Advertisement

Unification in the combination of disjoint theories

  • Peter Auer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 677)

Abstract

We consider unifaction modulo some equational theory E: Given are terms s, t ε Τ (E) built from the signature ε(E) of E and from variables x in V. A substitution unifies s,t if σ(s) ≡E σ(t), i.e. σ(s), σ(t) are equivalent modulo theory E.

In particular we give a unification algorithm for theories E = E1 ∪ ⋯ ∪ E n which are combinations of theories with disjoint signatures, ε(E i ) ∩ ε(E j ) = Φ for ij. Our method works if for each theory E i there exists a restricted unification algorithm: Given a set of equations P = {s1
t1, ..., s m
t m }, a linear ordering < of the variables in P, a set L of locked variables, the algorithm returns solutions σ with the following properties: • σ(s j ) Ei(t j ) • x does not occur in σ(y) if y < x • σ(x) = x if x ε L. No other restrictions are needed for the theories E i .

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Peter Auer. Unification with associative functions. PhD thesis, Technical University Vienna, 1992.Google Scholar
  2. [2]
    Franz Baader and Klaus Schulz. Unification in the union of disjoint equational theories: combining decision procedures. 1991. To be published in the proceedings of the IWWERT'91.Google Scholar
  3. [3]
    Alexander Herold. Combination of unification algorithms. In Proceedings of the 8th Conference on Automated Deduction, pages 450–496, Springer LNCS 230, 1986.Google Scholar
  4. [4]
    Claude Kirchner. A new unification method: a generalisation of Martelli-Montanari's algorithm. In Proceedings of the 7th International Conference on Automated Deduction, pages 224–247, Springer LNCS 170, May 1984.Google Scholar
  5. [5]
    Manfred Schmidt-Schau\. Unification in a combination of arbitrary disjoint equational theories. In Claude Kirchner, editor, Unification, pages 217–265, Academic Press, 1990.Google Scholar
  6. [6]
    Jörg H. Siekmann. Unification theory. In Claude Kirchner, editor, Unification, pages 1–68, Academic Press, 1990.Google Scholar
  7. [7]
    Erik Tiden. Unification in combinations of collapse-free theories with disjoint sets of function symbols. In Proceedings of the 8th Conference on Automated Deduction, pages 431–449, Springer LNCS 230, 1986.Google Scholar
  8. [8]
    Kathy Yelick. Combining unification algorithms for confined regular equational theories. In Proceedings of the 1st International Conference on Rewriting Techniques and Applications, pages 365–380, Springer LNCS 202, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Peter Auer
    • 1
  1. 1.Institut für ComputergraphikTechnical University ViennaAustria

Personalised recommendations