Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T00:41:08.981Z Has data issue: false hasContentIssue false
  • English
  • Français

A comparison between two logical formalisms for rewriting

Published online by Cambridge University Press:  01 January 2007

MIGUEL PALOMINO
MIGUEL PALOMINO*
Affiliation:
Departamento de Sistemas Informáticos y Programación, Facultad de Informática, Universidad Complutense de Madrid, Spain (e-mail: miguelpt@sip.ucm.es)
Get access Rights & Permissions [Opens in a new window]

Abstract

Meseguer's rewriting logic and the rewriting logic CRWL are two well-known approaches to rewriting as logical deduction that, despite some clear similarities, were designed with different objectives. Here we study the relationships between them, both at a syntactic and at a semantic level. Even though it is not possible to establish an entailment system map between them, both can be naturally simulated in each other. Semantically, there is no embedding between the corresponding institutions. Along the way, the notions of entailment and satisfaction in Meseguer's rewriting logic are generalized.

Keywords

rewriting logicconstructor-based rewriting logicinstitutions
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 7 , Issue 1-2 , January 2007 , pp. 183 - 213
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arenas-Sánchez, P. and Rodríguez-Artalejo, M. 2001. A general framework for lazy functional logic programming with algebraic polymorphic types. Theory and Practice of Logic Programming 1, 2, 185–245.Google Scholar
Barr, M. and Wells, C. 1999. Category Theory for Computing Science. Third Edition. Centre de Recherches Mathématiques.Google Scholar
Bosco, P. G., Giovannetti, E. and Moiso, C. 1988. Narrowing vs. SLD-resolution. Theoretical Computer Science 59, 3–23.CrossRefGoogle Scholar
Cengarle, M. V. 1998. The rewriting logic institution. Tech. Rep. 9801, Ludwig-Maximilians-Universität München, Institut für Informatik. May.Google Scholar
Diaconescu, R. and Futatsugi, K. 2002. Logical foundations of CafeOBJ. Theoretical Computer Science 285, 2, 289–318.CrossRefGoogle Scholar
Goguen, J. and Burstall, R. 1992. Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery 39, 1, 95–146.CrossRefGoogle Scholar
Goguen, J. and Roşu, G. 2002. Institution morphisms. Formal Aspects of Computing 13, 3–5, 274–307.CrossRefGoogle Scholar
González-Moreno, J. C., Hortalá-González, M. T., López-Fraguas, F. J., and Rodríguez-Artalejo, M. 1999. An approach to declarative programming based on a rewriting logic. Journal of Logic Programming 40, 47–87.CrossRefGoogle Scholar
González-Moreno, J. C., Hortalá-González, M. T. and Rodríguez-Artalejo, M. 2001. Polymorphic types in functional logic programming. Journal of Functional and Logic Programming 2001, 1. Special Issue 1, http://danae.uni-muenster.de/lehre/kuchen/JFLP.Google Scholar
Lambek, J. 1970. Subequalizers. Canadian Mathematical Bulletin 13, 337–349.CrossRefGoogle Scholar
Martí-Oliet, N. and Meseguer, J. 2002a. Rewriting logic as a logical and semantic framework. In Handbook of Philosophical Logic. Second Edition, Gabbay, D., Ed. Vol. 9. Kluwer Academic Press, 1–81.Google Scholar
Martí-Oliet, N. and Meseguer, J. 2002b. Rewriting logic: Roadmap and bibliography. Theoretical Computer Science 285, 2, 121–154.CrossRefGoogle Scholar
Meseguer, J. 1989. General logics. In Logic Colloquium'87, Ebbinghaus, H.-D., Fernández-Prida, J., Garrido, M., Lascar, D., and Rodríguez-Artalejo, M., Eds. North-Holland, 275–329.Google Scholar
Meseguer, J. 1990. Rewriting as a unified model of concurrency. Tech. Rep. SRI-CSL-90-02, SRI International, Computer Science Laboratory. Feb. Revised June 1990.Google Scholar
Meseguer, J. 1992. Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science 96, 1, 73–155.CrossRefGoogle Scholar
Meseguer, J. 1998. Membership algebra as a logical framework for equational specification. In Recent Trends in Algebraic Development Techniques, 12th International Workshop, WADT'97, Tarquinia, Italy, June 3–7, 1997, Selected Papers, Parisi-Presicce, F., Ed. Lecture Notes in Computer Science, vol. 1376. Springer-Verlag, 18–61.CrossRefGoogle Scholar
Meseguer, J. 2000. Rewriting logic and Maude: Concepts and applications. In Rewriting Techniques and Applications, 11th International Conference, RTA 2000, Norwich, UK, July 10–12, 2000, Proceedings, Bachmair, L., Ed. Lecture Notes in Computer Science, vol. 1833. Springer-Verlag, 1–26.Google Scholar
Miyoshi, H. 1996. Modelling conditional rewriting logic in structured categories. In Proceedings First International Workshop on Rewriting Logic and its Applications, WRLA'96, Asilomar, California, September 3–6, 1996, Meseguer, J., Ed. Electronic Notes in Theoretical Computer Science, vol. 4. Elsevier, 20–34. http://www.elsevier.com/locate/entcs/volume4.html.Google Scholar
Molina-Bravo, J. M. 2000. Modularidad en programación lógico-funcional de primer orden. Ph.D. thesis, Universidad de Málaga, Spain.Google Scholar
Palomino, M. 2001. Relating Meseguer's rewriting logic and the constructor-based rewriting logic. M.S. thesis, Facultad de Matemáticas, Universidad Complutense de Madrid. http://maude.cs.uiuc.edu/papers.Google Scholar
Thati, P., Sen, K. and Martí-Oliet, N. 2002. An executable specification of asynchronous pi-calculus. In Proceedings Fourth International Workshop on Rewriting Logic and its Applications, WRLA'02, Pisa, Italy, September 19–21, 2002, Gadducci, F. and Montanari, U., Eds. Electronic Notes in Theoretical Computer Science, vol. 71. Elsevier.Google Scholar
Verdejo, A. 2003. Técnicas de especificación formal de sistemas orientados a objetos basadas en lógica de reescritura. Ph.D. thesis, Universidad Complutense de Madrid, Spain.Google Scholar
Verdejo, A. and Martí-Oliet, N. 2002. Implementing CCS in Maude2. In Proceedings Fourth International Workshop on Rewriting Logic and its Applications, WRLA'02, Pisa, Italy, September 19–21, 2002, Gadducci, F. and Montanari, U., Eds. Electronic Notes in Theoretical Computer Science, vol. 71. Elsevier.Google Scholar