This article is about the computer science topic. For other uses of the term, see Unification (disambiguation).

In mathematical logic, in particular as applied to computer science, a unification of two terms is a join (in the lattice sense) with respect to a specialisation order. That is, we suppose a preorder on a set of terms, for which t* ≤ t means that t* is obtained from t by substituting some term(s) for one or more free variables in t. The unification u of s and t, if it exists, is a term that is a substitution instance of both s and t. If any common substitution instance of s and t is also an instance of u, u is called minimal unification.

For example, with polynomials, X² and Y³ can be unified to Z⁶ by taking X = Z³ and Y = Z².

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