Unification

The concept of unification is one of the main ideas behind Prolog. It represents the mechanism of binding the contents of variables and can be viewed as a kind of one-time assignment. In Prolog, this operation is denoted by symbol "=".

1. An uninstantiated variable X (i.e. no previous unification were performed on it) can be unified with an uninstantiated variable (and effectively becomes its alias), an atom or a term.
2. An atom can be unified only with the same atom.
3. A term is unified with another term, if the heads and arities of the terms are identic and the parameters are unified (note that this is a recursive behaviour).

Due to its declarative nature, the order in a sequence of unifications doesn't play (usually) any role.

Examples of unification

A=A

Succeeds (tautology)

A=B, B=abc

Both A and B are unified with the atom abc

xyz=C, C=D

Unification is symmetric

abc=abc

Unification succeeds

abc=xyz

Fails to unify, atoms are different

f(A)=f(B)

A is unified with B

f(A)=g(B)

Fails, the heads of terms are different

f(A)=f(B,C)

Fails to unify, because terms have different arity

f(g(A))=f(B)

Unifies B with the term g(A)

f(g(A), A)=f(B, xyz)

Unifies A with the atom xyz and B with the term g(xyz)

A=f(A)

Infinite unification, A is unified with f(f(f(f(...)))).

A=abc, xyz=X, A=X

Fails to unify; effectively abc=xyz