Z3
Public Member Functions
QuantifierRef Class Reference

Quantifiers. More...

+ Inheritance diagram for QuantifierRef:

Public Member Functions

def as_ast (self)
 
def get_id (self)
 
def sort (self)
 
def is_forall (self)
 
def is_exists (self)
 
def is_lambda (self)
 
def weight (self)
 
def num_patterns (self)
 
def pattern (self, idx)
 
def num_no_patterns (self)
 
def no_pattern (self, idx)
 
def body (self)
 
def num_vars (self)
 
def var_name (self, idx)
 
def var_sort (self, idx)
 
def children (self)
 
- Public Member Functions inherited from BoolRef
def __rmul__ (self, other)
 
def __mul__ (self, other)
 
- Public Member Functions inherited from ExprRef
def sort_kind (self)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 
def params (self)
 
def decl (self)
 
def num_args (self)
 
def arg (self, idx)
 
- Public Member Functions inherited from AstRef
def __init__ (self, ast, ctx=None)
 
def __del__ (self)
 
def __deepcopy__ (self, memo={})
 
def __str__ (self)
 
def __repr__ (self)
 
def __nonzero__ (self)
 
def __bool__ (self)
 
def sexpr (self)
 
def ctx_ref (self)
 
def eq (self, other)
 
def translate (self, target)
 
def __copy__ (self)
 
def hash (self)
 
- Public Member Functions inherited from Z3PPObject
def use_pp (self)
 

Additional Inherited Members

- Data Fields inherited from AstRef
 ast
 
 ctx
 

Detailed Description

Quantifiers.

Universally and Existentially quantified formulas.

Definition at line 1792 of file z3py.py.

Member Function Documentation

◆ as_ast()

def as_ast (   self)
Return a pointer to the corresponding C Z3_ast object.

Reimplemented from ExprRef.

Definition at line 1795 of file z3py.py.

1795  def as_ast(self):
1796  return self.ast
1797 

◆ body()

def body (   self)
Return the expression being quantified.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.body()
f(Var(0)) == 0

Definition at line 1903 of file z3py.py.

1903  def body(self):
1904  """Return the expression being quantified.
1905 
1906  >>> f = Function('f', IntSort(), IntSort())
1907  >>> x = Int('x')
1908  >>> q = ForAll(x, f(x) == 0)
1909  >>> q.body()
1910  f(Var(0)) == 0
1911  """
1912  return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
1913 
Z3_ast Z3_API Z3_get_quantifier_body(Z3_context c, Z3_ast a)
Return body of quantifier.

Referenced by QuantifierRef.children().

◆ children()

def children (   self)
Return a list containing a single element self.body()

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.children()
[f(Var(0)) == 0]

Reimplemented from ExprRef.

Definition at line 1958 of file z3py.py.

1958  def children(self):
1959  """Return a list containing a single element self.body()
1960 
1961  >>> f = Function('f', IntSort(), IntSort())
1962  >>> x = Int('x')
1963  >>> q = ForAll(x, f(x) == 0)
1964  >>> q.children()
1965  [f(Var(0)) == 0]
1966  """
1967  return [ self.body() ]
1968 

◆ get_id()

def get_id (   self)
Return unique identifier for object. It can be used for hash-tables and maps.

Reimplemented from ExprRef.

Definition at line 1798 of file z3py.py.

1798  def get_id(self):
1799  return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1800 
unsigned Z3_API Z3_get_ast_id(Z3_context c, Z3_ast t)
Return a unique identifier for t. The identifier is unique up to structural equality....

◆ is_exists()

def is_exists (   self)
Return `True` if `self` is an existential quantifier.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.is_exists()
False
>>> q = Exists(x, f(x) != 0)
>>> q.is_exists()
True

Definition at line 1821 of file z3py.py.

1821  def is_exists(self):
1822  """Return `True` if `self` is an existential quantifier.
1823 
1824  >>> f = Function('f', IntSort(), IntSort())
1825  >>> x = Int('x')
1826  >>> q = ForAll(x, f(x) == 0)
1827  >>> q.is_exists()
1828  False
1829  >>> q = Exists(x, f(x) != 0)
1830  >>> q.is_exists()
1831  True
1832  """
1833  return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
1834 
bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a)
Determine if ast is an existential quantifier.

◆ is_forall()

def is_forall (   self)
Return `True` if `self` is a universal quantifier.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.is_forall()
True
>>> q = Exists(x, f(x) != 0)
>>> q.is_forall()
False

Definition at line 1807 of file z3py.py.

1807  def is_forall(self):
1808  """Return `True` if `self` is a universal quantifier.
1809 
1810  >>> f = Function('f', IntSort(), IntSort())
1811  >>> x = Int('x')
1812  >>> q = ForAll(x, f(x) == 0)
1813  >>> q.is_forall()
1814  True
1815  >>> q = Exists(x, f(x) != 0)
1816  >>> q.is_forall()
1817  False
1818  """
1819  return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
1820 
bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a)
Determine if an ast is a universal quantifier.

◆ is_lambda()

def is_lambda (   self)
Return `True` if `self` is a lambda expression.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = Lambda(x, f(x))
>>> q.is_lambda()
True
>>> q = Exists(x, f(x) != 0)
>>> q.is_lambda()
False

Definition at line 1835 of file z3py.py.

1835  def is_lambda(self):
1836  """Return `True` if `self` is a lambda expression.
1837 
1838  >>> f = Function('f', IntSort(), IntSort())
1839  >>> x = Int('x')
1840  >>> q = Lambda(x, f(x))
1841  >>> q.is_lambda()
1842  True
1843  >>> q = Exists(x, f(x) != 0)
1844  >>> q.is_lambda()
1845  False
1846  """
1847  return Z3_is_lambda(self.ctx_ref(), self.ast)
1848 
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.

Referenced by QuantifierRef.sort().

◆ no_pattern()

def no_pattern (   self,
  idx 
)
Return a no-pattern.

Definition at line 1897 of file z3py.py.

1897  def no_pattern(self, idx):
1898  """Return a no-pattern."""
1899  if __debug__:
1900  _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
1901  return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
1902 
Z3_ast Z3_API Z3_get_quantifier_no_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th no_pattern.

◆ num_no_patterns()

def num_no_patterns (   self)
Return the number of no-patterns.

Definition at line 1893 of file z3py.py.

1893  def num_no_patterns(self):
1894  """Return the number of no-patterns."""
1895  return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
1896 
unsigned Z3_API Z3_get_quantifier_num_no_patterns(Z3_context c, Z3_ast a)
Return number of no_patterns used in quantifier.

Referenced by QuantifierRef.no_pattern().

◆ num_patterns()

def num_patterns (   self)
Return the number of patterns (i.e., quantifier instantiation hints) in `self`.

>>> f = Function('f', IntSort(), IntSort())
>>> g = Function('g', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
>>> q.num_patterns()
2

Definition at line 1863 of file z3py.py.

1863  def num_patterns(self):
1864  """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
1865 
1866  >>> f = Function('f', IntSort(), IntSort())
1867  >>> g = Function('g', IntSort(), IntSort())
1868  >>> x = Int('x')
1869  >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
1870  >>> q.num_patterns()
1871  2
1872  """
1873  return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
1874 
unsigned Z3_API Z3_get_quantifier_num_patterns(Z3_context c, Z3_ast a)
Return number of patterns used in quantifier.

Referenced by QuantifierRef.pattern().

◆ num_vars()

def num_vars (   self)
Return the number of variables bounded by this quantifier.

>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> x = Int('x')
>>> y = Int('y')
>>> q = ForAll([x, y], f(x, y) >= x)
>>> q.num_vars()
2

Definition at line 1914 of file z3py.py.

1914  def num_vars(self):
1915  """Return the number of variables bounded by this quantifier.
1916 
1917  >>> f = Function('f', IntSort(), IntSort(), IntSort())
1918  >>> x = Int('x')
1919  >>> y = Int('y')
1920  >>> q = ForAll([x, y], f(x, y) >= x)
1921  >>> q.num_vars()
1922  2
1923  """
1924  return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
1925 
unsigned Z3_API Z3_get_quantifier_num_bound(Z3_context c, Z3_ast a)
Return number of bound variables of quantifier.

Referenced by QuantifierRef.var_name(), and QuantifierRef.var_sort().

◆ pattern()

def pattern (   self,
  idx 
)
Return a pattern (i.e., quantifier instantiation hints) in `self`.

>>> f = Function('f', IntSort(), IntSort())
>>> g = Function('g', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
>>> q.num_patterns()
2
>>> q.pattern(0)
f(Var(0))
>>> q.pattern(1)
g(Var(0))

Definition at line 1875 of file z3py.py.

1875  def pattern(self, idx):
1876  """Return a pattern (i.e., quantifier instantiation hints) in `self`.
1877 
1878  >>> f = Function('f', IntSort(), IntSort())
1879  >>> g = Function('g', IntSort(), IntSort())
1880  >>> x = Int('x')
1881  >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
1882  >>> q.num_patterns()
1883  2
1884  >>> q.pattern(0)
1885  f(Var(0))
1886  >>> q.pattern(1)
1887  g(Var(0))
1888  """
1889  if __debug__:
1890  _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
1891  return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
1892 
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.

◆ sort()

def sort (   self)
Return the Boolean sort or sort of Lambda.

Reimplemented from BoolRef.

Definition at line 1801 of file z3py.py.

1801  def sort(self):
1802  """Return the Boolean sort or sort of Lambda."""
1803  if self.is_lambda():
1804  return _sort(self.ctx, self.as_ast())
1805  return BoolSort(self.ctx)
1806 
def BoolSort(ctx=None)
Definition: z3py.py:1512

◆ var_name()

def var_name (   self,
  idx 
)
Return a string representing a name used when displaying the quantifier.

>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> x = Int('x')
>>> y = Int('y')
>>> q = ForAll([x, y], f(x, y) >= x)
>>> q.var_name(0)
'x'
>>> q.var_name(1)
'y'

Definition at line 1926 of file z3py.py.

1926  def var_name(self, idx):
1927  """Return a string representing a name used when displaying the quantifier.
1928 
1929  >>> f = Function('f', IntSort(), IntSort(), IntSort())
1930  >>> x = Int('x')
1931  >>> y = Int('y')
1932  >>> q = ForAll([x, y], f(x, y) >= x)
1933  >>> q.var_name(0)
1934  'x'
1935  >>> q.var_name(1)
1936  'y'
1937  """
1938  if __debug__:
1939  _z3_assert(idx < self.num_vars(), "Invalid variable idx")
1940  return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
1941 
Z3_symbol Z3_API Z3_get_quantifier_bound_name(Z3_context c, Z3_ast a, unsigned i)
Return symbol of the i'th bound variable.

◆ var_sort()

def var_sort (   self,
  idx 
)
Return the sort of a bound variable.

>>> f = Function('f', IntSort(), RealSort(), IntSort())
>>> x = Int('x')
>>> y = Real('y')
>>> q = ForAll([x, y], f(x, y) >= x)
>>> q.var_sort(0)
Int
>>> q.var_sort(1)
Real

Definition at line 1942 of file z3py.py.

1942  def var_sort(self, idx):
1943  """Return the sort of a bound variable.
1944 
1945  >>> f = Function('f', IntSort(), RealSort(), IntSort())
1946  >>> x = Int('x')
1947  >>> y = Real('y')
1948  >>> q = ForAll([x, y], f(x, y) >= x)
1949  >>> q.var_sort(0)
1950  Int
1951  >>> q.var_sort(1)
1952  Real
1953  """
1954  if __debug__:
1955  _z3_assert(idx < self.num_vars(), "Invalid variable idx")
1956  return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
1957 
Z3_sort Z3_API Z3_get_quantifier_bound_sort(Z3_context c, Z3_ast a, unsigned i)
Return sort of the i'th bound variable.

◆ weight()

def weight (   self)
Return the weight annotation of `self`.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> q.weight()
1
>>> q = ForAll(x, f(x) == 0, weight=10)
>>> q.weight()
10

Definition at line 1849 of file z3py.py.

1849  def weight(self):
1850  """Return the weight annotation of `self`.
1851 
1852  >>> f = Function('f', IntSort(), IntSort())
1853  >>> x = Int('x')
1854  >>> q = ForAll(x, f(x) == 0)
1855  >>> q.weight()
1856  1
1857  >>> q = ForAll(x, f(x) == 0, weight=10)
1858  >>> q.weight()
1859  10
1860  """
1861  return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
1862 
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.