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 1952 of file z3py.py.

Member Function Documentation

◆ __getitem__()

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

Definition at line 2009 of file z3py.py.

2009  def __getitem__(self, arg):
2010  """Return the Z3 expression `self[arg]`.
2011  """
2012  if z3_debug():
2013  _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
2014  arg = self.sort().domain().cast(arg)
2015  return _to_expr_ref(Z3_mk_select(self.ctx_ref(), self.as_ast(), arg.as_ast()), self.ctx)
2016 
def z3_debug()
Definition: z3py.py:64
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 1955 of file z3py.py.

1955  def as_ast(self):
1956  return self.ast
1957 

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(), IntNumRef.as_binary_string(), BitVecNumRef.as_binary_string(), 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(), AlgebraicNumRef.index(), 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(), AlgebraicNumRef.poly(), 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 2071 of file z3py.py.

2071  def body(self):
2072  """Return the expression being quantified.
2073 
2074  >>> f = Function('f', IntSort(), IntSort())
2075  >>> x = Int('x')
2076  >>> q = ForAll(x, f(x) == 0)
2077  >>> q.body()
2078  f(Var(0)) == 0
2079  """
2080  return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
2081 
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 2126 of file z3py.py.

2126  def children(self):
2127  """Return a list containing a single element self.body()
2128 
2129  >>> f = Function('f', IntSort(), IntSort())
2130  >>> x = Int('x')
2131  >>> q = ForAll(x, f(x) == 0)
2132  >>> q.children()
2133  [f(Var(0)) == 0]
2134  """
2135  return [self.body()]
2136 
2137 

◆ 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 1958 of file z3py.py.

1958  def get_id(self):
1959  return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1960 
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 1981 of file z3py.py.

1981  def is_exists(self):
1982  """Return `True` if `self` is an existential quantifier.
1983 
1984  >>> f = Function('f', IntSort(), IntSort())
1985  >>> x = Int('x')
1986  >>> q = ForAll(x, f(x) == 0)
1987  >>> q.is_exists()
1988  False
1989  >>> q = Exists(x, f(x) != 0)
1990  >>> q.is_exists()
1991  True
1992  """
1993  return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
1994 
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 1967 of file z3py.py.

1967  def is_forall(self):
1968  """Return `True` if `self` is a universal quantifier.
1969 
1970  >>> f = Function('f', IntSort(), IntSort())
1971  >>> x = Int('x')
1972  >>> q = ForAll(x, f(x) == 0)
1973  >>> q.is_forall()
1974  True
1975  >>> q = Exists(x, f(x) != 0)
1976  >>> q.is_forall()
1977  False
1978  """
1979  return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
1980 
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 1995 of file z3py.py.

1995  def is_lambda(self):
1996  """Return `True` if `self` is a lambda expression.
1997 
1998  >>> f = Function('f', IntSort(), IntSort())
1999  >>> x = Int('x')
2000  >>> q = Lambda(x, f(x))
2001  >>> q.is_lambda()
2002  True
2003  >>> q = Exists(x, f(x) != 0)
2004  >>> q.is_lambda()
2005  False
2006  """
2007  return Z3_is_lambda(self.ctx_ref(), self.ast)
2008 
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 2065 of file z3py.py.

2065  def no_pattern(self, idx):
2066  """Return a no-pattern."""
2067  if z3_debug():
2068  _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
2069  return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2070 
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 2061 of file z3py.py.

2061  def num_no_patterns(self):
2062  """Return the number of no-patterns."""
2063  return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
2064 
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 2031 of file z3py.py.

2031  def num_patterns(self):
2032  """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2033 
2034  >>> f = Function('f', IntSort(), IntSort())
2035  >>> g = Function('g', IntSort(), IntSort())
2036  >>> x = Int('x')
2037  >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2038  >>> q.num_patterns()
2039  2
2040  """
2041  return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
2042 
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 2082 of file z3py.py.

2082  def num_vars(self):
2083  """Return the number of variables bounded by this quantifier.
2084 
2085  >>> f = Function('f', IntSort(), IntSort(), IntSort())
2086  >>> x = Int('x')
2087  >>> y = Int('y')
2088  >>> q = ForAll([x, y], f(x, y) >= x)
2089  >>> q.num_vars()
2090  2
2091  """
2092  return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
2093 
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 2043 of file z3py.py.

2043  def pattern(self, idx):
2044  """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2045 
2046  >>> f = Function('f', IntSort(), IntSort())
2047  >>> g = Function('g', IntSort(), IntSort())
2048  >>> x = Int('x')
2049  >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2050  >>> q.num_patterns()
2051  2
2052  >>> q.pattern(0)
2053  f(Var(0))
2054  >>> q.pattern(1)
2055  g(Var(0))
2056  """
2057  if z3_debug():
2058  _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
2059  return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2060 
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 1961 of file z3py.py.

1961  def sort(self):
1962  """Return the Boolean sort or sort of Lambda."""
1963  if self.is_lambda():
1964  return _sort(self.ctx, self.as_ast())
1965  return BoolSort(self.ctx)
1966 
def BoolSort(ctx=None)
Definition: z3py.py:1655

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 2094 of file z3py.py.

2094  def var_name(self, idx):
2095  """Return a string representing a name used when displaying the quantifier.
2096 
2097  >>> f = Function('f', IntSort(), IntSort(), IntSort())
2098  >>> x = Int('x')
2099  >>> y = Int('y')
2100  >>> q = ForAll([x, y], f(x, y) >= x)
2101  >>> q.var_name(0)
2102  'x'
2103  >>> q.var_name(1)
2104  'y'
2105  """
2106  if z3_debug():
2107  _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2108  return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
2109 
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 2110 of file z3py.py.

2110  def var_sort(self, idx):
2111  """Return the sort of a bound variable.
2112 
2113  >>> f = Function('f', IntSort(), RealSort(), IntSort())
2114  >>> x = Int('x')
2115  >>> y = Real('y')
2116  >>> q = ForAll([x, y], f(x, y) >= x)
2117  >>> q.var_sort(0)
2118  Int
2119  >>> q.var_sort(1)
2120  Real
2121  """
2122  if z3_debug():
2123  _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2124  return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
2125 
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 2017 of file z3py.py.

2017  def weight(self):
2018  """Return the weight annotation of `self`.
2019 
2020  >>> f = Function('f', IntSort(), IntSort())
2021  >>> x = Int('x')
2022  >>> q = ForAll(x, f(x) == 0)
2023  >>> q.weight()
2024  1
2025  >>> q = ForAll(x, f(x) == 0, weight=10)
2026  >>> q.weight()
2027  10
2028  """
2029  return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
2030 
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.