Equational Abstractions in Rewriting Logic and Maude

  • Narciso Martí-OlietEmail author
  • Francisco Durán
  • Alberto Verdejo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8941)


Maude is a high-level language and high-performance system supporting both equational and rewriting computation for a wide range of applications. Maude also provides a model checker for linear temporal logic. The model-checking procedure can be used to prove properties when the set of states reachable from an initial state in a system is finite; when this is not the case, it may be possible to use an equational abstraction technique for reducing the size of the state space. Abstraction reduces the problem of whether an infinite state system satisfies a temporal logic property to model checking that property on a finite state abstract version of the original infinite system. The most common abstractions are quotients of the original system. We present a simple method for defining quotient abstractions by means of equations identifying states. Our method yields the minimal quotient system together with a set of proof obligations that guarantee its executability, which can be discharged with tools such as those available in the Maude formal environment. The proposed method will be illustrated by means of detailed examples.


Maude Rewriting logic Model checking Abstraction Formal environment 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)Google Scholar
  2. 2.
    Durán, F., Meseguer, J.: On the Church-Rosser and coherence properties of conditional order-sorted rewrite theories. Journal of Logic and Algebraic Programming 81(7–8), 816–850 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Durán, F., Rocha, C., Álvarez, J.M.: Towards a Maude Formal Environment. In: Agha, G., Danvy, O., Meseguer, J. (eds.) Formal Modeling: Actors, Open Systems, Biological Systems. LNCS, vol. 7000, pp. 329–351. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Giesl, J., et al.: Proving termination of programs automatically with \({\sf AProVE}\). In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 184–191. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  5. 5.
    Meseguer, J., Palomino, M., Martí-Oliet, N.: Equational abstractions. Theoretical Computer Science 403(2–3), 239–264 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Meseguer, J., Palomino, M., Martí-Oliet, N.: Algebraic simulations. Journal of Logic and Algebraic Programming 79(2), 103–143 (2010)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Narciso Martí-Oliet
    • 1
    Email author
  • Francisco Durán
    • 2
  • Alberto Verdejo
    • 1
  1. 1.Facultad de InformáticaUniversidad Complutense de MadridMadridSpain
  2. 2.E.T.S.I. InformáticaUniversidad de MálagaMálagaSpain

Personalised recommendations