Unification:


function unify(E1, E2)
BEGIN
   case
   both E1 and E2 are constants or the empty list
      if E1 == E2 return {}      // {} is the empty list
      else return FAIL
   E1 is a variable
      if E1 occurs in E2 then return FAIL
      else return {E2/E1}       // assigns the value of E2 to E1
   E2 is a variable
      if E2 occurs in E1 then return FAIL
      else return {E1/E2}       // assigns the value of E1 to E2
   otherwise:
     BEGIN
        HE1 = first element of E1;
        HE2 = first element of E2;
        SUBS1 = unify(HE1,HE2);
        if SUBS1 == FAIL then return FAIL;
        TE1 = apply(SUBS1, rest of E1);
        TE2 = apply(SUBS1, rest of E2);
        SUBS2 = unify(TE1,TE2);
        if SUBS2 == FAIL then return FAIL;
        else return composition(SUBS1,SUBS2);
    END
END