The Collaborative International Dictionary of English v.0.48:

Unifier \U"ni*fi`er\, n.
   One who, or that which, unifies; as, a natural law is a
   unifier of phenomena.
   [1913 Webster]

The Free On-line Dictionary of Computing (30 December 2018):

unifier

   The unifier of a set of expressions is a set of substitutions
   of terms for variables such that the expressions are all
   equal.

   See also most general unifier, unification.

   (1994-12-06)