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 sort (self)
 
def __rmul__ (self, other)
 
def __mul__ (self, other)
 
- Public Member Functions inherited from ExprRef
def as_ast (self)
 
def get_id (self)
 
def sort (self)
 
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)
 
def children (self)
 
- 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 __eq__ (self, other)
 
def __hash__ (self)
 
def __nonzero__ (self)
 
def __bool__ (self)
 
def sexpr (self)
 
def as_ast (self)
 
def get_id (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 1811 of file z3py.py.

Member Function Documentation

◆ __getitem__()

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

Definition at line 1868 of file z3py.py.

1868 def __getitem__(self, arg):
1869 """Return the Z3 expression `self[arg]`.
1870 """
1871 if z3_debug():
1872 _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
1873 arg = self.sort().domain().cast(arg)
1874 return _to_expr_ref(Z3_mk_select(self.ctx_ref(), self.as_ast(), arg.as_ast()), self.ctx)
1875
1876
def z3_debug()
Definition: z3py.py:56
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 1814 of file z3py.py.

1814 def as_ast(self):
1815 return self.ast
1816

Referenced by AstRef.__del__(), SeqRef.__ge__(), QuantifierRef.__getitem__(), ArrayRef.__getitem__(), SeqRef.__getitem__(), SeqRef.__gt__(), BitVecRef.__invert__(), SeqRef.__le__(), SeqRef.__lt__(), ArithRef.__neg__(), BitVecRef.__neg__(), AlgebraicNumRef.approx(), ExprRef.arg(), RatNumRef.as_decimal(), AlgebraicNumRef.as_decimal(), IntNumRef.as_string(), RatNumRef.as_string(), BitVecNumRef.as_string(), FiniteDomainRef.as_string(), FiniteDomainNumRef.as_string(), FPRef.as_string(), FPRMRef.as_string(), FPNumRef.as_string(), SeqRef.as_string(), SeqRef.at(), ExprRef.decl(), ArrayRef.default(), RatNumRef.denominator(), AstRef.eq(), FPNumRef.exponent(), FPNumRef.exponent_as_bv(), FPNumRef.exponent_as_long(), AstRef.get_id(), SortRef.get_id(), FuncDeclRef.get_id(), ExprRef.get_id(), PatternRef.get_id(), QuantifierRef.get_id(), AstRef.hash(), SeqRef.is_string(), SeqRef.is_string_value(), FPNumRef.isInf(), FPNumRef.isNaN(), FPNumRef.isNegative(), FPNumRef.isNormal(), FPNumRef.isPositive(), FPNumRef.isSubnormal(), FPNumRef.isZero(), ExprRef.num_args(), RatNumRef.numerator(), AstRef.sexpr(), FPNumRef.sign(), FPNumRef.sign_as_bv(), FPNumRef.significand(), FPNumRef.significand_as_bv(), FPNumRef.significand_as_long(), ExprRef.sort(), BoolRef.sort(), QuantifierRef.sort(), ArithRef.sort(), BitVecRef.sort(), ArrayRef.sort(), DatatypeRef.sort(), FiniteDomainRef.sort(), FPRef.sort(), SeqRef.sort(), and AstRef.translate().

◆ 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 1931 of file z3py.py.

1931 def body(self):
1932 """Return the expression being quantified.
1933
1934 >>> f = Function('f', IntSort(), IntSort())
1935 >>> x = Int('x')
1936 >>> q = ForAll(x, f(x) == 0)
1937 >>> q.body()
1938 f(Var(0)) == 0
1939 """
1940 return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
1941
def IntSort(ctx=None)
Definition: z3py.py:2907
def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
Definition: z3py.py:2044
def Function(name, *sig)
Definition: z3py.py:799
def Var(idx, s)
Definition: z3py.py:1331
def Int(name, ctx=None)
Definition: z3py.py:3010
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 1986 of file z3py.py.

1986 def children(self):
1987 """Return a list containing a single element self.body()
1988
1989 >>> f = Function('f', IntSort(), IntSort())
1990 >>> x = Int('x')
1991 >>> q = ForAll(x, f(x) == 0)
1992 >>> q.children()
1993 [f(Var(0)) == 0]
1994 """
1995 return [ self.body() ]
1996

◆ 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 1817 of file z3py.py.

1817 def get_id(self):
1818 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1819
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 1840 of file z3py.py.

1840 def is_exists(self):
1841 """Return `True` if `self` is an existential quantifier.
1842
1843 >>> f = Function('f', IntSort(), IntSort())
1844 >>> x = Int('x')
1845 >>> q = ForAll(x, f(x) == 0)
1846 >>> q.is_exists()
1847 False
1848 >>> q = Exists(x, f(x) != 0)
1849 >>> q.is_exists()
1850 True
1851 """
1852 return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
1853
def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
Definition: z3py.py:2061
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 1826 of file z3py.py.

1826 def is_forall(self):
1827 """Return `True` if `self` is a universal quantifier.
1828
1829 >>> f = Function('f', IntSort(), IntSort())
1830 >>> x = Int('x')
1831 >>> q = ForAll(x, f(x) == 0)
1832 >>> q.is_forall()
1833 True
1834 >>> q = Exists(x, f(x) != 0)
1835 >>> q.is_forall()
1836 False
1837 """
1838 return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
1839
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 1854 of file z3py.py.

1854 def is_lambda(self):
1855 """Return `True` if `self` is a lambda expression.
1856
1857 >>> f = Function('f', IntSort(), IntSort())
1858 >>> x = Int('x')
1859 >>> q = Lambda(x, f(x))
1860 >>> q.is_lambda()
1861 True
1862 >>> q = Exists(x, f(x) != 0)
1863 >>> q.is_lambda()
1864 False
1865 """
1866 return Z3_is_lambda(self.ctx_ref(), self.ast)
1867
def Lambda(vs, body)
Definition: z3py.py:2081
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 1925 of file z3py.py.

1925 def no_pattern(self, idx):
1926 """Return a no-pattern."""
1927 if z3_debug():
1928 _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
1929 return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
1930
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 1921 of file z3py.py.

1921 def num_no_patterns(self):
1922 """Return the number of no-patterns."""
1923 return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
1924
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 1891 of file z3py.py.

1891 def num_patterns(self):
1892 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
1893
1894 >>> f = Function('f', IntSort(), IntSort())
1895 >>> g = Function('g', IntSort(), IntSort())
1896 >>> x = Int('x')
1897 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
1898 >>> q.num_patterns()
1899 2
1900 """
1901 return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
1902
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 1942 of file z3py.py.

1942 def num_vars(self):
1943 """Return the number of variables bounded by this quantifier.
1944
1945 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1946 >>> x = Int('x')
1947 >>> y = Int('y')
1948 >>> q = ForAll([x, y], f(x, y) >= x)
1949 >>> q.num_vars()
1950 2
1951 """
1952 return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
1953
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 1903 of file z3py.py.

1903 def pattern(self, idx):
1904 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
1905
1906 >>> f = Function('f', IntSort(), IntSort())
1907 >>> g = Function('g', IntSort(), IntSort())
1908 >>> x = Int('x')
1909 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
1910 >>> q.num_patterns()
1911 2
1912 >>> q.pattern(0)
1913 f(Var(0))
1914 >>> q.pattern(1)
1915 g(Var(0))
1916 """
1917 if z3_debug():
1918 _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
1919 return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
1920
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 1820 of file z3py.py.

1820 def sort(self):
1821 """Return the Boolean sort or sort of Lambda."""
1822 if self.is_lambda():
1823 return _sort(self.ctx, self.as_ast())
1824 return BoolSort(self.ctx)
1825
def BoolSort(ctx=None)
Definition: z3py.py:1533

Referenced by QuantifierRef.__getitem__(), FPNumRef.as_string(), ArrayRef.domain(), FPRef.ebits(), ArithRef.is_int(), ArithRef.is_real(), ArrayRef.range(), FPRef.sbits(), BitVecRef.size(), and ExprRef.sort_kind().

◆ 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 1954 of file z3py.py.

1954 def var_name(self, idx):
1955 """Return a string representing a name used when displaying the quantifier.
1956
1957 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1958 >>> x = Int('x')
1959 >>> y = Int('y')
1960 >>> q = ForAll([x, y], f(x, y) >= x)
1961 >>> q.var_name(0)
1962 'x'
1963 >>> q.var_name(1)
1964 'y'
1965 """
1966 if z3_debug():
1967 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
1968 return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
1969
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 1970 of file z3py.py.

1970 def var_sort(self, idx):
1971 """Return the sort of a bound variable.
1972
1973 >>> f = Function('f', IntSort(), RealSort(), IntSort())
1974 >>> x = Int('x')
1975 >>> y = Real('y')
1976 >>> q = ForAll([x, y], f(x, y) >= x)
1977 >>> q.var_sort(0)
1978 Int
1979 >>> q.var_sort(1)
1980 Real
1981 """
1982 if z3_debug():
1983 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
1984 return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
1985
def RealSort(ctx=None)
Definition: z3py.py:2923
def Real(name, ctx=None)
Definition: z3py.py:3058
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 1877 of file z3py.py.

1877 def weight(self):
1878 """Return the weight annotation of `self`.
1879
1880 >>> f = Function('f', IntSort(), IntSort())
1881 >>> x = Int('x')
1882 >>> q = ForAll(x, f(x) == 0)
1883 >>> q.weight()
1884 1
1885 >>> q = ForAll(x, f(x) == 0, weight=10)
1886 >>> q.weight()
1887 10
1888 """
1889 return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
1890
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.