A coverage checking algorithm for LF

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

Volumn 2758, Issue , 2003, Pages 120-135

  Schürmann, Carsten ^a   Pfenning, Frank ^b  

^a YALE UNIVERSITY   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FORMAL LOGIC; PATTERN MATCHING;

COVERAGE CHECKING; DEDUCTIVE SYSTEMS; DEPENDENT TYPES; FIRST ORDER; FREE VARIABLE; HIGHER-ORDER;

ALGORITHMS;

EID: 35248819262     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/10930755_8     Document Type: Article

References (23)

1. T. Coquand. An algorithm for testing conversion in type theory. In G. Huet and G. Plotkin, editors, Logical Frameworks, pages 255-279. Cambridge University Press, 1991.
2. T. Coquand. Pattern matching with dependent types. In Proceedings of the Workshop on Types for Proofs and Programs, pages 71-83, Båstad, Sweden, 1992.
3. K. Crary. Toward a foundational typed assembly language. In G. Morrisett, editor, Proceedings of the 30th Annual Symposium on Principles of Programming Languages, pages 198-212, New Orleans, Louisiana, Jan. 2003. ACM Press.
4. G. Dowek, T. Hardin, C. Kirchner, and F. Pfenning. Unification via explicit substitutions: The case of higher-order patterns. In M. Maher, editor, Proceedings of the Joint International Conference and Symposium on Logic Programming, pages 259-273, Bonn, Germany, Sept. 1996. MIT Press.
5. C. M. Elliott. Extensions and Applications of Higher-Order Unification. PhD thesis, School of Computer Science, Carnegie Mellon University, May 1990. Available. as Technical Report CMU-CS-90-134.
6. L.-H. Eriksson. Finitary Partial Inductive Definitions and General Logic. PhD thesis, Department of Computer and System Sciences, Royal Institute of Technology, Stockholm, 1993.
7. L. Hallnäs. Partial inductive definitions. Theoretical Computer Science, 87(1):115-142, Sept. 1991.
8. R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. Journal of the Association for Computing Machinery, 40(1):143-184, Jan. 1993.
9. M. Hofmann and T. Streicher. The groupoid model refutes uniqueness of identity proofs. In Proceedings of the 9th Annual Symposium on Logic in Computer Science (LICS'94), pages 208-212, Paris, France, 1994. IEEE Computer Society Press.
10. G. Huet. A unification algorithm for typed λ-calculus. Theoretical Computer Science, 1:27-57, 1975.
11. INRIA. The Coq Proof Assistant, version 7.4 edition, Feb. 2003. Reference Manual.
12. C. McBride. Dependently Typed Functional Programs and their Proofs. PhD thesis, University of Edinburgh, 1999. Available as Technical Report ECS-LFCS-00-419.
13. D. Miller. A logic programming language with lambda-abstraction, function variables, and simple unification. Journal of Logic and Computation, 1(4):497-536, 1991.
14. F. Pfenning. Logical frameworks. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, chapter 17, pages 1063-1147. Elsevier Science and MIT Press, 2001.
15. F. Pfenning and C. Schürmann. Algorithms for equality and unification in the presence of notational definitions. In T. Altenkirch, W. Naraschewski, and B. Reus, editors, Types for Proofs and Programs, pages 179-193, Kloster Irsee, Germany, Mar. 1998. Springer-Verlag LNCS 1657.
16. F. Pfenning and C. Schürmann. System description: Twelf - a meta-logical framework for deductive systems. In H. Ganzinger, editor, Proceedings of the 16th International Conference on Automated Deduction (CADE-16), pages 202-206, Trento, Italy, July 1999. Springer-Verlag LNAI 1632.
17. B. Pientka. Termination and reduction checking for higher-order logic programs. In First International Joint Conference on Automated Reasoning (IJCAR), pages 401-415, Siena, Italy, 2001. Springer Verlag, LNCS 2083.
18. B. Pientka and F. Pfenning. Optimizing higher-order pattern unification. In F. Baader, editor, Proceedings of the 19th Conference on Automated Deduction (CADE-19), Miami Beach, Florida, July 2003. Springer-Verlag LNCS. To appear.
19. E. Rohwedder and F. Pfenning. Mode and termination checking for higher-order logic programs. In H. R. Nielson, editor, Proceedings of the European Symposium on Programming, pages 296-310, Linköping, Sweden, Apr. 1996. Springer-Verlag LNCS 1058.
20. P. Schroeder-Heister. Rules of definitional reflection. In M. Vardi, editor, Proceedings of the Eighth Annual IEEE Symposium on Logic in Computer Science, pages 222-232, Montreal, Canada, June 1993.
21. C. Schürmann. Automating the Meta Theory of Deductive Systems. PhD thesis, Department of Computer Science, Carnegie Mellon University, Aug. 2000. Available as Technical Report CMU-CS-00-146.
22. C. Schürmann, R. Fontana, and Y. Liao. Delphin: Functional programming with deductive systems. Draft.
23. R. Virga. Higher-Order Rewriting with Dependent Types. PhD thesis, Department of Mathematical Sciences, Carnegie Mellon University, Sept. 1999. Available as Technical Report CMU-CS-99-167.