Z3
 All Data Structures Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Macros Modules Pages
Public Member Functions | Data Fields
Goal Class Reference
+ Inheritance diagram for Goal:

Public Member Functions

def __init__
 
def __deepcopy__
 
def __del__
 
def depth
 
def inconsistent
 
def prec
 
def precision
 
def size
 
def __len__
 
def get
 
def __getitem__
 
def assert_exprs
 
def append
 
def insert
 
def add
 
def convert_model
 
def __repr__
 
def sexpr
 
def dimacs
 
def translate
 
def __copy__
 
def __deepcopy__
 
def simplify
 
def as_expr
 
- Public Member Functions inherited from Z3PPObject
def use_pp
 

Data Fields

 ctx
 
 goal
 

Detailed Description

Goal is a collection of constraints we want to find a solution or show to be unsatisfiable (infeasible).

Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
A goal has a solution if one of its subgoals has a solution.
A goal is unsatisfiable if all subgoals are unsatisfiable.

Definition at line 5128 of file z3py.py.

Constructor & Destructor Documentation

def __init__ (   self,
  models = True,
  unsat_cores = False,
  proofs = False,
  ctx = None,
  goal = None 
)

Definition at line 5136 of file z3py.py.

5137  def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5138  if z3_debug():
5139  _z3_assert(goal is None or ctx is not None, "If goal is different from None, then ctx must be also different from None")
5140  self.ctx = _get_ctx(ctx)
5141  self.goal = goal
5142  if self.goal is None:
5143  self.goal = Z3_mk_goal(self.ctx.ref(), models, unsat_cores, proofs)
5144  Z3_goal_inc_ref(self.ctx.ref(), self.goal)
Z3_goal Z3_API Z3_mk_goal(Z3_context c, bool models, bool unsat_cores, bool proofs)
Create a goal (aka problem). A goal is essentially a set of formulas, that can be solved and/or trans...
def z3_debug
Definition: z3py.py:58
void Z3_API Z3_goal_inc_ref(Z3_context c, Z3_goal g)
Increment the reference counter of the given goal.
def __init__
Definition: z3py.py:5136
def __del__ (   self)

Definition at line 5148 of file z3py.py.

5149  def __del__(self):
5150  if self.goal is not None and self.ctx.ref() is not None:
5151  Z3_goal_dec_ref(self.ctx.ref(), self.goal)
def __del__
Definition: z3py.py:5148
void Z3_API Z3_goal_dec_ref(Z3_context c, Z3_goal g)
Decrement the reference counter of the given goal.

Member Function Documentation

def __copy__ (   self)

Definition at line 5382 of file z3py.py.

5383  def __copy__(self):
5384  return self.translate(self.ctx)
def __copy__
Definition: z3py.py:5382
def translate
Definition: z3py.py:5359
def __deepcopy__ (   self,
  memo = {} 
)

Definition at line 5145 of file z3py.py.

5146  def __deepcopy__(self, memo={}):
5147  return Goal(False, False, False, self.ctx, self.goal)
def __deepcopy__
Definition: z3py.py:5145
def __deepcopy__ (   self,
  memo = {} 
)

Definition at line 5385 of file z3py.py.

5386  def __deepcopy__(self, memo={}):
5387  return self.translate(self.ctx)
def __deepcopy__
Definition: z3py.py:5145
def translate
Definition: z3py.py:5359
def __getitem__ (   self,
  arg 
)
Return a constraint in the goal `self`.

>>> g = Goal()
>>> x, y = Ints('x y')
>>> g.add(x == 0, y > x)
>>> g[0]
x == 0
>>> g[1]
y > x

Definition at line 5256 of file z3py.py.

5257  def __getitem__(self, arg):
5258  """Return a constraint in the goal `self`.
5259 
5260  >>> g = Goal()
5261  >>> x, y = Ints('x y')
5262  >>> g.add(x == 0, y > x)
5263  >>> g[0]
5264  x == 0
5265  >>> g[1]
5266  y > x
5267  """
5268  if arg >= len(self):
5269  raise IndexError
5270  return self.get(arg)
def __getitem__
Definition: z3py.py:5256
def get
Definition: z3py.py:5243
def __len__ (   self)
Return the number of constraints in the goal `self`.

>>> g = Goal()
>>> len(g)
0
>>> x, y = Ints('x y')
>>> g.add(x == 0, y > x)
>>> len(g)
2

Definition at line 5230 of file z3py.py.

Referenced by AstVector.__getitem__(), and AstVector.__setitem__().

5231  def __len__(self):
5232  """Return the number of constraints in the goal `self`.
5233 
5234  >>> g = Goal()
5235  >>> len(g)
5236  0
5237  >>> x, y = Ints('x y')
5238  >>> g.add(x == 0, y > x)
5239  >>> len(g)
5240  2
5241  """
5242  return self.size()
def __len__
Definition: z3py.py:5230
def size
Definition: z3py.py:5217
def __repr__ (   self)

Definition at line 5348 of file z3py.py.

5349  def __repr__(self):
5350  return obj_to_string(self)
def __repr__
Definition: z3py.py:5348
def add (   self,
  args 
)
Add constraints.

>>> x = Int('x')
>>> g = Goal()
>>> g.add(x > 0, x < 2)
>>> g
[x > 0, x < 2]

Definition at line 5308 of file z3py.py.

Referenced by Fixedpoint.__iadd__(), and Optimize.__iadd__().

5309  def add(self, *args):
5310  """Add constraints.
5311 
5312  >>> x = Int('x')
5313  >>> g = Goal()
5314  >>> g.add(x > 0, x < 2)
5315  >>> g
5316  [x > 0, x < 2]
5317  """
5318  self.assert_exprs(*args)
def add
Definition: z3py.py:5308
def assert_exprs
Definition: z3py.py:5271
def append (   self,
  args 
)
Add constraints.

>>> x = Int('x')
>>> g = Goal()
>>> g.append(x > 0, x < 2)
>>> g
[x > 0, x < 2]

Definition at line 5286 of file z3py.py.

5287  def append(self, *args):
5288  """Add constraints.
5289 
5290  >>> x = Int('x')
5291  >>> g = Goal()
5292  >>> g.append(x > 0, x < 2)
5293  >>> g
5294  [x > 0, x < 2]
5295  """
5296  self.assert_exprs(*args)
def append
Definition: z3py.py:5286
def assert_exprs
Definition: z3py.py:5271
def as_expr (   self)
Return goal `self` as a single Z3 expression.

>>> x = Int('x')
>>> g = Goal()
>>> g.as_expr()
True
>>> g.add(x > 1)
>>> g.as_expr()
x > 1
>>> g.add(x < 10)
>>> g.as_expr()
And(x > 1, x < 10)

Definition at line 5408 of file z3py.py.

5409  def as_expr(self):
5410  """Return goal `self` as a single Z3 expression.
5411 
5412  >>> x = Int('x')
5413  >>> g = Goal()
5414  >>> g.as_expr()
5415  True
5416  >>> g.add(x > 1)
5417  >>> g.as_expr()
5418  x > 1
5419  >>> g.add(x < 10)
5420  >>> g.as_expr()
5421  And(x > 1, x < 10)
5422  """
5423  sz = len(self)
5424  if sz == 0:
5425  return BoolVal(True, self.ctx)
5426  elif sz == 1:
5427  return self.get(0)
5428  else:
5429  return And([ self.get(i) for i in range(len(self)) ], self.ctx)
def BoolVal
Definition: z3py.py:1540
expr range(expr const &lo, expr const &hi)
Definition: z3++.h:3358
def And
Definition: z3py.py:1672
def as_expr
Definition: z3py.py:5408
def get
Definition: z3py.py:5243
def assert_exprs (   self,
  args 
)
Assert constraints into the goal.

>>> x = Int('x')
>>> g = Goal()
>>> g.assert_exprs(x > 0, x < 2)
>>> g
[x > 0, x < 2]

Definition at line 5271 of file z3py.py.

Referenced by Goal.add(), Fixedpoint.add(), Optimize.add(), Goal.append(), Fixedpoint.append(), and Fixedpoint.insert().

5272  def assert_exprs(self, *args):
5273  """Assert constraints into the goal.
5274 
5275  >>> x = Int('x')
5276  >>> g = Goal()
5277  >>> g.assert_exprs(x > 0, x < 2)
5278  >>> g
5279  [x > 0, x < 2]
5280  """
5281  args = _get_args(args)
5282  s = BoolSort(self.ctx)
5283  for arg in args:
5284  arg = s.cast(arg)
5285  Z3_goal_assert(self.ctx.ref(), self.goal, arg.as_ast())
def BoolSort
Definition: z3py.py:1523
def assert_exprs
Definition: z3py.py:5271
void Z3_API Z3_goal_assert(Z3_context c, Z3_goal g, Z3_ast a)
Add a new formula a to the given goal. The formula is split according to the following procedure that...
def convert_model (   self,
  model 
)
Retrieve model from a satisfiable goal
>>> a, b = Ints('a b')
>>> g = Goal()
>>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
>>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
>>> r = t(g)
>>> r[0]
[Or(b == 0, b == 1), Not(0 <= b)]
>>> r[1]
[Or(b == 0, b == 1), Not(1 <= b)]
>>> # Remark: the subgoal r[0] is unsatisfiable
>>> # Creating a solver for solving the second subgoal
>>> s = Solver()
>>> s.add(r[1])
>>> s.check()
sat
>>> s.model()
[b = 0]
>>> # Model s.model() does not assign a value to `a`
>>> # It is a model for subgoal `r[1]`, but not for goal `g`
>>> # The method convert_model creates a model for `g` from a model for `r[1]`.
>>> r[1].convert_model(s.model())
[b = 0, a = 1]

Definition at line 5319 of file z3py.py.

5320  def convert_model(self, model):
5321  """Retrieve model from a satisfiable goal
5322  >>> a, b = Ints('a b')
5323  >>> g = Goal()
5324  >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
5325  >>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
5326  >>> r = t(g)
5327  >>> r[0]
5328  [Or(b == 0, b == 1), Not(0 <= b)]
5329  >>> r[1]
5330  [Or(b == 0, b == 1), Not(1 <= b)]
5331  >>> # Remark: the subgoal r[0] is unsatisfiable
5332  >>> # Creating a solver for solving the second subgoal
5333  >>> s = Solver()
5334  >>> s.add(r[1])
5335  >>> s.check()
5336  sat
5337  >>> s.model()
5338  [b = 0]
5339  >>> # Model s.model() does not assign a value to `a`
5340  >>> # It is a model for subgoal `r[1]`, but not for goal `g`
5341  >>> # The method convert_model creates a model for `g` from a model for `r[1]`.
5342  >>> r[1].convert_model(s.model())
5343  [b = 0, a = 1]
5344  """
5345  if z3_debug():
5346  _z3_assert(isinstance(model, ModelRef), "Z3 Model expected")
5347  return ModelRef(Z3_goal_convert_model(self.ctx.ref(), self.goal, model.model), self.ctx)
def convert_model
Definition: z3py.py:5319
Z3_model Z3_API Z3_goal_convert_model(Z3_context c, Z3_goal g, Z3_model m)
Convert a model of the formulas of a goal to a model of an original goal. The model may be null...
def z3_debug
Definition: z3py.py:58
def depth (   self)
Return the depth of the goal `self`. The depth corresponds to the number of tactics applied to `self`.

>>> x, y = Ints('x y')
>>> g = Goal()
>>> g.add(x == 0, y >= x + 1)
>>> g.depth()
0
>>> r = Then('simplify', 'solve-eqs')(g)
>>> # r has 1 subgoal
>>> len(r)
1
>>> r[0].depth()
2

Definition at line 5152 of file z3py.py.

5153  def depth(self):
5154  """Return the depth of the goal `self`. The depth corresponds to the number of tactics applied to `self`.
5155 
5156  >>> x, y = Ints('x y')
5157  >>> g = Goal()
5158  >>> g.add(x == 0, y >= x + 1)
5159  >>> g.depth()
5160  0
5161  >>> r = Then('simplify', 'solve-eqs')(g)
5162  >>> # r has 1 subgoal
5163  >>> len(r)
5164  1
5165  >>> r[0].depth()
5166  2
5167  """
5168  return int(Z3_goal_depth(self.ctx.ref(), self.goal))
def depth
Definition: z3py.py:5152
unsigned Z3_API Z3_goal_depth(Z3_context c, Z3_goal g)
Return the depth of the given goal. It tracks how many transformations were applied to it...
def dimacs (   self)
Return a textual representation of the goal in DIMACS format.

Definition at line 5355 of file z3py.py.

5356  def dimacs(self):
5357  """Return a textual representation of the goal in DIMACS format."""
5358  return Z3_goal_to_dimacs_string(self.ctx.ref(), self.goal)
Z3_string Z3_API Z3_goal_to_dimacs_string(Z3_context c, Z3_goal g)
Convert a goal into a DIMACS formatted string. The goal must be in CNF. You can convert a goal to CNF...
def dimacs
Definition: z3py.py:5355
def get (   self,
  i 
)
Return a constraint in the goal `self`.

>>> g = Goal()
>>> x, y = Ints('x y')
>>> g.add(x == 0, y > x)
>>> g.get(0)
x == 0
>>> g.get(1)
y > x

Definition at line 5243 of file z3py.py.

Referenced by Goal.__getitem__(), and Goal.as_expr().

5244  def get(self, i):
5245  """Return a constraint in the goal `self`.
5246 
5247  >>> g = Goal()
5248  >>> x, y = Ints('x y')
5249  >>> g.add(x == 0, y > x)
5250  >>> g.get(0)
5251  x == 0
5252  >>> g.get(1)
5253  y > x
5254  """
5255  return _to_expr_ref(Z3_goal_formula(self.ctx.ref(), self.goal, i), self.ctx)
def get
Definition: z3py.py:5243
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.
def inconsistent (   self)
Return `True` if `self` contains the `False` constraints.

>>> x, y = Ints('x y')
>>> g = Goal()
>>> g.inconsistent()
False
>>> g.add(x == 0, x == 1)
>>> g
[x == 0, x == 1]
>>> g.inconsistent()
False
>>> g2 = Tactic('propagate-values')(g)[0]
>>> g2.inconsistent()
True

Definition at line 5169 of file z3py.py.

5170  def inconsistent(self):
5171  """Return `True` if `self` contains the `False` constraints.
5172 
5173  >>> x, y = Ints('x y')
5174  >>> g = Goal()
5175  >>> g.inconsistent()
5176  False
5177  >>> g.add(x == 0, x == 1)
5178  >>> g
5179  [x == 0, x == 1]
5180  >>> g.inconsistent()
5181  False
5182  >>> g2 = Tactic('propagate-values')(g)[0]
5183  >>> g2.inconsistent()
5184  True
5185  """
5186  return Z3_goal_inconsistent(self.ctx.ref(), self.goal)
bool Z3_API Z3_goal_inconsistent(Z3_context c, Z3_goal g)
Return true if the given goal contains the formula false.
def inconsistent
Definition: z3py.py:5169
def insert (   self,
  args 
)
Add constraints.

>>> x = Int('x')
>>> g = Goal()
>>> g.insert(x > 0, x < 2)
>>> g
[x > 0, x < 2]

Definition at line 5297 of file z3py.py.

5298  def insert(self, *args):
5299  """Add constraints.
5300 
5301  >>> x = Int('x')
5302  >>> g = Goal()
5303  >>> g.insert(x > 0, x < 2)
5304  >>> g
5305  [x > 0, x < 2]
5306  """
5307  self.assert_exprs(*args)
def insert
Definition: z3py.py:5297
def assert_exprs
Definition: z3py.py:5271
def prec (   self)
Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.

>>> g = Goal()
>>> g.prec() == Z3_GOAL_PRECISE
True
>>> x, y = Ints('x y')
>>> g.add(x == y + 1)
>>> g.prec() == Z3_GOAL_PRECISE
True
>>> t  = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
>>> g2 = t(g)[0]
>>> g2
[x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
>>> g2.prec() == Z3_GOAL_PRECISE
False
>>> g2.prec() == Z3_GOAL_UNDER
True

Definition at line 5187 of file z3py.py.

Referenced by Goal.precision().

5188  def prec(self):
5189  """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5190 
5191  >>> g = Goal()
5192  >>> g.prec() == Z3_GOAL_PRECISE
5193  True
5194  >>> x, y = Ints('x y')
5195  >>> g.add(x == y + 1)
5196  >>> g.prec() == Z3_GOAL_PRECISE
5197  True
5198  >>> t = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
5199  >>> g2 = t(g)[0]
5200  >>> g2
5201  [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5202  >>> g2.prec() == Z3_GOAL_PRECISE
5203  False
5204  >>> g2.prec() == Z3_GOAL_UNDER
5205  True
5206  """
5207  return Z3_goal_precision(self.ctx.ref(), self.goal)
def prec
Definition: z3py.py:5187
Z3_goal_prec Z3_API Z3_goal_precision(Z3_context c, Z3_goal g)
Return the "precision" of the given goal. Goals can be transformed using over and under approximation...
def precision (   self)
Alias for `prec()`.

>>> g = Goal()
>>> g.precision() == Z3_GOAL_PRECISE
True

Definition at line 5208 of file z3py.py.

5209  def precision(self):
5210  """Alias for `prec()`.
5211 
5212  >>> g = Goal()
5213  >>> g.precision() == Z3_GOAL_PRECISE
5214  True
5215  """
5216  return self.prec()
def prec
Definition: z3py.py:5187
def precision
Definition: z3py.py:5208
def sexpr (   self)
Return a textual representation of the s-expression representing the goal.

Definition at line 5351 of file z3py.py.

Referenced by Fixedpoint.__repr__(), and Optimize.__repr__().

5352  def sexpr(self):
5353  """Return a textual representation of the s-expression representing the goal."""
5354  return Z3_goal_to_string(self.ctx.ref(), self.goal)
def sexpr
Definition: z3py.py:5351
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.
def simplify (   self,
  arguments,
  keywords 
)
Return a new simplified goal.

This method is essentially invoking the simplify tactic.

>>> g = Goal()
>>> x = Int('x')
>>> g.add(x + 1 >= 2)
>>> g
[x + 1 >= 2]
>>> g2 = g.simplify()
>>> g2
[x >= 1]
>>> # g was not modified
>>> g
[x + 1 >= 2]

Definition at line 5388 of file z3py.py.

5389  def simplify(self, *arguments, **keywords):
5390  """Return a new simplified goal.
5391 
5392  This method is essentially invoking the simplify tactic.
5393 
5394  >>> g = Goal()
5395  >>> x = Int('x')
5396  >>> g.add(x + 1 >= 2)
5397  >>> g
5398  [x + 1 >= 2]
5399  >>> g2 = g.simplify()
5400  >>> g2
5401  [x >= 1]
5402  >>> # g was not modified
5403  >>> g
5404  [x + 1 >= 2]
5405  """
5406  t = Tactic('simplify')
5407  return t.apply(self, *arguments, **keywords)[0]
def simplify
Definition: z3py.py:5388
def size (   self)
Return the number of constraints in the goal `self`.

>>> g = Goal()
>>> g.size()
0
>>> x, y = Ints('x y')
>>> g.add(x == 0, y > x)
>>> g.size()
2

Definition at line 5217 of file z3py.py.

Referenced by Goal.__len__().

5218  def size(self):
5219  """Return the number of constraints in the goal `self`.
5220 
5221  >>> g = Goal()
5222  >>> g.size()
5223  0
5224  >>> x, y = Ints('x y')
5225  >>> g.add(x == 0, y > x)
5226  >>> g.size()
5227  2
5228  """
5229  return int(Z3_goal_size(self.ctx.ref(), self.goal))
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.
def size
Definition: z3py.py:5217
def translate (   self,
  target 
)
Copy goal `self` to context `target`.

>>> x = Int('x')
>>> g = Goal()
>>> g.add(x > 10)
>>> g
[x > 10]
>>> c2 = Context()
>>> g2 = g.translate(c2)
>>> g2
[x > 10]
>>> g.ctx == main_ctx()
True
>>> g2.ctx == c2
True
>>> g2.ctx == main_ctx()
False

Definition at line 5359 of file z3py.py.

Referenced by Goal.__copy__(), AstVector.__copy__(), FuncInterp.__copy__(), Goal.__deepcopy__(), AstVector.__deepcopy__(), and FuncInterp.__deepcopy__().

5360  def translate(self, target):
5361  """Copy goal `self` to context `target`.
5362 
5363  >>> x = Int('x')
5364  >>> g = Goal()
5365  >>> g.add(x > 10)
5366  >>> g
5367  [x > 10]
5368  >>> c2 = Context()
5369  >>> g2 = g.translate(c2)
5370  >>> g2
5371  [x > 10]
5372  >>> g.ctx == main_ctx()
5373  True
5374  >>> g2.ctx == c2
5375  True
5376  >>> g2.ctx == main_ctx()
5377  False
5378  """
5379  if z3_debug():
5380  _z3_assert(isinstance(target, Context), "target must be a context")
5381  return Goal(goal=Z3_goal_translate(self.ctx.ref(), self.goal, target.ref()), ctx=target)
Z3_goal Z3_API Z3_goal_translate(Z3_context source, Z3_goal g, Z3_context target)
Copy a goal g from the context source to the context target.
def translate
Definition: z3py.py:5359
def z3_debug
Definition: z3py.py:58

Field Documentation

ctx

Definition at line 5139 of file z3py.py.

Referenced by Goal.__copy__(), AstVector.__copy__(), FuncInterp.__copy__(), Goal.__deepcopy__(), AstVector.__deepcopy__(), AstMap.__deepcopy__(), FuncEntry.__deepcopy__(), FuncInterp.__deepcopy__(), Fixedpoint.__deepcopy__(), Optimize.__deepcopy__(), ApplyResult.__deepcopy__(), Tactic.__deepcopy__(), Probe.__deepcopy__(), Probe.__eq__(), Probe.__ge__(), AstVector.__getitem__(), AstMap.__getitem__(), ApplyResult.__getitem__(), Probe.__gt__(), Probe.__le__(), Probe.__lt__(), Probe.__ne__(), Fixedpoint.add_rule(), Optimize.add_soft(), Tactic.apply(), FuncEntry.arg_value(), Goal.as_expr(), ApplyResult.as_expr(), Optimize.assert_and_track(), Goal.assert_exprs(), Fixedpoint.assert_exprs(), Optimize.assert_exprs(), Optimize.assertions(), Goal.convert_model(), FuncInterp.else_value(), FuncInterp.entry(), Goal.get(), Fixedpoint.get_answer(), Fixedpoint.get_assertions(), Fixedpoint.get_cover_delta(), Fixedpoint.get_ground_sat_answer(), Fixedpoint.get_rule_names_along_trace(), Fixedpoint.get_rules(), Fixedpoint.get_rules_along_trace(), AstMap.keys(), Optimize.model(), Optimize.objectives(), Fixedpoint.param_descrs(), Optimize.param_descrs(), Tactic.param_descrs(), Fixedpoint.parse_file(), Fixedpoint.parse_string(), Fixedpoint.query(), Fixedpoint.set(), Optimize.set(), Tactic.solver(), Fixedpoint.statistics(), Optimize.statistics(), Solver.to_smt2(), Optimize.unsat_core(), Fixedpoint.update_rule(), and FuncEntry.value().

goal

Definition at line 5140 of file z3py.py.

Referenced by Goal.__deepcopy__(), Goal.__del__(), Goal.assert_exprs(), Goal.convert_model(), Goal.depth(), Goal.dimacs(), Goal.get(), Goal.inconsistent(), Goal.prec(), Goal.sexpr(), Goal.size(), and Goal.translate().