Rank 2 types for term graph rewriting: Extended abstract

Electronic Notes in Theoretical Computer Science

Volumn 75, Issue , 2003, Pages 1-20

  Van Bakel, Steffen ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTABILITY AND DECIDABILITY; COMPUTATIONAL METHODS; COMPUTER PROGRAMMING LANGUAGES; GRAPH THEORY; SET THEORY; THEOREM PROVING;

FUNCTIONAL PROGRAMMING; GENERALIZATION; TERM GRAPH REWRITING; UNIFICATION;

COMPUTER SCIENCE;

EID: 18944383102     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1571-0661(04)80776-X     Document Type: Conference Paper

References (39)

1. Z. M. Ariola and J. W. Klop. Equational term graph rewriting. Fundamentae Informaticae, 26(3,4):207-240, 1996. Extended version: CWI Report CS-R9552.
2. van Bakel S. Complete restrictions of the Intersection Type Discipline. Theoretical Computer Science. 102:(1):1992;135-163
3. van Bakel S. Intersection Type Assignment Systems. Theoretical Computer Science. 151:(2):1995;385-435
4. van Bakel S. Rank 2 Intersection Type Assignment in Term Rewriting Systems. Fundamenta Informaticae. 2:(26):1996;141-166
5. S. van Bakel, F. Barbanera, and M. Fernández. Polymorphic Intersection Type Assignment for Rewrite Systems with Abstraction and β-rule. In Thierry Coquand, Peter Dybjer, Bengt Nordström, and Jan Smith, editors, Types for Proofs and Programs. International Workshop TYPES'99, Lökeberg, Sweden, Sected Papers, volume 1956 of Lecture Notes in Computer Science, pages 41-60. Springer-Verlag, 2000.
6. van Bakel S., Fernández M. Normalization Results for Typeable Rewrite Systems. Information and Computation. 133:(2):1997;73-116
7. S. van Bake, S. Smetsers, and S. Brock. Partial Type Assignment in Left Linear Applicative Term Rewriting Systems. In J.-C. Raoult, editor, Proceedings of CAAP '92. 17th Colloquim on Trees in Algebra and Programming, Rennes, France, volume 581 of Lecture Notes in Computer Science, pages 300-321. Springer-Verlag, 1992.
8. Barendregt H. The Lambda Calculus: its Syntax and Semantics. 1984;North-Holland, Amsterdam, revised edition
9. Barendregt H., Coppo M., Dezani-Ciancaglini M. A filter lambda model and the completeness of type assignment. Journal of Symbolic Logic. 48:(4):1983;931-940
10. H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W. Glauert, J.R. Kennaway, M.J. Plasmeijer, and M.R. Sleep. Term graph rewriting. In Proceedings of PARLE, Parallel Architectures and Languages Europe, nEindhoven, The Netherlands, volume 259-II of Lecture Notes in Computer Science, pages 141-158. Springer-Verlag, 1987.
11. H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W. Glauert, J.R. Kennaway, M.J. Plasmeijer, and M.R. Sleep. Towards an Intermediate Language based on Graph Rewriting. In Proceedings of PARLE, Parallel Architectures and Languages Europe, Eindhoven, The Netherlands, volume 259-II of Lecture Notes in Computer Science, pages 159-175. Springer-Verlag. 1987.
12. E. Barendsen and S. Smetsers. Extending Graph Rewriting with Copying. In Hans Jürgen Schneider and Hartmut Ehrig, editors, Proceedings of International Workshop 'graph Transformations in Computer Science', Daghstuhl, Germany, January 1993, volume 776 of Lecture Notes in Computer Science, pages 51-70. Springer-Verlag, 1994.
13. Barendsen E., Smetsers S. Conventional and Uniqueness Typing in Graph Rewrite Systems. Mathematical Structures of Computer Science. 1996
14. A. Bucciarelli, S. De Lorenzis, A. Piperno, and I. Salvo. Some computational properties of intersection types. In Proc. Symposium on Logic in Computer Science (LIC'99), pages 109-118, 1996.
15. L.M.M. Damas. Type Assignment in Programming Languages. PhD thesis, University of Edinburgh, Department of Computer Science, Edinburgh, 1985. Thesis CST-33-85.
16. F. Damiani. Typing local definitions and conditional expressions with rank 2 intersection. In Proceedings of FOSSACS'00, volume 1784 of Lecture Notes in Computer Science, pages 82-97. springer-Verlag, 2000.
17. F. Damiani and P. Giannini. A Decidable Intersection type System based on Relevance. In M. Hagiya and J.C. Mitchell, editors, Proceedings of TACS '94. International Symposium on Theoretical Aspects of Computer Software, Sendai, japan, volume 789 of Lecture Notes in Computer Science, pages 707-725. Springer-Verlag, 1994.
18. F. Damiani and F. Prost. Detecting and Removing Dead-code using Rank 2 Intersection. In Proceedings of International Workshop TYPES'96, Selected Papers, volume 1512 of Lecture Notes in Computer Science, pages 66-87. springer-Verlag, 1998.
19. Dershowitz N., Jouannaud J.P. Rewrite systems. van Leeuwen J. Handbook of Theoretical Computer Science, volume B, chapter 6. 1990;245-320 North-Holland
20. M. Eekelen, S. Smetsers, and R. Plasmeijer. Graph Rewriting Semantics for Functional Programming Languages. In Dirk van Dalen, editor, Proceedings of CSL '96, Fifth Annual conference of the European Association for Computer Science Logic(EACSL), volume 1258 of Lecture Notes in Computer Science, pages 106-128. Springer-Verlag, 1996.
21. Girard J.Y. The System F of Variable Types, Fifteen years later. Theoretical Computer Science. 45:1986;159-192
22. Hindley J.R. The principal type scheme of an object in combinatory logic. Transactions of the American Mathematical Society. 146:1969;29-60
23. T. Jim. Rank 2 type systems and recursive definitions. Technical Memorandum MIT/LCS/TM-531, Laboratory for Computer Science Massachusetts Institute of Technology, 1995.
24. T. Jim. What are principal typings and what are they good for? In Proceedings of POPL'96. ACM Symposium on Principles of Programming Languages, 1996.
25. Kennaway J.R., Klop J.W., Sleep M.R., de Vries F.J. The adequacy of term graph rewriting for simulating term rewriting. Sleep M.R., Plasmeijer M.J., van Eekelen M.C.D.J. Term Graph Rewriting: Teory and Practice. 1993;157-168 John Wiley & Sons
26. A. Kfoury and J. Wells. Principality and decidable type inference for finite-rank intersection types. In Proceedings of POPL '99: 26th ACM Symposium on the Principles of Programming. Languages, pages 161-174, 1999.
27. A.J. Kfoury, H.G. Mairson, F.A. Turbak, and J.B. Wells. Relating Typability and Expressibility in Finite-Rank Intersection Type Systems. In Proceedings of ICFP '99, International Conference on Functional Programming, pages 90-101, 1999.
28. Kfoury A.J., Tiuryn J. Type reconstruction in finite-rank fragments of the second-order λ-calculus. Information and Computation. 98:(2):1992;228-257
29. A.J. Kfoury and J. Wells. A Direct Algorithm for Type Inference in the Rank-2 Fragment of the Second-Order λ-Calculus. In Proceedings of LFP'94: ACM Conference of LISP Functional Programming, pages 196-207, 1994.
30. Klop J.W. Term Rewriting Systems. Abramsky S., Gabbay Dov M., Maibaum T.S.E. Handbook of Logic in Computer Science, volume 2, chapter 1n. 1992;1-16 Clarendon Press
31. J. Launchbury and S.L. Peyton Jones. Lazy functional state threads. In PLDI, 1994.
32. Milner R. A theory of type polymorphism in programming. Journal of Computer and System Sciences. 17:1978;348-375
33. E.G.J.M.H. Nöocker, J.E.W. Smetsers, M.C.J.D. van Eekelen, and M.J. Plasmeijer. Concurrent Clean. In Proceedings of PARLE '91, Parallel Architectures and Languages Europe, Eindhoven, The Netherlands, volume 506-II of Lecture Notes in Computer Science, pages 202-219. Springer-Verlag, 1991.
34. J.C. Reynolds. Towards a Theory of Type Structures. In B. Robinet, editor, Proceedings of Programming Symposium, Paris, France, volume 19 of Lecture Notes in Computer Science, pages 408-425. Springer-Verlag, 1974.
35. Robinson J.A. A machine-oriented logic based on the resolution principle. Journal of the ACM. 12:(1):1965;23-41
36. Ronchi S., Rocca Della, Venneri B. Principal type schemes for an extended type theory. Theoretical Computer Science. 28:1984;151-169
37. Sleep R., Plasmeijer M.J., van Eekelen M.C.J.C. Term Graph Rewriting. Theory and Practice. 1993;Wiley
38. J. Wells. Typeability and type checking in Second order λ-calculus are equal and undecidable. In Proceedings of the ninth Annual IEEE symposium on Logic in Computer Science, Paris, France, 1994.
39. Yokohuchi H. Embedding a Second-Order Type System into an Intersection Type System. Information and Computation. 117:1995;206-220