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 __getitem__ (self, arg)
 
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 1815 of file z3py.py.

Member Function Documentation

◆ __getitem__()

def __getitem__ (   self,
  arg 
)
Return the Z3 expression `self[arg]`.

Definition at line 1872 of file z3py.py.

1872  def __getitem__(self, arg):
1873  """Return the Z3 expression `self[arg]`.
1874  """
1875  if z3_debug():
1876  _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
1877  arg = self.sort().domain().cast(arg)
1878  return _to_expr_ref(Z3_mk_select(self.ctx_ref(), self.as_ast(), arg.as_ast()), self.ctx)
1879 
1880 
def z3_debug()
Definition: z3py.py:58
Z3_ast Z3_API Z3_mk_select(Z3_context c, Z3_ast a, Z3_ast i)
Array read. The argument a is the array and i is the index of the array that gets read.

◆ as_ast()

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

Reimplemented from ExprRef.

Definition at line 1818 of file z3py.py.

1818  def as_ast(self):
1819  return self.ast
1820 

◆ 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 1935 of file z3py.py.

1935  def body(self):
1936  """Return the expression being quantified.
1937 
1938  >>> f = Function('f', IntSort(), IntSort())
1939  >>> x = Int('x')
1940  >>> q = ForAll(x, f(x) == 0)
1941  >>> q.body()
1942  f(Var(0)) == 0
1943  """
1944  return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
1945 
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 1990 of file z3py.py.

1990  def children(self):
1991  """Return a list containing a single element self.body()
1992 
1993  >>> f = Function('f', IntSort(), IntSort())
1994  >>> x = Int('x')
1995  >>> q = ForAll(x, f(x) == 0)
1996  >>> q.children()
1997  [f(Var(0)) == 0]
1998  """
1999  return [ self.body() ]
2000 

◆ 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 1821 of file z3py.py.

1821  def get_id(self):
1822  return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1823 
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 1844 of file z3py.py.

1844  def is_exists(self):
1845  """Return `True` if `self` is an existential quantifier.
1846 
1847  >>> f = Function('f', IntSort(), IntSort())
1848  >>> x = Int('x')
1849  >>> q = ForAll(x, f(x) == 0)
1850  >>> q.is_exists()
1851  False
1852  >>> q = Exists(x, f(x) != 0)
1853  >>> q.is_exists()
1854  True
1855  """
1856  return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
1857 
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 1830 of file z3py.py.

1830  def is_forall(self):
1831  """Return `True` if `self` is a universal quantifier.
1832 
1833  >>> f = Function('f', IntSort(), IntSort())
1834  >>> x = Int('x')
1835  >>> q = ForAll(x, f(x) == 0)
1836  >>> q.is_forall()
1837  True
1838  >>> q = Exists(x, f(x) != 0)
1839  >>> q.is_forall()
1840  False
1841  """
1842  return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
1843 
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 1858 of file z3py.py.

1858  def is_lambda(self):
1859  """Return `True` if `self` is a lambda expression.
1860 
1861  >>> f = Function('f', IntSort(), IntSort())
1862  >>> x = Int('x')
1863  >>> q = Lambda(x, f(x))
1864  >>> q.is_lambda()
1865  True
1866  >>> q = Exists(x, f(x) != 0)
1867  >>> q.is_lambda()
1868  False
1869  """
1870  return Z3_is_lambda(self.ctx_ref(), self.ast)
1871 
bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a)
Determine if ast is a lambda expression.

Referenced by QuantifierRef.__getitem__(), and QuantifierRef.sort().

◆ no_pattern()

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

Definition at line 1929 of file z3py.py.

1929  def no_pattern(self, idx):
1930  """Return a no-pattern."""
1931  if z3_debug():
1932  _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
1933  return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
1934 
Z3_ast Z3_API Z3_get_quantifier_no_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th no_pattern.
def z3_debug()
Definition: z3py.py:58

◆ num_no_patterns()

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

Definition at line 1925 of file z3py.py.

1925  def num_no_patterns(self):
1926  """Return the number of no-patterns."""
1927  return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
1928 
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 1895 of file z3py.py.

1895  def num_patterns(self):
1896  """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
1897 
1898  >>> f = Function('f', IntSort(), IntSort())
1899  >>> g = Function('g', IntSort(), IntSort())
1900  >>> x = Int('x')
1901  >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
1902  >>> q.num_patterns()
1903  2
1904  """
1905  return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
1906 
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 1946 of file z3py.py.

1946  def num_vars(self):
1947  """Return the number of variables bounded by this quantifier.
1948 
1949  >>> f = Function('f', IntSort(), IntSort(), IntSort())
1950  >>> x = Int('x')
1951  >>> y = Int('y')
1952  >>> q = ForAll([x, y], f(x, y) >= x)
1953  >>> q.num_vars()
1954  2
1955  """
1956  return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
1957 
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 1907 of file z3py.py.

1907  def pattern(self, idx):
1908  """Return a pattern (i.e., quantifier instantiation hints) in `self`.
1909 
1910  >>> f = Function('f', IntSort(), IntSort())
1911  >>> g = Function('g', IntSort(), IntSort())
1912  >>> x = Int('x')
1913  >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
1914  >>> q.num_patterns()
1915  2
1916  >>> q.pattern(0)
1917  f(Var(0))
1918  >>> q.pattern(1)
1919  g(Var(0))
1920  """
1921  if z3_debug():
1922  _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
1923  return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
1924 
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.
def z3_debug()
Definition: z3py.py:58

◆ sort()

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

Reimplemented from BoolRef.

Definition at line 1824 of file z3py.py.

1824  def sort(self):
1825  """Return the Boolean sort or sort of Lambda."""
1826  if self.is_lambda():
1827  return _sort(self.ctx, self.as_ast())
1828  return BoolSort(self.ctx)
1829 
def BoolSort(ctx=None)
Definition: z3py.py:1535

◆ 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 1958 of file z3py.py.

1958  def var_name(self, idx):
1959  """Return a string representing a name used when displaying the quantifier.
1960 
1961  >>> f = Function('f', IntSort(), IntSort(), IntSort())
1962  >>> x = Int('x')
1963  >>> y = Int('y')
1964  >>> q = ForAll([x, y], f(x, y) >= x)
1965  >>> q.var_name(0)
1966  'x'
1967  >>> q.var_name(1)
1968  'y'
1969  """
1970  if z3_debug():
1971  _z3_assert(idx < self.num_vars(), "Invalid variable idx")
1972  return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
1973 
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.
def z3_debug()
Definition: z3py.py:58

◆ 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 1974 of file z3py.py.

1974  def var_sort(self, idx):
1975  """Return the sort of a bound variable.
1976 
1977  >>> f = Function('f', IntSort(), RealSort(), IntSort())
1978  >>> x = Int('x')
1979  >>> y = Real('y')
1980  >>> q = ForAll([x, y], f(x, y) >= x)
1981  >>> q.var_sort(0)
1982  Int
1983  >>> q.var_sort(1)
1984  Real
1985  """
1986  if z3_debug():
1987  _z3_assert(idx < self.num_vars(), "Invalid variable idx")
1988  return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
1989 
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.
def z3_debug()
Definition: z3py.py:58

◆ 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 1881 of file z3py.py.

1881  def weight(self):
1882  """Return the weight annotation of `self`.
1883 
1884  >>> f = Function('f', IntSort(), IntSort())
1885  >>> x = Int('x')
1886  >>> q = ForAll(x, f(x) == 0)
1887  >>> q.weight()
1888  1
1889  >>> q = ForAll(x, f(x) == 0, weight=10)
1890  >>> q.weight()
1891  10
1892  """
1893  return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
1894 
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.