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Goal Class Reference
Inheritance diagram for Goal:

Public Member Functions

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

Data Fields

 ctx = _get_ctx(ctx)
 goal = goal

Additional Inherited Members

Protected Member Functions inherited from Z3PPObject
 _repr_html_ (self)

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 5637 of file z3py.py.

Constructor & Destructor Documentation

◆ __init__()

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

Definition at line 5645 of file z3py.py.

5645 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5646 if z3_debug():
5647 _z3_assert(goal is None or ctx is not None,
5648 "If goal is different from None, then ctx must be also different from None")
5649 self.ctx = _get_ctx(ctx)
5650 self.goal = goal
5651 if self.goal is None:
5652 self.goal = Z3_mk_goal(self.ctx.ref(), models, unsat_cores, proofs)
5653 Z3_goal_inc_ref(self.ctx.ref(), self.goal)
5654
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__()

__del__ ( self)

Definition at line 5655 of file z3py.py.

5655 def __del__(self):
5656 if self.goal is not None and self.ctx.ref() is not None and Z3_goal_dec_ref is not None:
5657 Z3_goal_dec_ref(self.ctx.ref(), self.goal)
5658
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__()

__copy__ ( self)

Definition at line 5890 of file z3py.py.

5890 def __copy__(self):
5891 return self.translate(self.ctx)
5892

◆ __deepcopy__()

__deepcopy__ ( self,
memo = {} )

Definition at line 5893 of file z3py.py.

5893 def __deepcopy__(self, memo={}):
5894 return self.translate(self.ctx)
5895

◆ __getitem__()

__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 5764 of file z3py.py.

5764 def __getitem__(self, arg):
5765 """Return a constraint in the goal `self`.
5766
5767 >>> g = Goal()
5768 >>> x, y = Ints('x y')
5769 >>> g.add(x == 0, y > x)
5770 >>> g[0]
5771 x == 0
5772 >>> g[1]
5773 y > x
5774 """
5775 if arg >= len(self):
5776 raise IndexError
5777 return self.get(arg)
5778

◆ __len__()

__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 5738 of file z3py.py.

5738 def __len__(self):
5739 """Return the number of constraints in the goal `self`.
5740
5741 >>> g = Goal()
5742 >>> len(g)
5743 0
5744 >>> x, y = Ints('x y')
5745 >>> g.add(x == 0, y > x)
5746 >>> len(g)
5747 2
5748 """
5749 return self.size()
5750

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

◆ __repr__()

__repr__ ( self)

Definition at line 5856 of file z3py.py.

5856 def __repr__(self):
5857 return obj_to_string(self)
5858

◆ add()

add ( self,
* args )
Add constraints.

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

Definition at line 5816 of file z3py.py.

5816 def add(self, *args):
5817 """Add constraints.
5818
5819 >>> x = Int('x')
5820 >>> g = Goal()
5821 >>> g.add(x > 0, x < 2)
5822 >>> g
5823 [x > 0, x < 2]
5824 """
5825 self.assert_exprs(*args)
5826

Referenced by Solver.__iadd__().

◆ append()

append ( self,
* args )
Add constraints.

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

Definition at line 5794 of file z3py.py.

5794 def append(self, *args):
5795 """Add constraints.
5796
5797 >>> x = Int('x')
5798 >>> g = Goal()
5799 >>> g.append(x > 0, x < 2)
5800 >>> g
5801 [x > 0, x < 2]
5802 """
5803 self.assert_exprs(*args)
5804

◆ as_expr()

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 5916 of file z3py.py.

5916 def as_expr(self):
5917 """Return goal `self` as a single Z3 expression.
5918
5919 >>> x = Int('x')
5920 >>> g = Goal()
5921 >>> g.as_expr()
5922 True
5923 >>> g.add(x > 1)
5924 >>> g.as_expr()
5925 x > 1
5926 >>> g.add(x < 10)
5927 >>> g.as_expr()
5928 And(x > 1, x < 10)
5929 """
5930 sz = len(self)
5931 if sz == 0:
5932 return BoolVal(True, self.ctx)
5933 elif sz == 1:
5934 return self.get(0)
5935 else:
5936 return And([self.get(i) for i in range(len(self))], self.ctx)
5937

◆ assert_exprs()

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 5779 of file z3py.py.

5779 def assert_exprs(self, *args):
5780 """Assert constraints into the goal.
5781
5782 >>> x = Int('x')
5783 >>> g = Goal()
5784 >>> g.assert_exprs(x > 0, x < 2)
5785 >>> g
5786 [x > 0, x < 2]
5787 """
5788 args = _get_args(args)
5789 s = BoolSort(self.ctx)
5790 for arg in args:
5791 arg = s.cast(arg)
5792 Z3_goal_assert(self.ctx.ref(), self.goal, arg.as_ast())
5793
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 add(), Solver.add(), append(), Solver.append(), insert(), and Solver.insert().

◆ convert_model()

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 5827 of file z3py.py.

5827 def convert_model(self, model):
5828 """Retrieve model from a satisfiable goal
5829 >>> a, b = Ints('a b')
5830 >>> g = Goal()
5831 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
5832 >>> t = Then(Tactic('split-clause'), Tactic('solve-eqs'))
5833 >>> r = t(g)
5834 >>> r[0]
5835 [Or(b == 0, b == 1), Not(0 <= b)]
5836 >>> r[1]
5837 [Or(b == 0, b == 1), Not(1 <= b)]
5838 >>> # Remark: the subgoal r[0] is unsatisfiable
5839 >>> # Creating a solver for solving the second subgoal
5840 >>> s = Solver()
5841 >>> s.add(r[1])
5842 >>> s.check()
5843 sat
5844 >>> s.model()
5845 [b = 0]
5846 >>> # Model s.model() does not assign a value to `a`
5847 >>> # It is a model for subgoal `r[1]`, but not for goal `g`
5848 >>> # The method convert_model creates a model for `g` from a model for `r[1]`.
5849 >>> r[1].convert_model(s.model())
5850 [b = 0, a = 1]
5851 """
5852 if z3_debug():
5853 _z3_assert(isinstance(model, ModelRef), "Z3 Model expected")
5854 return ModelRef(Z3_goal_convert_model(self.ctx.ref(), self.goal, model.model), self.ctx)
5855
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,...

◆ depth()

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 5659 of file z3py.py.

5659 def depth(self):
5660 """Return the depth of the goal `self`.
5661 The depth corresponds to the number of tactics applied to `self`.
5662
5663 >>> x, y = Ints('x y')
5664 >>> g = Goal()
5665 >>> g.add(x == 0, y >= x + 1)
5666 >>> g.depth()
5667 0
5668 >>> r = Then('simplify', 'solve-eqs')(g)
5669 >>> # r has 1 subgoal
5670 >>> len(r)
5671 1
5672 >>> r[0].depth()
5673 2
5674 """
5675 return int(Z3_goal_depth(self.ctx.ref(), self.goal))
5676
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.

◆ dimacs()

dimacs ( self,
include_names = True )
Return a textual representation of the goal in DIMACS format.

Definition at line 5863 of file z3py.py.

5863 def dimacs(self, include_names=True):
5864 """Return a textual representation of the goal in DIMACS format."""
5865 return Z3_goal_to_dimacs_string(self.ctx.ref(), self.goal, include_names)
5866
Z3_string Z3_API Z3_goal_to_dimacs_string(Z3_context c, Z3_goal g, bool include_names)
Convert a goal into a DIMACS formatted string. The goal must be in CNF. You can convert a goal to CNF...

◆ get()

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 5751 of file z3py.py.

5751 def get(self, i):
5752 """Return a constraint in the goal `self`.
5753
5754 >>> g = Goal()
5755 >>> x, y = Ints('x y')
5756 >>> g.add(x == 0, y > x)
5757 >>> g.get(0)
5758 x == 0
5759 >>> g.get(1)
5760 y > x
5761 """
5762 return _to_expr_ref(Z3_goal_formula(self.ctx.ref(), self.goal, i), self.ctx)
5763
Z3_ast Z3_API Z3_goal_formula(Z3_context c, Z3_goal g, unsigned idx)
Return a formula from the given goal.

Referenced by __getitem__(), and as_expr().

◆ inconsistent()

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 5677 of file z3py.py.

5677 def inconsistent(self):
5678 """Return `True` if `self` contains the `False` constraints.
5679
5680 >>> x, y = Ints('x y')
5681 >>> g = Goal()
5682 >>> g.inconsistent()
5683 False
5684 >>> g.add(x == 0, x == 1)
5685 >>> g
5686 [x == 0, x == 1]
5687 >>> g.inconsistent()
5688 False
5689 >>> g2 = Tactic('propagate-values')(g)[0]
5690 >>> g2.inconsistent()
5691 True
5692 """
5693 return Z3_goal_inconsistent(self.ctx.ref(), self.goal)
5694
bool Z3_API Z3_goal_inconsistent(Z3_context c, Z3_goal g)
Return true if the given goal contains the formula false.

◆ insert()

insert ( self,
* args )
Add constraints.

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

Definition at line 5805 of file z3py.py.

5805 def insert(self, *args):
5806 """Add constraints.
5807
5808 >>> x = Int('x')
5809 >>> g = Goal()
5810 >>> g.insert(x > 0, x < 2)
5811 >>> g
5812 [x > 0, x < 2]
5813 """
5814 self.assert_exprs(*args)
5815

◆ prec()

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 5695 of file z3py.py.

5695 def prec(self):
5696 """Return the precision (under-approximation, over-approximation, or precise) of the goal `self`.
5697
5698 >>> g = Goal()
5699 >>> g.prec() == Z3_GOAL_PRECISE
5700 True
5701 >>> x, y = Ints('x y')
5702 >>> g.add(x == y + 1)
5703 >>> g.prec() == Z3_GOAL_PRECISE
5704 True
5705 >>> t = With(Tactic('add-bounds'), add_bound_lower=0, add_bound_upper=10)
5706 >>> g2 = t(g)[0]
5707 >>> g2
5708 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5709 >>> g2.prec() == Z3_GOAL_PRECISE
5710 False
5711 >>> g2.prec() == Z3_GOAL_UNDER
5712 True
5713 """
5714 return Z3_goal_precision(self.ctx.ref(), self.goal)
5715
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 precision().

◆ precision()

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

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

Definition at line 5716 of file z3py.py.

5716 def precision(self):
5717 """Alias for `prec()`.
5718
5719 >>> g = Goal()
5720 >>> g.precision() == Z3_GOAL_PRECISE
5721 True
5722 """
5723 return self.prec()
5724

◆ sexpr()

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

Definition at line 5859 of file z3py.py.

5859 def sexpr(self):
5860 """Return a textual representation of the s-expression representing the goal."""
5861 return Z3_goal_to_string(self.ctx.ref(), self.goal)
5862
Z3_string Z3_API Z3_goal_to_string(Z3_context c, Z3_goal g)
Convert a goal into a string.

◆ simplify()

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 5896 of file z3py.py.

5896 def simplify(self, *arguments, **keywords):
5897 """Return a new simplified goal.
5898
5899 This method is essentially invoking the simplify tactic.
5900
5901 >>> g = Goal()
5902 >>> x = Int('x')
5903 >>> g.add(x + 1 >= 2)
5904 >>> g
5905 [x + 1 >= 2]
5906 >>> g2 = g.simplify()
5907 >>> g2
5908 [x >= 1]
5909 >>> # g was not modified
5910 >>> g
5911 [x + 1 >= 2]
5912 """
5913 t = Tactic("simplify")
5914 return t.apply(self, *arguments, **keywords)[0]
5915

◆ size()

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 5725 of file z3py.py.

5725 def size(self):
5726 """Return the number of constraints in the goal `self`.
5727
5728 >>> g = Goal()
5729 >>> g.size()
5730 0
5731 >>> x, y = Ints('x y')
5732 >>> g.add(x == 0, y > x)
5733 >>> g.size()
5734 2
5735 """
5736 return int(Z3_goal_size(self.ctx.ref(), self.goal))
5737
unsigned Z3_API Z3_goal_size(Z3_context c, Z3_goal g)
Return the number of formulas in the given goal.

Referenced by __len__().

◆ translate()

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 5867 of file z3py.py.

5867 def translate(self, target):
5868 """Copy goal `self` to context `target`.
5869
5870 >>> x = Int('x')
5871 >>> g = Goal()
5872 >>> g.add(x > 10)
5873 >>> g
5874 [x > 10]
5875 >>> c2 = Context()
5876 >>> g2 = g.translate(c2)
5877 >>> g2
5878 [x > 10]
5879 >>> g.ctx == main_ctx()
5880 True
5881 >>> g2.ctx == c2
5882 True
5883 >>> g2.ctx == main_ctx()
5884 False
5885 """
5886 if z3_debug():
5887 _z3_assert(isinstance(target, Context), "target must be a context")
5888 return Goal(goal=Z3_goal_translate(self.ctx.ref(), self.goal, target.ref()), ctx=target)
5889
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 AstVector.__copy__(), FuncInterp.__copy__(), __copy__(), ModelRef.__copy__(), AstVector.__deepcopy__(), FuncInterp.__deepcopy__(), __deepcopy__(), and ModelRef.__deepcopy__().

Field Documentation

◆ ctx

ctx = _get_ctx(ctx)

Definition at line 5649 of file z3py.py.

Referenced by AstMap.__contains__(), AstVector.__copy__(), FuncInterp.__copy__(), __copy__(), ModelRef.__copy__(), AstMap.__deepcopy__(), AstVector.__deepcopy__(), FuncEntry.__deepcopy__(), FuncInterp.__deepcopy__(), __deepcopy__(), ModelRef.__deepcopy__(), Statistics.__deepcopy__(), AstMap.__del__(), AstVector.__del__(), FuncEntry.__del__(), FuncInterp.__del__(), __del__(), ModelRef.__del__(), Solver.__del__(), Statistics.__del__(), AstMap.__getitem__(), AstVector.__getitem__(), ModelRef.__getitem__(), Statistics.__getitem__(), AstMap.__len__(), AstVector.__len__(), ModelRef.__len__(), Statistics.__len__(), AstMap.__repr__(), Statistics.__repr__(), AstMap.__setitem__(), AstVector.__setitem__(), FuncEntry.arg_value(), FuncInterp.arity(), as_expr(), Solver.assert_and_track(), assert_exprs(), Solver.assert_exprs(), Solver.check(), convert_model(), ModelRef.decls(), depth(), dimacs(), FuncInterp.else_value(), FuncInterp.entry(), AstMap.erase(), ModelRef.eval(), get(), ModelRef.get_interp(), Statistics.get_key_value(), ModelRef.get_sort(), ModelRef.get_universe(), inconsistent(), AstMap.keys(), Statistics.keys(), Solver.model(), FuncEntry.num_args(), FuncInterp.num_entries(), Solver.num_scopes(), ModelRef.num_sorts(), Solver.pop(), prec(), ModelRef.project(), ModelRef.project_with_witness(), AstVector.push(), Solver.push(), AstMap.reset(), Solver.reset(), AstVector.resize(), Solver.set(), AstVector.sexpr(), sexpr(), ModelRef.sexpr(), size(), AstVector.translate(), translate(), ModelRef.translate(), and FuncEntry.value().

◆ goal

goal = goal