Higher-order equational unification via explicit substitutions

  • Claude Kirchner
  • Christophe Ringeissen
Higher-Order Methods

DOI: 10.1007/BFb0027003

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1298)
Cite this paper as:
Kirchner C., Ringeissen C. (1997) Higher-order equational unification via explicit substitutions. In: Hanus M., Heering J., Meinke K. (eds) Algebraic and Logic Programming. Lecture Notes in Computer Science, vol 1298. Springer, Berlin, Heidelberg

Abstract

We show how to reduce the unification problem modulo βη-conversion and a first-order equational theory E, into a first-order unification problem in a union of two non-disjoint equational theories including E and a calculus of explicit substitutions. A rule-based unification procedure in this combined theory is described and may be viewed as an extension of the one initially designed by G. Dowek, T. Hardin and C. Kirchner for performing unification of simply typed λ-terms in a first-order setting via the λσ-calculus of explicit substitutions. Additional rules are used to deal with the interaction between E and λσ.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Claude Kirchner
    • 1
  • Christophe Ringeissen
    • 1
  1. 1.INRIA-Lorraine & CRIN-CNRSVillers-lés-Nancy CedexFrance

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