Admissibility of fixpoint induction over partial types

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

Volumn 1421, Issue , 1998, Pages 270-285

  Crary, Karl ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATION;

FIXED POINTS; FIXPOINTS; MONOTONICITY; PARTIAL FUNCTIONS; PRODUCT TYPES; RECURSIONS; TYPE THEORY; UPPER BOUND THEOREMS;

THEOREM PROVING;

EID: 0347107487     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0054265     Document Type: Conference Paper

References (24)

1. S. Allen. A non-type-theoretic definition of Martin-Löf s types. In Second IEEE Symposium on Logic in Computer Science, pages 215-221, Ithaca, New York, June 1987.
2. P. Audebaud. Partial objects in the calculus of constructions. In Sixth IEEE Symposium on Logic in Computer Science, pages 86-95, Amsterdam, July 1991.
3. B. Barras, S. Boutin, C. Cornes, J. Courant, J.-C. Filliâtre, E. Giménez, H. Her-belin, G. Huet, C. Muñoz, C. Murthy, C. Parent, C. Paulin-Mohring, A. Saïbi, and B. Werner. The Coq Proof Assistant Reference Manual. INRIA-Rocquencourt, CNRS and ENS Lyon, 1996.
4. D.A. Basin. An environment for automated reasoning about partial functions. In Ninth International Conference on Automated Deduction, volume 310 of Lecture Notes in Computer Science. Springer-Verlag, 1988.
5. R. Constable, S. Allen, H. Bromley, W. Cleaveland, J. Cremer, R. Harper, D. Howe, T. Knoblock, N. Mendler, P. Panangaden, J. Sasaki, and S. Smith. Implementing Mathematics with the Nuprl Proof Development System. Prentice-Hall, 1986.
6. R.L. Constable and K. Crary. Computational complexity and induction for partial computable functions in type theory. Technical report, Department of Computer Science, Cornell University, 1997.
7. R.L. Constable and S.F. Smith. Partial objects in constructive type theory. In Second IEEE Symposium on Logic in Computer Science, pages 183-193, Ithaca, New York, June 1987.
8. R.L. Constable and S.F. Smith. Computational foundations of basic recursive function theory. In Third IEEE Symposium on Logic in Computer Science, pages 360-371, Edinburgh, Scotland, July 1988.
9. T. Coquand and G. Huet. The calculus of constructions. Information and Computation, 76: 95-120, 1988.
10. K. Crary. Admissibility of fixpoint induction over partial types. Technical Report TR98-1674, Department of Computer Science, Cornell University, Apr. 1998.
11. K. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, 1998. Forthcoming.
12. M.J. Gordon, A.J. Milner, and C.P. Wadsworth. Edinburgh LCF: A Mechanised Logic of Computation, volume 78 of Lecture Notes in Computer Science. Springer-Verlag, 1979.
13. R. Harper. Constructing type systems over an operational semantics. Journal of Symbolic Computation, 14: 71-84, 1992.
14. W. Howard. The formulas-as-types notion of construction. In J.P. Seldin and J.R. Hindley, editors, To H.B. Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism, pages 479-490. Academic Press, 1980.
15. D.J. Howe. Equality in lazy computation systems. In Fourth IEEE Symposium on Logic in Computer Science, 1989.
16. S. Igarashi. Admissibility of fixed-point induction in first-order logic of typed theories. Technical Report AIM-168, Computer Science Department, Stanford University, May 1972.
17. P.B. Jackson. Enhancing the Nuprl Proof Development System and Applying it to Computational Abstract Algebra. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, Jan. 1995.
18. D. MacQueen. Using dependent types to express modular structure. In Thirteenth ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, pages 277-286, St. Petersburg Beach, Florida, Jan. 1986.
19. P. Martin-Löf. Constructive mathematics and computer programming. In Sixth International Congress of Logic, Methodology and Philosophy of Science, volume 104 of Studies in Logic and the Foundations of Mathematics, pages 153-175. North-Holland, 1982.
20. L.C. Paulson. Logic and Computation: Interactive Proof with Cambridge LCF. Cambridge University Press, 1987.
21. B.C. Pierce and D.N. Turner. Simple type-theoretic foundations for object-oriented programming. Journal of Functional Programming, 4(2): 207-247, Apr. 1994.
22. D. Scott. Outline of a mathematical theory of computation. In Fourth Princeton Conference on Information Sciences and Systems, pages 169-176, 1970.
23. D. Scott. Lattice theoretic models for various type-free calculi. In Fourth International Congress of Logic, Methodology and Philosophy of Science. North-Holland, 1972.
24. S.F. Smith. Partial Objects in Type Theory. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, Jan. 1989.