Formalizing and Proving Semantic Relations between Specifications by Reflection

  • Manuel Clavel
  • Narciso Martí-Oliet
  • Miguel Palomino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3116)


This work contains both a theoretical development and a novel application of ideas introduced in [1] for using reflection in formal metareasoning. From the theoretical side, we extend the metareasoning principles proposed in [1] to cover the case of metatheorems about equational theories which are unrelated by the inclusion relation. From the practical side, we apply the newly introduced metareasoning principles to formalize and prove semantic relations between equational theories used in formal specification.


Semantic Relation Atomic Formula Logical Framework Universal Theory Ground Term 


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  1. 1.
    Basin, D., Clavel, M., Meseguer, J.: Reflective metalogical frameworks. ACM Transactions on Computational Logic (2004) (to appear),
  2. 2.
    Bouhoula, J.-P.: Jouannaud, and J. Meseguer. Specification and proof in membership equational logic. Theoretical Computer Science 236, 35–132 (2000)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Clavel, M.: Reflection in Rewriting Logic: Metalogical Foundations and Metaprogramming Applications. CSLI Publications, Stanford (2000)MATHGoogle Scholar
  4. 4.
    Clavel, M.: The ITP tool’s home page (2004),
  5. 5.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Mart´ı-Oliet, N., Meseguer, J., Quesada, J.F.: Maude: Specification and programming in rewriting logic. Theoretical Computer Science 285, 187–243 (2002)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Mart´ı-Oliet, N., Meseguer, J., Talcott, C.: Maude Manual (Version 2.1). Manual distributed as documentation of the Maude system (2004),
  7. 7.
    Clavel, M., Martí-Oliet, N., Palomino, M.: Formalizing and proving semantic relations between specifications by reflection, extended version (2004),
  8. 8.
    Clavel, M., Meseguer, J.: Axiomatizing reflective logics and languages. In: Kiczales, G. (ed.) Proc. Reflection 1996. Xerox PARC, pp. 263–288 (1996)Google Scholar
  9. 9.
    Clavel, M., Meseguer, J., Palomino, M.: Reflection in membership equational logic, many-sorted equational logic, Horn logic with equality, and rewriting logic. In: Gadducci, F., Montanari, U. (eds.) Proc. Fourth International Workshop on Rewriting Logic and its Applications. Electronic Notes in Theoretical Computer Science, vol. 71, pp. 63–78. Elsevier, Amsterdam (2002),
  10. 10.
    Ehrig, H., Mahr, B.: Fundamentals of Algebraic Specification 1, EATCS Monographs on Theoretical Computer Science, vol. 6. Springer, Heidelberg (1985)Google Scholar
  11. 11.
    Loeckx, J., Ehrich, H.-D., Wolf, M.: Specification of Abstract Data Types. J. Wiley & Sons and B.G. Teubner (1996)Google Scholar
  12. 12.
    Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Manuel Clavel
    • 1
  • Narciso Martí-Oliet
    • 1
  • Miguel Palomino
    • 1
  1. 1.Departamento de Sistemas Informáticos y ProgramaciónUniversidad Complutense de MadridSpain

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