu/Dienst/UI/1.0/Display/ncstrl.cornell/ TR2002-1869 TR2002-1869, Cornell University, April 2002. See also http://nogin.org/papers/quotients.html.
23. Aleksey Nogin and Jason Hickey. Sequent schema for derivedrules. Acceptedto TPHOLs 2002, 2002.
24. Bengt Nordstrom and Kent Petersson. Types andspecifications. In IFIP'93. Elsvier, 1983.
25. Bengt Nordstroom, Kent Petersson, and Jan M. Smith. Programming in Martin-Lof's Type Theory. OxfordSciences Publication, Oxford, 1990.
26. Frank Pfenning and Rowan Davies. Judgmental reconstruction of modal logic. Mathematical Structures in Computer Science, 11(4), August 2001.
27. Simon Thompson. Type Theory and Functional Programming. Addison-Wesley, 1991.
28. Anne Sjerp Troelstra. Metamathematical Investigation ofIntuitionistic Mathematics, volume 344 of Lecture Notes in Mathematics. Springer-Verlag, 1973.