Second-order unification in the presence of linear shallow algebraic equations

  • Zhenyu Qian
Chapter 7 Extension Of Unification And Narrowing Techniques
Part of the Lecture Notes in Computer Science book series (LNCS, volume 516)


This paper presents an algorithm to compute unifiers of simply typed λ-terms w.r.t. the union of α, β and η conversion and a set of first-order equational theory ε, where a λ-unification algorithm and an algorithm to check the word problem w.r.t. ε are assumed to be given. If the above given algorithms are terminating and complete, then our algorithm is terminating and complete, provided that λ-terms are second-order and ε is consistent, linear and shallow. An equational theory is called shallow if its axioms are all of the form f(x1, ..., xm)=g(y1, ..., yn) or f(x1, ..., xn)=y1, where f,g are function symbols, x1, ..., xn, y1, ..., yn are variables and m,n≥0. Equations defining projections or commutativity of functions are examples of such equational theories.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Zhenyu Qian
    • 1
  1. 1.FB3-Dept. of Computer ScienceUniversity of BremenBremen 33Fed. Rep. Germany

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