Inductive types in the Calculus of Algebraic Constructions

Fundamenta Informaticae

Volumn 65, Issue 1-2, 2005, Pages 61-86

  Blanqui, Frédéric ^a  

^a LORIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; MATRIX ALGEBRA;

ALGEBRAIC CONSTRUCTIONS; CALCULUS OF INDUCTIVE CONSTRUCTIONS (CIC); REWRITE RULES;

MATHEMATICAL TECHNIQUES;

EID: 24044480666     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (32)

1. Abel, A.: Termination Checking with Types, Technical Report 0201, Ludwig Maximilians Universität, München, Germany, 2002.
2. Barbanera, F., Fernández, M., Geuvers, H.: Modularity of strong normalization and confluence in the algebraic-λ-cube, Proceedings of the 9th IEEE Symposium on Logic in Computer Science, 1994.
3. Barendregt, H.: Lambda Calculi with types, in: Handbook of logic in computer science (S. Abramski, D. Gabbay, T. Maibaum, Eds.), vol. 2, Oxford University Press, 1992.
4. Blanqui, F.: Definitions by rewriting in the Calculus of Constructions (extended abstract), Proceedings of the 16th IEEE Symposium on Logic in Computer Science, 2001.
5. Blanqui, F.: Théorie des Types et Récriture, Ph.D. Thesis, Université Paris XI, Orsay, France, 2001, Available in english as "Type Theory and Rewriting".
6. Blanqui, F.: Definitions by rewriting in the Calculus of Constructions, Mathematical Structures in Computer Science, 15(1), 2005, 37-92.
7. Breazu-Tannen, V., Gallier, J.: Polymorphic Rewriting Conserves Algebraic Strong Normalization, Proceedings of the 16th International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science 372, 1989.
8. Coq-Development-Team: The Coq Proof Assistant Reference Manual - Version 8.0, INRIA Rocquencourt, France, 2004, http://coq.inria.fr/.
9. Coquand, T.: An Analysis of Girard's Paradox, Proceedings of the 1st IEEE Symposium on Logic in Computer Science, 1986.
10. Coquand, T., Huet, G.: The Calculus of Constructions, Information and Computation, 76(2-3), 1988, 95-120.
11. Coquand, T., Paulin-Mohring, C.: Inductively defined types, Proceedings of the International Conference on Computer Logic, Lecture Notes in Computer Science 417, 1988.
12. Dershowitz, N., Jouannaud, J.-P.: Rewrite Systems, in: Handbook of Theoretical Computer Science (J. van Leeuwen, Ed.), vol. B, chapter 6, North-Holland, 1990.
13. Dybjer, P.: A general formulation of simultaneous inductive-recursive definitions in type theory, Journal of Symbolic Logic, 65(2), 2000, 525-549.
14. Girard, J.-Y., Lafont, Y., Taylor, P.: Proofs and Types, Cambridge University Press, 1988.
15. Harper, R., Mitchell, J.: Parametricity and variants of Girard's J operator, Information Processing Letters, 70, 1999, 1-5.
16. Jouannaud, J.-P., Okada, M.: Executable Higher-Order Algebraic Specification Languages, Proceedings of the 6th IEEE Symposium on Logic in Computer Science, 1991.
17. Jouannaud, J.-P, Okada, M.: Abstract Data Type Systems, Theoretical Computer Science, 173(2), 1997, 349-391.
18. Klop, J. W., van Oostrom, V., van Raamsdonk, F.: Combinatory reduction systems: introduction and survey, Theoretical Computer Science, 121, 1993, 279-308.
19. Matthes, R.: Extensions of System F by Iteration and Primitive Recursion on Monotone Inductive Types, Ph.D. Thesis, Ludwig Maximilians Universität, München, Germany, 1998.
20. McBride, C.: Dependently typed functional programs and their proofs, Ph.D. Thesis, University of Edinburgh, United Kingdom, 1999.
21. Mendler, N. P.: Inductive Definition in Type Theory, Ph.D. Thesis, Cornell University, United States, 1987.
22. Müller, F.: Confluence of the lambda calculus with left-linear algebraic rewriting, Information Processing Letters, 41(6), 1992, 293-299.
23. Nederpelt, R.: Strong normalization in a typed lambda calculus with lambda structured types, Ph.D. Thesis, Technische Universiteit Eindhoven, The Netherlands, 1973.
24. Okada, M.: Strong Normalizability for the Combined System of the Typed Lambda Calculus and an Arbitrary Convergent Term Rewrite System, Proceedings of the 1989 International Symposium on Symbolic and Algebraic Computation, ACM Press.
25. van Oostrom, V.: Confluence for Abstract and Higher-Order Rewriting, Ph.D. Thesis, Vrije Universiteit Amsterdam, The Netherlands, 1994.
26. Paulin-Mohring, C: Personal communication, 2001.
27. Pollack, R.: Dependently typed records in type theory, Formal Aspects of Computing, 13(3-5), 2002, 341-363.
28. Rusinowitch, M.: On termination of the direct sum of term-rewriting systems, Information Processing Letters, 26(2), 1987, 65-70.
29. Stefanova, M.: Properties of Typing Systems, Ph.D. Thesis, Katholiecke Universiteit Nijmegen, The Netherlands, 1998.
30. Toyama, Y.: Counterexamples to termination for the direct sum of term rewriting systems, Information Processing Letters, 25(3), 1987, 141-143.
31. Walukiewicz-Chrza̧szcz, D.: Termination of rewriting in the Calculus of Constructions, Journal of Functional Programming, 13(2), 2003, 339-414.
32. Werner, B.: Une Théorie des Constructions Inductives, Ph.D. Thesis, Université Paris VII, France, 1994.