Partial recursive functions in higher-order logic

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

Volumn 4130 LNAI, Issue , 2006, Pages 589-603

  Krauss, Alexander ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; AUTOMATION; COMPUTER SCIENCE; FUNCTION EVALUATION; PARTIAL DIFFERENTIAL EQUATIONS; PATTERN MATCHING; SET THEORY;

PARTIAL RECURSIVE FUNCTIONS; TERMINATION ARGUMENTS; TERMINATION PROOFS; TOTAL FUNCTIONS;

FORMAL LOGIC;

EID: 33749564499     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11814771_48     Document Type: Conference Paper

References (21)

1. G. Barthe, J. Forest, D. Pichardie, and V. Rusu. Defining and reasoning about recursive functions: a practical tool for the Coq proof assistant. In Functional and Logic Programming (FLOPS'06), LNCS 3945. Springer, 2006. To Appear.
2. S. Berghofer and M. Wenzel. Inductive datatypes in HOL - lessons learned in formal-logic engineering. In Y. Bertot, G. Dowek, A. Hirschowitz, C. Paulin, and L. Théry, editors, Theorem Proving in Higher Order Logics, TPHOLs '99, LNCS 1690, pages 19-36. Springer, 1999.
3. Y. Bertot and P. Castéran. Interactive theorem proving and program development: Coq'Art: the calculus of inductive constructions. Texts in theoretical comp. science. Springer, 2004.
4. A. Bove and V. Capretta. Modelling general recursion in type theory. Mathematical Structures in Computer Science, 15(4):671-708, 2005.
5. R. S. Boyer and J. S. Moore. A Computational Logic. Academic Press, New York, 1979.
6. C. Dubois and V. Donzeau-Gouge. A step towards the mechanization of partial functions: domains as inductive predicates. In CADE-15 Workshop on mechanization of partial functions, 1998.
7. J. Giesl. Termination of nested and mutually recursive algorithms. Journal of Automated Reasoning, 19(1):1-29, Aug. 1997.
8. J. Giesl, R. Thiemann, and P. Schneider-Kamp. Proving and disproving termination of higher-order functions. In B. Gramlich, editor, FroCos, LNCS 3717, pages 216-231. Springer, 2005.
9. M. Gordon and T. Melham, editors. Introduction to HOL: A theorem proving environment for higher order logic. Cambridge University Press, 1993.
10. J. Harrison. The HOL Light theorem prover. http://www.cl.cam.ac.uk/users/ jrh/hol-light.
11. S. Krstić and J. Matthews. Inductive invariants for nested recursion. In D. A. Basin and B. Wolff, editors, Theorem Proving in Higher Order Logics, TPHOLs 2003, LNCS 2758, pages 253-269. Springer, 2003.
12. C. S. Lee, N. D. Jones, and A. M. Ben-Amram. The size-change principle for program termination. In ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 81-92, 2001.
13. P. Manolios and J. S. Moore. Partial functions in ACL2. J. Autom. Reasoning, 31(2):107-127, 2003.
14. O. Müller and K. Slind. Treating partiality in a logic of total functions. The Computer Journal, 40(10):640-652, 1997.
15. T. Nipkow, L. C. Paulson, and M. Wenzel. Isabelle/HOL -A Proof Assistant for Higher-Order Logic. LNCS 2283. Springer, 2002.
16. L. C. Paulson. A fixedpoint approach to implementing (co)inductive definitions. In A. Bundy, editor, Automated Deduction - CADE-12, LNCS 814, pages 148-161. Springer, 1994.
17. K. Slind. Function definition in Higher-Order Logic. In J. von Wright, J. Grundy, and J. Harrison, editors, Theorem Proving in Higher Order Logics, TPHOLs '96, LNCS 1125, pages 381-397. Springer, 1996.
18. K. Slind. Reasoning About Terminating Functional Programs, PhD thesis, Institut für Informatik, TU München, 1999.
19. K. Slind. Another look at nested recursion. In M. Aagaard and J. Harrison, editors, Theorem Proving in Higher Order Logics, TPHOLS 2000, LNCS 1869, pages 498-518. Springer, 2000.
20. C. Urban and C. Tasson. Nominal techniques in Isabelle/HOL. In R. Nieuwenhuis, editor, Automated Deduction - CADE-20, LNCS 3632, pages 38-53. Springer, 2005.
21. C. Walther. On proving the termination of algorithms by machine. Artif. Intell., 71(1):101-157, 1994.