Higher Order Unification via Explicit Substitutions

@article{Dowek2000HigherOU,
  title={Higher Order Unification via Explicit Substitutions},
  author={Gilles Dowek and Th{\'e}r{\`e}se Hardin and Claude Kirchner},
  journal={Inf. Comput.},
  year={2000},
  volume={157},
  pages={183-235}
}
Higher order unification is equational unification for βη-conversion. But it is not first order equational unification, as substitution has to avoid capture. Thus, the methods for equational unification (such as narrowing) built upon grafting (i.e., substitution without renaming) cannot be used for higher order unification, which needs specific algorithms. Our goal in this paper is to reduce higher order unification to first order equational unification in a suitable theory. This is achieved by… 
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