Article

Innermost termination of context-sensitive rewriting

Authors:

Aart MiddeldorpAuthors Info & Claims

DLT'02: Proceedings of the 6th international conference on Developments in language theory

Pages 231 - 244

Published: 18 September 2002 Publication History

Abstract

Context-sensitive rewriting is a restriction of term rewriting used to model evaluation strategies in functional programming and in programming languages like OBJ. For example, under certain conditions termination of an OBJ program is equivalent to innermost termination of the corresponding context-sensitive rewrite system [18]. To prove termination of context-sensitive rewriting, several methods have been proposed in the literature which transform context-sensitive rewrite systems into ordinary rewrite systems such that termination of the transformed ordinary system implies termination of the original context-sensitive system. Most of these transformations are not very satisfactory when it comes to proving innermost termination. We investigate the relationship between termination and innermost termination of context-sensitive rewriting and we examine the applicability of the different transformations for innermost termination proofs. Finally, we present a simple transformation which is both sound and complete for innermost termination.

References

[1]

T. Arts and J. Giesl. Termination of term rewriting using dependency pairs. Theoretical Computer Science, 236:133-178, 2000.

Digital Library

[2]

F. Baader and T. Nipkow. Term Rewriting and All That. Cambr. Univ. Pr., 1998.

Digital Library

[3]

C. Borralleras, S. Lucas, and A. Rubio. Recursive path orderings can be context-sensitive. In Proc. 18th CADE, volume 2392 of LNAI, pages 314-331, 2002.

Digital Library

[4]

M. Clavel, S. Eker, P. Lincoln, and J. Meseguer. Principles of Maude. In Proc. 1st WRLA, volume 4 of ENTCS, 1996.

[5]

R. Diaconescu and K. Futatsugi. CafeOBJ Report, volume 6 of AMAST Series in Computing. World Scientific, 1998.

[6]

S. Eker. Term rewriting with operator evaluation strategies. In Proc. 2nd WRLA, volume 15 of ENTCS, pages 1-20, 1998.

[7]

M.C.F. Ferreira and A.L. Ribeiro. Context-sensitive AC-rewriting. In Proc. 10th RTA, volume 1631 of LNCS, pages 173-187, 1999.

Digital Library

[8]

O. Fissore, I. Gnaedig, and H. Kirchner. Induction for termination with local strategies. In Proc. 4th International Workshop on Strategies in Automated Deduction, volume 58 of ENTCS, 2001.

[9]

J. Giesl and A. Middeldorp. Transforming context-sensitive rewrite systems. In Proc. 10th RTA, volume 1631 of LNCS, pages 271-285, 1999.

Digital Library

[10]

J. Giesl and A. Middeldorp. Innermost termination of context-sensitive rewriting. Technical Report AIB-2002-048, RWTH Aachen, Germany, 2002.

[11]

J. Giesl and A. Middeldorp. Transformation techniques for context-sensitive rewrite systems. Technical Report AIB-2002-028, RWTH Aachen, Germany, 2002. Extended version of {9}.

[12]

J. Goguen, T. Winkler, J. Meseguer, K. Futatsugi, and J.-P. Jouannaud. Introducing OBJ. In J. Goguen and G. Malcolm, editors, Software Engineering with OBJ: algebraic specification in action. Kluwer, 2000.

[13]

B. Gramlich. Abstract relations between restricted termination and confluence properties of rewrite systems. Fundamenta Informaticae, 24:3-23, 1995.

Digital Library

[14]

B. Gramlich and S. Lucas. Modular termination of context-sensitive rewriting. In Proc. 4th PPDP, pages 50-61. ACM Press, 2002.

Digital Library

[15]

B. Gramlich and S. Lucas. Simple termination of context-sensitive rewriting. In Proc. 3rd Workshop on Rule-Based Programming, pages 29-41. ACM Press, 2002.

Digital Library

[16]

S. Lucas. Termination of context-sensitive rewriting by rewriting. In Proc. 23rd ICALP, volume 1099 of LNCS, pages 122-133, 1996.

Digital Library

[17]

S. Lucas. Context-sensitive computations in functional and functional logic programs. Journal of Functional and Logic Programming, 1:1-61, 1998.

[18]

S. Lucas. Termination of rewriting with strategy annotations. In Proc. 8th LPAR, volume 2250 of LNAI, pages 669-684, 2001.

Digital Library

[19]

S. Lucas, 2001-2002. Personal communication.

[20]

S. Lucas. Termination of (canonical) context-sensitive rewriting. In Proc. 13th RTA, volume 2378 of LNCS, pages 296-310, 2002.

Digital Library

[21]

T. Nagaya. Reduction Strategies for Term Rewriting Systems. PhD thesis, School of Information Science, Japan Advanced Institute of Science and Technology, 1999.

[22]

M. Nakamura and K. Ogata. The evaluation strategy for head normal form with and without on-demand flags. In Proc. 3rd WRLA, volume 36 of ENTCS, 2001.

[23]

H. Zantema. Termination of context-sensitive rewriting. In Proc. 8th RTA, volume 1232 of LNCS, pages 172-186, 1997.

Digital Library

Cited By

Alarcón BLucas S(2009)Using Context-Sensitive Rewriting for Proving Innermost Termination of RewritingElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2009.07.055248(3-17)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1016/j.entcs.2009.07.055
Gnaedig IKirchner H(2007)Narrowing, abstraction and constraints for proving properties of reduction relationsRewriting Computation and Proof10.5555/2391276.2391280(44-67)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.5555/2391276.2391280
Alarcón BLucas S(2007)Termination of Innermost Context-Sensitive Rewriting Using Dependency PairsProceedings of the 6th international symposium on Frontiers of Combining Systems10.1007/978-3-540-74621-8_5(73-87)Online publication date: 10-Sep-2007
https://dl.acm.org/doi/10.1007/978-3-540-74621-8_5

Innermost termination of context-sensitive rewriting
1. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
  2. Semantics and reasoning

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Published In

cover image Guide Proceedings

DLT'02: Proceedings of the 6th international conference on Developments in language theory

September 2002

428 pages

ISBN:3540404317

Editors:
Masami Ito
Kyoto Sangyo University, Faculty of Science and Faculty of Engineering, Kyoto, Japan
,
Masafumi Toyama
Kyoto Sangyo University, Faculty of Science and Faculty of Engineering, Kyoto, Japan

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 18 September 2002

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Cited By

Alarcón BLucas S(2009)Using Context-Sensitive Rewriting for Proving Innermost Termination of RewritingElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2009.07.055248(3-17)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1016/j.entcs.2009.07.055
Gnaedig IKirchner H(2007)Narrowing, abstraction and constraints for proving properties of reduction relationsRewriting Computation and Proof10.5555/2391276.2391280(44-67)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.5555/2391276.2391280
Alarcón BLucas S(2007)Termination of Innermost Context-Sensitive Rewriting Using Dependency PairsProceedings of the 6th international symposium on Frontiers of Combining Systems10.1007/978-3-540-74621-8_5(73-87)Online publication date: 10-Sep-2007
https://dl.acm.org/doi/10.1007/978-3-540-74621-8_5

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