Contextual modal type theory

ACM Transactions on Computational Logic

Volumn 9, Issue 3, 2008, Pages

  Nanevski, Aleksandar ^a,d   Pfenning, Frank ^b,e   Pientka, Brigitte ^c  

^a HARVARD UNIVERSITY   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

^c MCGILL UNIVERSITY   (Canada)

^d HARVARD UNIVERSITY   (United States)

^e Carnegie Mellon University ^*  (United States)

Author keywords

Intuitionistic modal logic; Logical frameworks; Type theory

Indexed keywords

EXPLICIT SUBSTITUTIONS; LOGICAL FRAMEWORK (LF); METAVARIABLES; MODAL LOGICS; SOME APPLICATIONS; TYPE THEORIES;

COMPUTER PROGRAMMING; FUNCTIONAL PROGRAMMING;

FUZZY LOGIC;

EID: 45749090964     PISSN: 15293785     EISSN: 1557945X     Source Type: Journal    
DOI: 10.1145/1352582.1352591     Document Type: Article

References (64)

1. ABADI, M., CARDELLI, L., CURIEN, P.-L., AND LÈVY, J.-J. 1990. Explicit substitutions. In Proceedings of the Symposium on Principles of Programming Languages (POPL'90, San Francisco, CA). 31-46.
2. ALECHINA, N., MENDLER, M., DE PAIVA, V., AND RITTER, E. 2001. Categorical and Kripke semantics for Constructive S4 modal logic. In International Workshop on Computer Science Logic, CSL'01, L. Fribourg, Ed. LectureNotesinComputerScience, vol. 2142.Springer,Berlin, Germany, France, 292-307.
3. ATTARDI, G. AND SIMI, M. 1994. Proofs in context. In Principles of Knowledge Representation and Reasoning, J. Doyle, E. Sandewall, and P. Torasso, Eds. Morgan Kaufman, San Francisco, CA, 16-26.
4. ATTARDI, G. AND SIMI, M. 1995. A formalization of viewpoints. Fundamenta Informaticae 23, 3, 149-173.
5. BJØRNER, N. AND MUÑOZ, C. 2000. Absolute explicit unification. In International Conference on Rewriting Techniques and Applications, RTA'00. Lecture Notes in Computer Science, vol. 1833. Springer, Berlin, Germany, 31-46.
6. BOGNAR, M. AND DE VRIJER, R. 2001. A calculus of lambda calculus context. J. Automat. Reason. 27, 1, 29-59.
7. BUVAČ, S. 1996. Quantificational logic of context. In Proceedings of the Thirteenth National Conference on Artificial Intelligence. 600-606.
8. BUVAČ, S., BUVAČ, V., AND MASON, I. 1995. Metamathematics of contexts. Fundamenta Informaticae 23, 3, 412-419.
9. CALCAGNO, C., MOGGI, E., AND TAHA, W. 2004. ML-like inference for classifiers. In European Symposium on Programming, ESOP'04, D. Schmidt, Ed. Lecture Notes in Computer Science, 2986. Springer-Verlag, Berlin, Germany, 79-93.
10. CARTMELL, J. 1986. Generalized algebraic theories and contextual categories. Ann. Pure Appl. Log. 32, 209-243.
11. CERVESATO, I. AND PFENNING, F. 2002. A linear logical framework. Inform. Computat. 179, 1 (Nov.), 19-75.
12. DAMI, L. 1998. A lambda-calculus for dynamic binding. Theoret. Comput. Sci. 192, 2, 201-231.
13. DAVIES, R. 1996. A temporal logic approach to binding-time analysis. In Symposium on Logic in Computer Science (LICS'96), E. Clarke, Ed. IEEE Computer Society Press, Los Alamitos, CA, NJ, 184-195.
14. DAVIES, R. AND PFENNING, F. 2001. A modal analysis of staged computation. J. ACM 48, 3 (May), 555-604.
15. DE GROOTE, P. 2002. On the strong normalisation of intuitionistic natural deduction with permutation-conversions. Inform. Computat. 178, 2 (Nov.), 441-464.
16. DE PAIVA, V. 2003. Natural deduction and context as (constructive) modality. In Modelling and Using Context, P. Blackburn, C. Ghidini, R. M. Turner, and F. Giunchiglia, Eds. Lecture Notes in Artificial Inteligence, vol. 2680. Springer, Berlin, Germany, 116-129.
17. DOWEK, G., HARDIN, T., AND KIRCHNER, C. 1995. Higher-order unification via explicit substitutions. In Symposium on Logic in Computer Science (LICS'95). D. Kozen, Ed. IEEE Computer Society Press, Los Alamitos, CA, 366-374.
18. DOWEK, G., HARDIN, T., KIRCHNER, C., AND PFENNING, F. 1996. Unification via explicit substitutions: The case of higher-order patterns. In Proceedings of the Joint International Conference and Symposium on Logic Programming, M. Maher, Ed. MIT Press, Cambridge, MA, 259-273.
19. GEUVERS, H. AND JOJGOV, G. I. 2002. Open proofs and open terms: a basis for interactive logic. In International Workshop on Computer Science Logic, CSL'02, J. C. Bradfield, Ed. Lecture Notes in Computer Science, vol. 2471. Springer, Berlin, Germany, 537-552.
20. GIUNCHIGLIA, F. 1993. Contextual reasoning. Epistemologica 16, 345-364.
21. GIUNCHIGLIA, F. AND SERAFINI, L. 1994. Multilanguage hierarchical logics, or: How to do without modal logics. Artific. Intell. 65, 1, 29-70.
22. HARPER, R., HONSELL, F., AND PLOTKIN, G. 1993. A framework for defining logics. JACM. 40, 1 (Jan.), 143-184.
23. HASHIMOTO, M. AND OHORI, A. 2001. A typed context calculus. Theoret. Comput. Sci. 266, 1-2, 249-272.
24. HODAS, J. AND MILLER, D. 1994. Logic programming in a fragment of intuitionistic linear logic. Inform. Computat. 110, 2, 327-365.
25. JOJGOV, G. I. 2003. Holes with binding power. In Types for Proofs and Programs, Second International Workshop, TYPES 2002, Berg en Dal, The Netherlands, April 24-28, 2002, Selected Papers, H. Geuvers and F. Wiedijk, Eds. Lecture Notes in Computer Science, vol. 2646. Springer, Berlin, Germany, 162-181.
26. KRIPKE, S. 1959. A completeness theorem in modal logic. J. Symbol. Log. 24, 1-14.
27. LEE, S.-D. AND FRIEDMAN, D. P. 1996. Enriching the lambda calculus with contexts: Toward a theory of incremental program construction. In Proceedings of the International Conference on Functional Programming (ICFP'96). 239-250.
28. LIANG, C. AND NADATHUR, G. 2002. Tradeoffs in the intensional representation of lambda terms. In International Conference on Rewriting Techniques and Applications, RTA'02, S. Tison, Ed. Lecture Notes in Computer Science, vol. 2378. Springer-Verlag, Berlin, Germany, 192-206.
29. MAGNUSSON, L. 1995. The implementation of ALF - a proof editor based on Martin-Löf's monomorphic type theory with explicit substitutions. Ph.D. dissertation. Chalmers University of Technology and Göteborg University, Göteborg, Sweden.
30. MARTIN-LÖF, P. 1996. On the meanings of the logical constants and the justifications of the logical laws. Nordic J. Philosoph. Log. 1, 1, 11-60.
31. MASON, I. A. 1999. Computing with contexts. Higher-Order Symbol. Computat. 12, 2, 171-201.
32. MCCARTHY, J. 1987. Generality in artificial intelligence. Commun. ACM 30, 12, 1030-1035.
33. MCCARTHY, J. 1993. Notes on formalizing contexts. In Proceedings of the International Joint Conference on Artificial Intelligence (Chambery, France). 555-560.
34. MILLER, D. 1991. A logic programming language with lambda-abstraction, function variables, and simple unification. J. Log. Computat. 1, 4, 497-536.
35. MONTAGUE, R. 1963. Syntactical treatment of modalities, with corollaries on reflexion principles and finite axiomatizability. Acta Philosophica Fennica 16, 153-167.
36. MOODY, J. 2003. Modal logic as a basis for distributed computation. Tech. rep. CMU-CS-03-194. Carnegie Mellon University, Pittsburgh, PA.
37. MUÑOZ, C. 2001. Dependent types and explicit substitutions. Math. Struct. Comput. Sci. 11, 1 (Feb.), 91-129.
38. MURPHY VII, T., CRARY, K., HARPER, R., AND PFENNING, F. 2004. A symmetric modal lambda calculus for distributed computing. In Symposium on Logic in Computer Science, H. Ganzinger, Ed. (LICS 04, Turku, Finland). 286-295.
39. NANEVSKI, A. 2003. From dynamic binding to state via modal possibility. In Proceedings of the International Conference on Principles and Practice of Declarative Programming (PPDP'03. Uppsala, Sweden). 207-218.
40. NANEVSKI, A. 2004. Functional programming with names and necessity. Ph.D. dissertation. Computer Science Department, Carnegie Mellon University, Pittsburgh, PA.
41. NANEVSKI, A. AND PFENNING, F. 2005. Staged computation with names and necessity. J. Funct. Programm. 15, 6 (Nov.), 837-891.
42. NANEVSKI, A., PIENTKA, B., AND PFENNING, F. 2003. A modal foundation for meta variables. In Proceedings of MERλIN 2003 (Uppsala, Sweden).
43. PFENNING, F. 2000. Structural cut elimination I. Intuitionistic and classical logic. Inform. Computat. 157, 1/2 (Mar.), 84-141.
44. PFENNING, F. 2001. Intensionality, extensionality, and proof irrelevance in modal type theory. In Symposium on Logic in Computer Science (LICS'01), J. Halpern, Ed. IEEE Computer Society Press, Los Alamitos, CA, 221-230.
45. PFENNING, F. AND DAVIES, R. 2001. A judgmental reconstruction of modal logic. Math. Struct. Comput. Sci. 11, 4, 511-540.
46. PFENNING, F. AND SCHÜRMANN, C. 1999. System description: Twelf - a meta-logical framework for deductive systems. In International Conference on Automated Deduction, CADE'99, H. Ganzinger, Ed. Lecture Notes in Artificial Inteligence, vol. 1632. Springer-Verlag, Berlin, Germany, 202-206.
47. PIENTKA, B. 2003. Tabled higher-order logic programming. Ph.D. dissertation. Computer Science Department, Carnegie Mellon University, Pittsburgh, PA.
48. PIENTKA, B. AND PFENNNING, F. 2003. Optimizing higher-order pattern unification. In International Conference on Automated Deduction, CADE'03, F. Baader, Ed. Lecture Notes in Computer Science, vol. 2741. Springer, Berlin, Germany, 473-487.
49. SATO, M., SAKURAI, T., AND BURSTALL, R. 2001. Explicit environments. Fundamenta Informaticae 45, 1-2, 79-115.
50. SATO, M., SAKURAI, T., AND KAMEYAMA, Y. 2002. A simply typed context calculus with first-class environments. J. Funct. Log. Programm. 2002, 4 (Mar.).
51. SATO, M., SAKURAI, T., KAMEYAMA, Y., AND IGARASHI, A. 2003. Calculi of meta-variables. In International Workshop on Computer Science Logic, CSL'03, M. Baaz and J. A. Makowsky, Eds. Lecture Notes in Computer Science, vol. 2803. Springer, Berlin, Germany, 484-497.
52. SCHÜRMANN, C., POSWOLSKY, A., AND SARNAT, J. 2005. The ▽-calculus: Functional programming with higher-order encodings. In International Conference on Typed Lambda Calculus and Applications, TLCA'05, P. Urzyczyn, Ed. Lecture Notes in Computer Science, vol. 3461. Springer, Berlin, Germany, 339-353.
53. SERAFINI, L. AND BOUQUET, P. 2004. Comparing formal theories of context in AI. Artific. Intell. 155, 1-2, 41-67.
54. SERAFINI, L. AND GIUNCHIGLIA, F. 2002. ML system: A proof theory for contexts. J. Log. Lang. Inform. 11, 4, 471-518.
55. SIMPSON, A. K. 1994. The proof theory and semantics of intuitionistic modal logic. Ph.D. thesis, University of Edinburgh.
56. STRECKER, M. 1999. Construction and deduction in type theories. Ph.D. dissertation. Universität Ulm, Ulm, Germany.
57. TAHA, W. AND NIELSEN, M. F. 2003. Environment classifiers. In Proceedings of the Symposium on Principles of Programming Languages (POPL'03, New Orleans, LA). G. Morrisett, Ed. ACM Press, New York, NY, 26-37.
58. TAHA, W. AND SHEARD,T. 1997. Multi-stage programmingwith explicit annotations. In Proceedings of the Workshop on Partial Evaluation and Semantics-Based Program Manipulation (PEPM'97. Amsterdam, The Netherland). 203-217.
59. THOMASON, R. H. 1999. Type theoretic foundations for context, part 1: Contexts as complex type-theoretic objects. In Proceedings of the Second International and Interdisciplinary Conference on Modeling and Using Contexts (CONTEXT'99, Trento, Italy), P. Bouquet, L. Serafini, P. Brézillon, M. Benerecetti, and F. Castellani, Eds. 352-374.
60. THOMASON, R. H. 2003. Dynamic contextual intensional logic: Logical foundations and an application. In Modeling and Using Context, P. Blackburn, C. Ghidini, R. M. Turner, and F. Giunchiglia, Eds. Lecture Notes in Artificial Inteligence, vol. 2680. Springer, Berlin, Germany, 328-341.
61. WATKINS, K., CERVESATO, I., PFENNING, F., AND WALKER, D. 2002. A concurrent logical framework I: Judgments and properties. Tech. rep. CMU-CS-02-101, Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA. Revised May 2003.
62. WEYHRAUCH, R. W. 1979. Prolegomena to a theory of mechanized formal reasoning. Artific. Intell. 13, 1-2, 133-170.
63. WICKLINE, P., LEE, P., AND PFENNING, F. 1998a. Run-time code generation and Modal-ML. In Proceedings of the Conference on Programming Language Design and Implementation (PLDI'98, Montreal, P. Q., Canada), K. D. Cooper, Ed. ACM Press, 224-235.
64. WICKLINE, P., LEE, P., PFENNING, F., AND DAVIES, R. 1998b. Modal types as staging specifications for run-time code generation. ACM Comput. Surv. 30, 3es.