Ricardo Caferra
ABSTRACT
We define a new class of rewrite systems operating over term-graphs. Our aim is twofold. First we propose to extend classical first-order rewrite rules in order to process easily data-structures with pointers (e.g., circular lists, doubly linked lists etc). For that, our rules provide specific features such as pointer (edges) redirections, relabeling of existing nodes etc. Unfortunately, such features are very often source of non confluence. Our second aim is then to ensure confluence of the considered rewrite systems in the new class. We introduce the notion of term-graphs with priority and show that orthogonal rewrite systems are confluent in our setting
- H. Aït-Kaci and A. Podelski. Towards a Meaning of LIFE. J. Log. Program., 16(3):195--234, 1993.]]Google Scholar
Cross Ref
- S. Antoy, R. Echahed, and M. Hanus. A needed narrowing strategy. In Proc. 21st ACM. Symp. on Principles of Programming Languages, pages 268--279, 1994.]] Google ScholarDigital Library
- Z. M. Ariola and S. Blom. Cyclic λ calculi. In TACS, pages 77--106, 1997.]] Google ScholarDigital Library
- Z. M. Ariola and S. Blom. Skew and mega-skew confluence and abstract böhm semantics. In Processes, Terms and Cycles, pages 368--403, 2005.]] Google ScholarDigital Library
- Z. M. Ariola, J. W. Klop, and D. Plump. Bisimilarity in term graph rewriting. Inf. Comput., 156(1-2):2--24, 2000.]] Google ScholarDigital Library
- R. Banach. Term Graph Rewriting and Garbage Collection Using Ppfibrations. Theor. Comput. Sci., 131(1):29--94, 1994.]] Google ScholarDigital Library
- H. Barendregt, M. van Eekelen, J. Glauert, R. Kenneway, M. J. Plasmeijer, and M. Sleep. Term Graph Rewriting. In PARLE'87, pages 141--158. Springer, LNCS 259, 1987.]] Google ScholarDigital Library
- C. Bertolissi. The graph rewriting calculus: Confluence and expressiveness. In 9th Italian Conference on Theoretical Computer Science, LNCS 3701, pages 113--127, 2005.]] Google ScholarDigital Library
- C. Bertolissi, P. Baldan, H. Cirstea, and C. Kirchner. A rewriting calculus for cyclic higher-order term graphs. Electr. Notes Theor. Comput. Sci., 127(5):21--41, 2005.]] Google ScholarDigital Library
- H. Cirstea, C. Kirchner, L. Liquori, and B. Wack. Rewrite strategies in the rewriting calculus. Electr. Notes Theor. Comput. Sci., 86(4), 2003.]]Google Scholar
- A. Corradini. Term Rewriting in CTΕ. In Proc. of the 4th International Joint Conference CAAP-FASE (TAPSOFT'93), pages 468--484. LNCS 668, 1993.]] Google ScholarDigital Library
- A. Corradini and F. Gadducci. Rewriting on cyclic structures: Equivalence between the operational and the categorical description. ITA, 33(4/5):467--493, 1999.]]Google Scholar
- N. Dershowitz and J.-P. Jouannaud. Rewrite systems. In Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics (B), pages 243--320. 1990.]] Google ScholarDigital Library
- D. J. Dougherty, P. Lescanne, L. Liquori, and F. Lang. Addressed term rewriting systems: Syntax, semantics, and pragmatics: Extended abstract. Electr. Notes Theor. Comput. Sci., 127(5):57--82, 2005.]] Google ScholarDigital Library
- R. Echahed and J.-C. Janodet. Admissible graph rewriting and narrowing. In Proceedings of 15th International Conference and Symposium on Logic Programming, pages 325--340, Manchester, 1998. MIT Press.]] Google ScholarDigital Library
- R. Echahed and J. C. Janodet. Parallel admissible graph rewriting. In Recent Developments in Algebraic Development Techniques, pages 121--135. LNCS 1589, 1999.]] Google ScholarDigital Library
- M. Hanus. The integration of functions into logic programming: From theory to practice. Journal of Logic Programming, 19&20:583--628, 1994.]]Google ScholarCross Ref
- J. R. Kennaway, J. K. Klop, M. R. Sleep, and F. J. De Vries. On the Adequacy of Graph Rewriting for Simulating Term Rewriting. ACM Transactions on Programming Languages and Systems, 16(3):493--523, 1994.]] Google ScholarDigital Library
- J. R. Kennaway, J. K. Klop, M. R. Sleep, and F. J. De Vries. Transfinite Reduction in Orthogonal Term Rewriting Systems. Information and Computation, 119(1):18--38, 1995.]] Google ScholarDigital Library
- R. Plasmeijer and M. van Eekelen. Functional Programming and Parallel Graph Rewriting. Addison-Wesley, 1993.]] Google ScholarDigital Library
- D. Plump. Term graph rewriting. In H. Ehrig, G. Engels, H. Kreowski, and G. Rozenberg, editors, Handbook of Graph Grammars and Computing by Graph Transformation, volume 2. World Scientific, 1998.]] Google ScholarDigital Library
- D. Plump. Confluence of graph transformation revisited. In Processes, Terms and Cycles, pages 280--308, 2005.]] Google ScholarDigital Library
- H. Schorr and W. M. Waite. An Efficient Machine Independent Procedure for Garbage Collection in Various List Structures. Communication of the ACM, 10:501--506, August 1967.]] Google ScholarDigital Library
- E. Visser. A survey of strategies in rule-based program transformation systems. J. Symb. Comput., 40(1):831--873, 2005.]] Google ScholarDigital Library
Index Terms
- Rewriting term-graphs with priority
Recommendations
Confluent term rewriting systems
RTA'05: Proceedings of the 16th international conference on Term Rewriting and ApplicationsThe confluence property is one of the most important properties of term rewriting systems, and various sufficient criteria for proving this property have been widely investigated. A necessary and sufficient criterion for confluence of terminating term ...
Conditions for confluence of innermost terminating term rewriting systems
This paper presents a counterexample for the open conjecture whether innermost joinability of all critical pairs ensures confluence of innermost terminating term rewriting systems. We then show that innermost joinability of all normalized instances of ...
Decidability of Innermost Termination and Context-Sensitive Termination for Semi-Constructor Term Rewriting Systems
Yi and Sakai [Y. Wang and M. Sakai. Decidability of termination for semi-constructor trss, left-linear shallow trss and related systems. In the 17th International Conference on Rewriting Techniques and Applications, volume 4098 of Lecture Notes in ...
Comments