MPI-INF/SWS Research Reports 1991-2021

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Unification and matching in Church's Original Lambda Calculus

Hustadt, Ullrich

June 1992, 16 pages.

Status: available - back from printing

In current implementations of higher-order logics higher-orderunification is used to lift the resolution principle from the first-order case to the higher-order case. Higher-order matching is the core of implementations of higher-order rewriting systems and some systems for program transformation. In this paper I argue that Church's original lambda calculus, called non-forgetful lambda calculus, is an appropriate basis for higher-order matching. I provide two correct and complete algorithms for unification in the non-forgetful lambda calculus. Finally, I show how these unification algorithms can be used for matching in the non-forgetful lambda calculus.

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  AUTHOR = {Hustadt, Ullrich},
  TITLE = {Unification and matching in Church's Original Lambda Calculus},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-92-219},
  MONTH = {June},
  YEAR = {1992},
  ISSN = {0946-011X},