Unification revisited

  • J -L. Lassez
  • M. J. Maher
  • K. Marriott
Part 1: Invited Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 306)


In the literature unification is often treated as a simple and straightforward matter, even though it is recognized as a deep and fundamental concept. However when a thorough presentation is attempted, it is then realized that the matter is fairly subtle and treacherous. For instance the notion of most general unifier and its property of being unique up to renaming are open to different interpretations. In fact there are several approaches to unification, based on different mathematical concepts, which are not equivalent. We present here the alternatives and clarify their relationships. In the process new results are obtained related to the notions of equation solving, most specific generalization and constraint solving. This leads to a comprehensive presentation of an elementary theory of unification.


Logic Program General Unifier Function Symbol Complete Lattice Unification Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Chang, C.L. and Lee, R. [1973] Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.Google Scholar
  2. Colmerauer, A. [1984] Equations and Inequations on Finite and Infinite Trees, FGCS'84 Proceedings, Nov. 1984, 85–99.Google Scholar
  3. Eder, E. [1985] Properties of Substitutions and Unifications, Journal of Symbolic Computation, 1985, 1, 31–46.Google Scholar
  4. Herbrand, J. [1930] Recherches sur la theorie de la demonstration (These), Universite de Paris. (In: Ecrits logiques de Jacques Herbrand, Paris, PUF, 1968).Google Scholar
  5. Huet, G. [1976] Resolution d'Equations Dans Des Langages D'Ordre, 1, 2,...,ω (These d'Etat), Universite de Paris VII, Dec. 1976.Google Scholar
  6. Huet, G. and Oppen, D.C. [1980] Equations and Rewrite Rules: A Survey, Formal Languages: Perspectives and Open Problems, (R. Book Ed.), Academic Press, 1980.Google Scholar
  7. Jaffar, J. and Lassez, J-L. [1987] Constraint Logic Programming, Proc. POPL'87, January 1987, 111–119.Google Scholar
  8. Kirchner, C. and Lescanne, P. [1987] Solving Disequations, Proc. Logic in Computer Science Conf., to appear.Google Scholar
  9. Kunen, K. [1987a] Negation in Logic Programming, Journal of Logic Programming, to appear.Google Scholar
  10. Kunen, K. [1987b] Answer Sets and Negation as Failure, Proc. ICLP 4, MIT Press, May 1987, 219–228.Google Scholar
  11. Lassez, J-L. and Marriott, K.G. [1986] Explicit Representation of Terms Defined by Counter Examples, Proc. FST & TCS Conference, LNCS 241, December 1986. Full version to appear in Journal of Automated Reasoning.Google Scholar
  12. Lloyd, J.W. [1984] Foundations of Logic Programming, Springer-Verlag, 1984.Google Scholar
  13. Maher, M.J. [1987] Logic Semantics for a Class of Committed-choice Programs, Proc. ICLP 4, MIT Press, May 1987, 858–876.Google Scholar
  14. Makowsky, J. [1984] Model Theoretic Issues in Theoretical Computer Science Part 1: Relational Databases and Abstract Data Types, Logic Colloquium 82, (G. Lolli, G. Longo & A. Marcja Eds.), Elsevier, 1984.Google Scholar
  15. Martelli, A. and Montanari, U. [1982] An Efficient Unification Algorithm, TOPLAS, Vol. 4, No. 2, April 1982, 258–282.CrossRefGoogle Scholar
  16. Manna, Z. and Waldinger, R. [1980] Problematic Features of Programming Languages: a Situational-calculus Approach, Report No. STAN-CS-80-779, Stanford University, 1980.Google Scholar
  17. Manna, Z. and Waldinger, R. [1981] Deductive Synthesis of the Unification Algorithm, Science of Computer Programming, Vol 1, 5–48, 1981.CrossRefGoogle Scholar
  18. Naish, L. [1986] Negation & Quantifiers in NU-Prolog, Proc. 3rd Conf. on Logic Programming, LNCS 225, 624–634, July 1986.Google Scholar
  19. Paterson, M. and Wegman, M. [1978] Linear Unification, Journal of Computer and System Sciences, Vol 16, No 2, 1978, 158–167.CrossRefGoogle Scholar
  20. Plotkin, G. [1970] A Note on Inductive Generalization, Machine Intelligence 5, (B. Meltzer & D. Michie Eds.), 1970 153–163.Google Scholar
  21. Plotkin, G. [1971] A Further Note on Inductive Generalization, Machine Intellgence 6, (B. Meltzer & D. Michie Eds.), 1971, 101–124.Google Scholar
  22. Reynolds, J. [1970] Transformational Systems and the Algebraic Structure of Atomic Formulas, Machine Intelligence 5, (B. Meltzer & D. Michie Eds.), 1970, 135–152.Google Scholar
  23. Robinson, J.A. [1965] A Machine-Oriented Logic Based on the Resolution Principle, JACM, Vol. 12, No. 1, Jan. 1965, 23–41.CrossRefGoogle Scholar
  24. Robinson, J.A. [1979] Logic: Form and Function — The Mechanization of Deductive Reasoning, North-Holland, New York, 1979.Google Scholar
  25. Sato, T. [1986] Declarative Logic Programming, Research Memo, Electrotechnical Laboratory, 1986.Google Scholar
  26. Sterling, L. and Shapiro, E.Y. [1986] The Art of PROLOG, MIT Press, 1986.Google Scholar
  27. Vere, S.A. [1975] Induction of Concepts in the Predicate Calculus, IJCAI-75, 1975, 281–287.Google Scholar
  28. Vere, S.A. [1977] Induction of Relational Productions in the Presence of Background Information, IJCAI-77, 1977, 349–355.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • J -L. Lassez
    • 1
  • M. J. Maher
    • 1
  • K. Marriott
    • 1
    • 2
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA
  2. 2.Department of Computer ScienceUniversity of MelbourneParkvilleAustralia

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