Herbrand Terms: Syntactic Equality

• The only constraint allowed between Herbrand terms is =/2
• Its meaning is syntactic equality (unification)
• Roughly speaking,
  • An equation $f(t_1, \ldots, t_n) = f(u_1, \ldots, u_n)$ is solved by solving $t_1 = u_1, \ldots, t_n = u_n$
  • An equation $v = t$, where $v$ is a variable and $t$ is a term which do not contains $v$ is solved with the binding $v/t$
  • Equations like $t = t$ can be deleted
  • If none of the above can be applied, the initial terms cannot be unified
• Example:

  ?- X = f(a, b).
  X = f(a, b)
  
  ?- X = f(T, a), T = b.
  T = b, X = f(b,a)
  
  ?- f(X, g(X, Y), Y) = f(a, T, b).
  X = a, Y = b, T = g(a, b)