Z3
Public Member Functions | Data Fields
Goal Class Reference
+ Inheritance diagram for Goal:

Public Member Functions

def __init__ (self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None)
 
def __deepcopy__ (self, memo={})
 
def __del__ (self)
 
def depth (self)
 
def inconsistent (self)
 
def prec (self)
 
def precision (self)
 
def size (self)
 
def __len__ (self)
 
def get (self, i)
 
def __getitem__ (self, arg)
 
def assert_exprs (self, *args)
 
def append (self, *args)
 
def insert (self, *args)
 
def add (self, *args)
 
def convert_model (self, model)
 
def __repr__ (self)
 
def sexpr (self)
 
def dimacs (self)
 
def translate (self, target)
 
def __copy__ (self)
 
def __deepcopy__ (self, memo={})
 
def simplify (self, *arguments, **keywords)
 
def as_expr (self)
 
- Public Member Functions inherited from Z3PPObject
def use_pp (self)
 

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 5148 of file z3py.py.

Constructor & Destructor Documentation

◆ __init__()

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

Definition at line 5156 of file z3py.py.

5156 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5157 if z3_debug():
5158 _z3_assert(goal is None or ctx is not None, "If goal is different from None, then ctx must be also different from None")
5159 self.ctx = _get_ctx(ctx)
5160 self.goal = goal
5161 if self.goal is None:
5162 self.goal = Z3_mk_goal(self.ctx.ref(), models, unsat_cores, proofs)
5163 Z3_goal_inc_ref(self.ctx.ref(), self.goal)
5164
def z3_debug()
Definition: z3py.py:56
void Z3_API Z3_goal_inc_ref(Z3_context c, Z3_goal g)
Increment the reference counter of the given 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...

◆ __del__()

def __del__ (   self)

Definition at line 5168 of file z3py.py.

5168 def __del__(self):
5169 if self.goal is not None and self.ctx.ref() is not None:
5170 Z3_goal_dec_ref(self.ctx.ref(), self.goal)
5171
void Z3_API Z3_goal_dec_ref(Z3_context c, Z3_goal g)
Decrement the reference counter of the given goal.

Member Function Documentation

◆ __copy__()

def __copy__ (   self)

Definition at line 5402 of file z3py.py.

5402 def __copy__(self):
5403 return self.translate(self.ctx)
5404

◆ __deepcopy__() [1/2]

def __deepcopy__ (   self,
  memo = {} 
)

Definition at line 5165 of file z3py.py.

5165 def __deepcopy__(self, memo={}):
5166 return Goal(False, False, False, self.ctx, self.goal)
5167

◆ __deepcopy__() [2/2]

def __deepcopy__ (   self,
  memo = {} 
)

Definition at line 5405 of file z3py.py.

5405 def __deepcopy__(self, memo={}):
5406 return self.translate(self.ctx)
5407

◆ __getitem__()

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 5276 of file z3py.py.

5276 def __getitem__(self, arg):
5277 """Return a constraint in the goal `self`.
5278
5279 >>> g = Goal()
5280 >>> x, y = Ints('x y')
5281 >>> g.add(x == 0, y > x)
5282 >>> g[0]
5283 x == 0
5284 >>> g[1]
5285 y > x
5286 """
5287 if arg >= len(self):
5288 raise IndexError
5289 return self.get(arg)
5290
def Ints(names, ctx=None)
Definition: z3py.py:3022

◆ __len__()

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 5250 of file z3py.py.

5250 def __len__(self):
5251 """Return the number of constraints in the goal `self`.
5252
5253 >>> g = Goal()
5254 >>> len(g)
5255 0
5256 >>> x, y = Ints('x y')
5257 >>> g.add(x == 0, y > x)
5258 >>> len(g)
5259 2
5260 """
5261 return self.size()
5262

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

◆ __repr__()

def __repr__ (   self)

Definition at line 5368 of file z3py.py.

5368 def __repr__(self):
5369 return obj_to_string(self)
5370

◆ add()

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 5328 of file z3py.py.

5328 def add(self, *args):
5329 """Add constraints.
5330
5331 >>> x = Int('x')
5332 >>> g = Goal()
5333 >>> g.add(x > 0, x < 2)
5334 >>> g
5335 [x > 0, x < 2]
5336 """
5337 self.assert_exprs(*args)
5338
def Int(name, ctx=None)
Definition: z3py.py:3010

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

◆ append()

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 5306 of file z3py.py.

5306 def append(self, *args):
5307 """Add constraints.
5308
5309 >>> x = Int('x')
5310 >>> g = Goal()
5311 >>> g.append(x > 0, x < 2)
5312 >>> g
5313 [x > 0, x < 2]
5314 """
5315 self.assert_exprs(*args)
5316

◆ as_expr()

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 5428 of file z3py.py.

5428 def as_expr(self):
5429 """Return goal `self` as a single Z3 expression.
5430
5431 >>> x = Int('x')
5432 >>> g = Goal()
5433 >>> g.as_expr()
5434 True
5435 >>> g.add(x > 1)
5436 >>> g.as_expr()
5437 x > 1
5438 >>> g.add(x < 10)
5439 >>> g.as_expr()
5440 And(x > 1, x < 10)
5441 """
5442 sz = len(self)
5443 if sz == 0:
5444 return BoolVal(True, self.ctx)
5445 elif sz == 1:
5446 return self.get(0)
5447 else:
5448 return And([ self.get(i) for i in range(len(self)) ], self.ctx)
5449
expr range(expr const &lo, expr const &hi)
Definition: z3++.h:3431
def BoolVal(val, ctx=None)
Definition: z3py.py:1550
def And(*args)
Definition: z3py.py:1680

◆ assert_exprs()

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 5291 of file z3py.py.

5291 def assert_exprs(self, *args):
5292 """Assert constraints into the goal.
5293
5294 >>> x = Int('x')
5295 >>> g = Goal()
5296 >>> g.assert_exprs(x > 0, x < 2)
5297 >>> g
5298 [x > 0, x < 2]
5299 """
5300 args = _get_args(args)
5301 s = BoolSort(self.ctx)
5302 for arg in args:
5303 arg = s.cast(arg)
5304 Z3_goal_assert(self.ctx.ref(), self.goal, arg.as_ast())
5305
def BoolSort(ctx=None)
Definition: z3py.py:1533
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...

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

◆ convert_model()

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 5339 of file z3py.py.

5339 def convert_model(self, model):
5340 """Retrieve model from a satisfiable goal
5341 >>> a, b = Ints('a b')
5342 >>> g = Goal()
5343 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
5344 >>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
5345 >>> r = t(g)
5346 >>> r[0]
5347 [Or(b == 0, b == 1), Not(0 <= b)]
5348 >>> r[1]
5349 [Or(b == 0, b == 1), Not(1 <= b)]
5350 >>> # Remark: the subgoal r[0] is unsatisfiable
5351 >>> # Creating a solver for solving the second subgoal
5352 >>> s = Solver()
5353 >>> s.add(r[1])
5354 >>> s.check()
5355 sat
5356 >>> s.model()
5357 [b = 0]
5358 >>> # Model s.model() does not assign a value to `a`
5359 >>> # It is a model for subgoal `r[1]`, but not for goal `g`
5360 >>> # The method convert_model creates a model for `g` from a model for `r[1]`.
5361 >>> r[1].convert_model(s.model())
5362 [b = 0, a = 1]
5363 """
5364 if z3_debug():
5365 _z3_assert(isinstance(model, ModelRef), "Z3 Model expected")
5366 return ModelRef(Z3_goal_convert_model(self.ctx.ref(), self.goal, model.model), self.ctx)
5367
def Not(a, ctx=None)
Definition: z3py.py:1649
def Then(*ts, **ks)
Definition: z3py.py:7766
def Or(*args)
Definition: z3py.py:1713
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,...

Referenced by Goal.convert_model().

◆ depth()

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 5172 of file z3py.py.

5172 def depth(self):
5173 """Return the depth of the goal `self`. The depth corresponds to the number of tactics applied to `self`.
5174
5175 >>> x, y = Ints('x y')
5176 >>> g = Goal()
5177 >>> g.add(x == 0, y >= x + 1)
5178 >>> g.depth()
5179 0
5180 >>> r = Then('simplify', 'solve-eqs')(g)
5181 >>> # r has 1 subgoal
5182 >>> len(r)
5183 1
5184 >>> r[0].depth()
5185 2
5186 """
5187 return int(Z3_goal_depth(self.ctx.ref(), self.goal))
5188
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.

Referenced by Goal.depth().

◆ dimacs()

def dimacs (   self)
Return a textual representation of the goal in DIMACS format.

Definition at line 5375 of file z3py.py.

5375 def dimacs(self):
5376 """Return a textual representation of the goal in DIMACS format."""
5377 return Z3_goal_to_dimacs_string(self.ctx.ref(), self.goal)
5378
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...

◆ get()

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 5263 of file z3py.py.

5263 def get(self, i):
5264 """Return a constraint in the goal `self`.
5265
5266 >>> g = Goal()
5267 >>> x, y = Ints('x y')
5268 >>> g.add(x == 0, y > x)
5269 >>> g.get(0)
5270 x == 0
5271 >>> g.get(1)
5272 y > x
5273 """
5274 return _to_expr_ref(Z3_goal_formula(self.ctx.ref(), self.goal, i), self.ctx)
5275
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.

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

◆ inconsistent()

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 5189 of file z3py.py.

5189 def inconsistent(self):
5190 """Return `True` if `self` contains the `False` constraints.
5191
5192 >>> x, y = Ints('x y')
5193 >>> g = Goal()
5194 >>> g.inconsistent()
5195 False
5196 >>> g.add(x == 0, x == 1)
5197 >>> g
5198 [x == 0, x == 1]
5199 >>> g.inconsistent()
5200 False
5201 >>> g2 = Tactic('propagate-values')(g)[0]
5202 >>> g2.inconsistent()
5203 True
5204 """
5205 return Z3_goal_inconsistent(self.ctx.ref(), self.goal)
5206
bool Z3_API Z3_goal_inconsistent(Z3_context c, Z3_goal g)
Return true if the given goal contains the formula false.

◆ insert()

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 5317 of file z3py.py.

5317 def insert(self, *args):
5318 """Add constraints.
5319
5320 >>> x = Int('x')
5321 >>> g = Goal()
5322 >>> g.insert(x > 0, x < 2)
5323 >>> g
5324 [x > 0, x < 2]
5325 """
5326 self.assert_exprs(*args)
5327

◆ prec()

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 5207 of file z3py.py.

5207 def prec(self):
5208 """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5209
5210 >>> g = Goal()
5211 >>> g.prec() == Z3_GOAL_PRECISE
5212 True
5213 >>> x, y = Ints('x y')
5214 >>> g.add(x == y + 1)
5215 >>> g.prec() == Z3_GOAL_PRECISE
5216 True
5217 >>> t = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
5218 >>> g2 = t(g)[0]
5219 >>> g2
5220 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5221 >>> g2.prec() == Z3_GOAL_PRECISE
5222 False
5223 >>> g2.prec() == Z3_GOAL_UNDER
5224 True
5225 """
5226 return Z3_goal_precision(self.ctx.ref(), self.goal)
5227
def With(t, *args, **keys)
Definition: z3py.py:7834
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...

Referenced by Goal.precision().

◆ precision()

def precision (   self)
Alias for `prec()`.

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

Definition at line 5228 of file z3py.py.

5228 def precision(self):
5229 """Alias for `prec()`.
5230
5231 >>> g = Goal()
5232 >>> g.precision() == Z3_GOAL_PRECISE
5233 True
5234 """
5235 return self.prec()
5236

◆ sexpr()

def sexpr (   self)
Return a textual representation of the s-expression representing the goal.

Definition at line 5371 of file z3py.py.

5371 def sexpr(self):
5372 """Return a textual representation of the s-expression representing the goal."""
5373 return Z3_goal_to_string(self.ctx.ref(), self.goal)
5374
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.

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

◆ simplify()

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 5408 of file z3py.py.

5408 def simplify(self, *arguments, **keywords):
5409 """Return a new simplified goal.
5410
5411 This method is essentially invoking the simplify tactic.
5412
5413 >>> g = Goal()
5414 >>> x = Int('x')
5415 >>> g.add(x + 1 >= 2)
5416 >>> g
5417 [x + 1 >= 2]
5418 >>> g2 = g.simplify()
5419 >>> g2
5420 [x >= 1]
5421 >>> # g was not modified
5422 >>> g
5423 [x + 1 >= 2]
5424 """
5425 t = Tactic('simplify')
5426 return t.apply(self, *arguments, **keywords)[0]
5427
def simplify(a, *arguments, **keywords)
Utils.
Definition: z3py.py:8182

◆ size()

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 5237 of file z3py.py.

5237 def size(self):
5238 """Return the number of constraints in the goal `self`.
5239
5240 >>> g = Goal()
5241 >>> g.size()
5242 0
5243 >>> x, y = Ints('x y')
5244 >>> g.add(x == 0, y > x)
5245 >>> g.size()
5246 2
5247 """
5248 return int(Z3_goal_size(self.ctx.ref(), self.goal))
5249
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.

Referenced by ParamDescrsRef.__len__(), Goal.__len__(), BitVecNumRef.as_signed_long(), and BitVecSortRef.subsort().

◆ translate()

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 5379 of file z3py.py.

5379 def translate(self, target):
5380 """Copy goal `self` to context `target`.
5381
5382 >>> x = Int('x')
5383 >>> g = Goal()
5384 >>> g.add(x > 10)
5385 >>> g
5386 [x > 10]
5387 >>> c2 = Context()
5388 >>> g2 = g.translate(c2)
5389 >>> g2
5390 [x > 10]
5391 >>> g.ctx == main_ctx()
5392 True
5393 >>> g2.ctx == c2
5394 True
5395 >>> g2.ctx == main_ctx()
5396 False
5397 """
5398 if z3_debug():
5399 _z3_assert(isinstance(target, Context), "target must be a context")
5400 return Goal(goal=Z3_goal_translate(self.ctx.ref(), self.goal, target.ref()), ctx=target)
5401
def main_ctx()
Definition: z3py.py:211
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.

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

Field Documentation

◆ ctx

ctx

Definition at line 5159 of file z3py.py.

Referenced by ArithRef.__add__(), BitVecRef.__add__(), FPRef.__add__(), BitVecRef.__and__(), FuncDeclRef.__call__(), Probe.__call__(), AstMap.__contains__(), AstRef.__copy__(), Goal.__copy__(), AstVector.__copy__(), FuncInterp.__copy__(), ModelRef.__copy__(), Solver.__copy__(), AstRef.__deepcopy__(), Datatype.__deepcopy__(), ParamsRef.__deepcopy__(), ParamDescrsRef.__deepcopy__(), Goal.__deepcopy__(), AstVector.__deepcopy__(), AstMap.__deepcopy__(), FuncEntry.__deepcopy__(), FuncInterp.__deepcopy__(), ModelRef.__deepcopy__(), Statistics.__deepcopy__(), Solver.__deepcopy__(), Fixedpoint.__deepcopy__(), Optimize.__deepcopy__(), ApplyResult.__deepcopy__(), Tactic.__deepcopy__(), Probe.__deepcopy__(), Context.__del__(), AstRef.__del__(), ScopedConstructor.__del__(), ScopedConstructorList.__del__(), ParamsRef.__del__(), ParamDescrsRef.__del__(), Goal.__del__(), AstVector.__del__(), AstMap.__del__(), FuncEntry.__del__(), FuncInterp.__del__(), ModelRef.__del__(), Statistics.__del__(), Solver.__del__(), Fixedpoint.__del__(), Optimize.__del__(), ApplyResult.__del__(), Tactic.__del__(), Probe.__del__(), ArithRef.__div__(), BitVecRef.__div__(), FPRef.__div__(), ExprRef.__eq__(), Probe.__eq__(), ArithRef.__ge__(), BitVecRef.__ge__(), Probe.__ge__(), FPRef.__ge__(), SeqRef.__ge__(), QuantifierRef.__getitem__(), ArrayRef.__getitem__(), AstVector.__getitem__(), SeqRef.__getitem__(), ModelRef.__getitem__(), Statistics.__getitem__(), ApplyResult.__getitem__(), AstMap.__getitem__(), ArithRef.__gt__(), BitVecRef.__gt__(), Probe.__gt__(), FPRef.__gt__(), SeqRef.__gt__(), BitVecRef.__invert__(), ArithRef.__le__(), BitVecRef.__le__(), Probe.__le__(), FPRef.__le__(), SeqRef.__le__(), AstVector.__len__(), AstMap.__len__(), ModelRef.__len__(), Statistics.__len__(), ApplyResult.__len__(), BitVecRef.__lshift__(), ArithRef.__lt__(), BitVecRef.__lt__(), Probe.__lt__(), FPRef.__lt__(), SeqRef.__lt__(), ArithRef.__mod__(), BitVecRef.__mod__(), ArithRef.__mul__(), BitVecRef.__mul__(), FPRef.__mul__(), ExprRef.__ne__(), Probe.__ne__(), ArithRef.__neg__(), BitVecRef.__neg__(), BitVecRef.__or__(), ArithRef.__pow__(), ArithRef.__radd__(), BitVecRef.__radd__(), FPRef.__radd__(), BitVecRef.__rand__(), ArithRef.__rdiv__(), BitVecRef.__rdiv__(), FPRef.__rdiv__(), ParamsRef.__repr__(), ParamDescrsRef.__repr__(), AstMap.__repr__(), Statistics.__repr__(), BitVecRef.__rlshift__(), ArithRef.__rmod__(), BitVecRef.__rmod__(), ArithRef.__rmul__(), BitVecRef.__rmul__(), FPRef.__rmul__(), BitVecRef.__ror__(), ArithRef.__rpow__(), BitVecRef.__rrshift__(), BitVecRef.__rshift__(), ArithRef.__rsub__(), BitVecRef.__rsub__(), FPRef.__rsub__(), BitVecRef.__rxor__(), AstVector.__setitem__(), AstMap.__setitem__(), ArithRef.__sub__(), BitVecRef.__sub__(), FPRef.__sub__(), BitVecRef.__xor__(), DatatypeSortRef.accessor(), Fixedpoint.add_cover(), Fixedpoint.add_rule(), Optimize.add_soft(), Tactic.apply(), AlgebraicNumRef.approx(), ExprRef.arg(), FuncEntry.arg_value(), FuncInterp.arity(), Goal.as_expr(), ApplyResult.as_expr(), FPNumRef.as_string(), Solver.assert_and_track(), Optimize.assert_and_track(), Goal.assert_exprs(), Solver.assert_exprs(), Fixedpoint.assert_exprs(), Optimize.assert_exprs(), Solver.assertions(), Optimize.assertions(), SeqRef.at(), SeqSortRef.basis(), ReSortRef.basis(), QuantifierRef.body(), BoolSortRef.cast(), Solver.check(), Optimize.check(), Solver.consequences(), DatatypeSortRef.constructor(), Goal.convert_model(), AstRef.ctx_ref(), ExprRef.decl(), ModelRef.decls(), ArrayRef.default(), RatNumRef.denominator(), Goal.depth(), Goal.dimacs(), Solver.dimacs(), ArraySortRef.domain(), FuncDeclRef.domain(), FuncInterp.else_value(), FuncInterp.entry(), AstMap.erase(), ModelRef.eval(), FPNumRef.exponent(), FPNumRef.exponent_as_bv(), FPNumRef.exponent_as_long(), Solver.from_file(), Optimize.from_file(), Solver.from_string(), Optimize.from_string(), Goal.get(), Fixedpoint.get_answer(), Fixedpoint.get_assertions(), Fixedpoint.get_cover_delta(), ParamDescrsRef.get_documentation(), Fixedpoint.get_ground_sat_answer(), ModelRef.get_interp(), Statistics.get_key_value(), ParamDescrsRef.get_kind(), ParamDescrsRef.get_name(), Fixedpoint.get_num_levels(), Fixedpoint.get_rule_names_along_trace(), Fixedpoint.get_rules(), Fixedpoint.get_rules_along_trace(), ModelRef.get_sort(), ModelRef.get_universe(), Solver.help(), Fixedpoint.help(), Optimize.help(), Tactic.help(), Solver.import_model_converter(), Goal.inconsistent(), FPNumRef.isInf(), FPNumRef.isNaN(), FPNumRef.isNegative(), FPNumRef.isNormal(), FPNumRef.isPositive(), FPNumRef.isSubnormal(), FPNumRef.isZero(), AstMap.keys(), Statistics.keys(), SortRef.kind(), Optimize.maximize(), Optimize.minimize(), Solver.model(), Optimize.model(), SortRef.name(), FuncDeclRef.name(), QuantifierRef.no_pattern(), Solver.non_units(), FuncEntry.num_args(), FuncInterp.num_entries(), Solver.num_scopes(), ModelRef.num_sorts(), RatNumRef.numerator(), Optimize.objectives(), Solver.param_descrs(), Fixedpoint.param_descrs(), Optimize.param_descrs(), Tactic.param_descrs(), FuncDeclRef.params(), Fixedpoint.parse_file(), Fixedpoint.parse_string(), QuantifierRef.pattern(), Optimize.pop(), Solver.pop(), Goal.prec(), Solver.proof(), Solver.push(), Optimize.push(), AstVector.push(), Fixedpoint.query(), Fixedpoint.query_from_lvl(), FuncDeclRef.range(), ArraySortRef.range(), Solver.reason_unknown(), Fixedpoint.reason_unknown(), Optimize.reason_unknown(), DatatypeSortRef.recognizer(), Context.ref(), Fixedpoint.register_relation(), AstMap.reset(), Solver.reset(), AstVector.resize(), Solver.set(), Fixedpoint.set(), Optimize.set(), ParamsRef.set(), Fixedpoint.set_predicate_representation(), Goal.sexpr(), AstVector.sexpr(), ModelRef.sexpr(), Solver.sexpr(), Fixedpoint.sexpr(), Optimize.sexpr(), ApplyResult.sexpr(), FPNumRef.sign(), FPNumRef.sign_as_bv(), FPNumRef.significand(), FPNumRef.significand_as_bv(), FPNumRef.significand_as_long(), ParamDescrsRef.size(), Goal.size(), Tactic.solver(), ExprRef.sort(), BoolRef.sort(), QuantifierRef.sort(), ArithRef.sort(), BitVecRef.sort(), ArrayRef.sort(), DatatypeRef.sort(), FiniteDomainRef.sort(), FPRef.sort(), SeqRef.sort(), Solver.statistics(), Fixedpoint.statistics(), Optimize.statistics(), Solver.to_smt2(), Fixedpoint.to_string(), Solver.trail(), Solver.trail_levels(), AstVector.translate(), FuncInterp.translate(), AstRef.translate(), Goal.translate(), ModelRef.translate(), Solver.translate(), Solver.units(), Solver.unsat_core(), Optimize.unsat_core(), Fixedpoint.update_rule(), ParamsRef.validate(), FuncEntry.value(), QuantifierRef.var_name(), and QuantifierRef.var_sort().

◆ goal

goal