Higher-order unification via combinators

Higher-order unification via combinators. Dougherty, D. J.\ Theoretical Computer Science, 114(2):273--298, 1993.

We present an algorithm for unification in the simply typed lambda calculus which enumerates complete sets of unifiers using a finitely branching search space. In fact, the types of terms may contain type-variables, so that a solution may involve typesubstitution as well as term-substitution. the problem is first translated into the problem of unification with respect to extensional equality in combinatory logic, and the algorithm is defined in terms of transformations on systems of combinatory terms. These transformations are based on a new method (itself based on systems) for deciding extensional equality between typed combinatory logic terms.

@article{ a_tcs93,
  author = {Daniel J.\ Dougherty},
  title = {Higher-order unification via combinators},
  journal = {Theoretical Computer Science},
  volume = {114},
  number = {2},
  pages = {273--298},
  day = {21},
  year = {1993},
  abstract = {We present an algorithm for unification in the
                  simply typed lambda calculus which enumerates
                  complete sets of unifiers using a finitely
                  branching search space. In fact, the types of
                  terms may contain type-variables, so that a
                  solution may involve typesubstitution as well
                  as term-substitution. the problem is first
                  translated into the problem of unification with
                  respect to extensional equality in combinatory
                  logic, and the algorithm is defined in terms of
                  transformations on systems of combinatory
                  terms. These transformations are based on a new
                  method (itself based on systems) for deciding
                  extensional equality between typed combinatory
                  logic terms. },
  url = {tcs93.pdf}
}

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