A general framework for R-unification problems

  • Sébastien Limet
  • Frédéric Saubion
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1490)


E-unification (i.e. solving equations modulo an equational theory E) is an essential technique in automated reasoning, functional logic programming and symbolic constraint solving but, in general E-unification is undecidable. In this paper, we focus on R-unification (i.e. E-unification where theories E are presented by term rewriting systems R). We propose a general method based on tree tuple languages which allows one to decide if two terms are unifiable modulo a term rewriting system R and to represent the set of solutions. As an application, we prove a new decidability result using primal grammars.


R-unification Rewrite techniques Tree languages 


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  1. 1.
    A. Antoy, R. Echahed, and M. Hanus. A Needed Narrowing Strategy. In Proceedings 21st ACM Symposium on Principle of Programming Languages, Portland, pages 268–279, 1994.Google Scholar
  2. 2.
    F. Baader and J. Siekmann. Unification Theory. In D.M. Gabbay, C.J. Hogger, and Robinson J.A., editors, Handbook of Logic in Artificial Intelligence and Logic Programming. Oxford University Press, Oxford, UK, 1993.Google Scholar
  3. 3.
    A. Bockmayr, S. Krischer, and A. Werner. Narrowing strategies for arbitrary canonical systems. Fundamenta Informaticae, 24(1,2):125–155, 1995.MATHMathSciNetGoogle Scholar
  4. 4.
    H. Comon. On unification of terms with integer exponents. Math. Systems Theory, 28:67–88, 1995.MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    H. Comon, M. Dauchet, R. Gilleron, D. Lugiez, S. Tison, and M. Tommasi. Tree Automata Techniques and Applications. 1997.Google Scholar
  6. 6.
    N. Dershowitz and J.-P. Jouannaud. Rewrite Systems. In J. Van Leuven, editor, Handbook of Theoretical Computer Science. Elsevier Science Publishers, 1990.Google Scholar
  7. 7.
    H. Faßbender and S. Maneth. A Strict Border for the Decidability of E-Unification for Recursive Functions. In proceedings of the intern. Conf. on Algebraic and Logic Programming., number 1139 in LNCS, pages 194–208. Springer-Verlag, 1996.Google Scholar
  8. 8.
    M. Hanus. The Integration of Functions into Logic Programming: From Theory to Practice. Journal of Logic Programming, 19 & 20:583–628, May/July 1994.MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    M. Hanus. A unified computation model for functional and logic programming. In Proc. 24st ACM Symposium on Principles of Programming Languages (POPL'97), pages 80–93, 1997.Google Scholar
  10. 10.
    M. Hermann and R. Galbavý. Unification of infinite sets of terms schematized by primal grammars. Theoretical Computer Science, 176, 1997.Google Scholar
  11. 11.
    S. Limet and P. Réty. E-Unification by Means of Tree Tuple Synchronized Grammars. Discrete Mathematics and Theoritical Computer Science (http://www.chapmanhall.com/dm), 1:69–98, 1997.MATHGoogle Scholar
  12. 12.
    S. Limet and P. Réty. Solving Disequations modulo some Class of Rewrite System. In Proceedings of 9th Conference on Rewriting Techniques and Applications, volume 1379 of LNCS, pages 121–135. Springer-Verlag, 1998.Google Scholar
  13. 13.
    A. Middeldorp, S. Okui, and T. Ida. Lazy Narrowing: Strong Completeness and Eager Variable Elimination. In procedings of the 20th Colloquium on Trees in Algebra and Programming, LNCS, 1995.Google Scholar
  14. 14.
    S. Mitra. Semantic Unification for Convergent Rewrite Systems. Phd thesis, Univ. Illinois at Urbana-Champaign, 1994.Google Scholar
  15. 15.
    R. Caballero Rold n, P. L pez Fraguas, and S nchez Hern ndez J.. User's manual for toy. Technical Report 57-97, Departamento de Sistemas Inform ticos y Programaci n, Facultad de Matem ticas (UCM), Madrid, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Sébastien Limet
    • 1
  • Frédéric Saubion
    • 2
  1. 1.LIFOUniversité d'OrléansFrance
  2. 2.LERIAUniversité d'AngersFrance

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