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 1954 of file z3py.py.

Member Function Documentation

◆ __getitem__()

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

Definition at line 2011 of file z3py.py.

2011  def __getitem__(self, arg):
2012  """Return the Z3 expression `self[arg]`.
2013  """
2014  if z3_debug():
2015  _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
2016  arg = self.sort().domain().cast(arg)
2017  return _to_expr_ref(Z3_mk_select(self.ctx_ref(), self.as_ast(), arg.as_ast()), self.ctx)
2018 
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.
def z3_debug()
Definition: z3py.py:64

◆ as_ast()

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

Reimplemented from ExprRef.

Definition at line 1957 of file z3py.py.

1957  def as_ast(self):
1958  return self.ast
1959 

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 2073 of file z3py.py.

2073  def body(self):
2074  """Return the expression being quantified.
2075 
2076  >>> f = Function('f', IntSort(), IntSort())
2077  >>> x = Int('x')
2078  >>> q = ForAll(x, f(x) == 0)
2079  >>> q.body()
2080  f(Var(0)) == 0
2081  """
2082  return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
2083 
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 2128 of file z3py.py.

2128  def children(self):
2129  """Return a list containing a single element self.body()
2130 
2131  >>> f = Function('f', IntSort(), IntSort())
2132  >>> x = Int('x')
2133  >>> q = ForAll(x, f(x) == 0)
2134  >>> q.children()
2135  [f(Var(0)) == 0]
2136  """
2137  return [self.body()]
2138 
2139 

◆ 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 1960 of file z3py.py.

1960  def get_id(self):
1961  return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1962 
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 1983 of file z3py.py.

1983  def is_exists(self):
1984  """Return `True` if `self` is an existential quantifier.
1985 
1986  >>> f = Function('f', IntSort(), IntSort())
1987  >>> x = Int('x')
1988  >>> q = ForAll(x, f(x) == 0)
1989  >>> q.is_exists()
1990  False
1991  >>> q = Exists(x, f(x) != 0)
1992  >>> q.is_exists()
1993  True
1994  """
1995  return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
1996 
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 1969 of file z3py.py.

1969  def is_forall(self):
1970  """Return `True` if `self` is a universal quantifier.
1971 
1972  >>> f = Function('f', IntSort(), IntSort())
1973  >>> x = Int('x')
1974  >>> q = ForAll(x, f(x) == 0)
1975  >>> q.is_forall()
1976  True
1977  >>> q = Exists(x, f(x) != 0)
1978  >>> q.is_forall()
1979  False
1980  """
1981  return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
1982 
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 1997 of file z3py.py.

1997  def is_lambda(self):
1998  """Return `True` if `self` is a lambda expression.
1999 
2000  >>> f = Function('f', IntSort(), IntSort())
2001  >>> x = Int('x')
2002  >>> q = Lambda(x, f(x))
2003  >>> q.is_lambda()
2004  True
2005  >>> q = Exists(x, f(x) != 0)
2006  >>> q.is_lambda()
2007  False
2008  """
2009  return Z3_is_lambda(self.ctx_ref(), self.ast)
2010 
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 2067 of file z3py.py.

2067  def no_pattern(self, idx):
2068  """Return a no-pattern."""
2069  if z3_debug():
2070  _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
2071  return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2072 
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 2063 of file z3py.py.

2063  def num_no_patterns(self):
2064  """Return the number of no-patterns."""
2065  return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
2066 
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 2033 of file z3py.py.

2033  def num_patterns(self):
2034  """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2035 
2036  >>> f = Function('f', IntSort(), IntSort())
2037  >>> g = Function('g', IntSort(), IntSort())
2038  >>> x = Int('x')
2039  >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2040  >>> q.num_patterns()
2041  2
2042  """
2043  return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
2044 
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 2084 of file z3py.py.

2084  def num_vars(self):
2085  """Return the number of variables bounded by this quantifier.
2086 
2087  >>> f = Function('f', IntSort(), IntSort(), IntSort())
2088  >>> x = Int('x')
2089  >>> y = Int('y')
2090  >>> q = ForAll([x, y], f(x, y) >= x)
2091  >>> q.num_vars()
2092  2
2093  """
2094  return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
2095 
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 2045 of file z3py.py.

2045  def pattern(self, idx):
2046  """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2047 
2048  >>> f = Function('f', IntSort(), IntSort())
2049  >>> g = Function('g', IntSort(), IntSort())
2050  >>> x = Int('x')
2051  >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2052  >>> q.num_patterns()
2053  2
2054  >>> q.pattern(0)
2055  f(Var(0))
2056  >>> q.pattern(1)
2057  g(Var(0))
2058  """
2059  if z3_debug():
2060  _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
2061  return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2062 
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 1963 of file z3py.py.

1963  def sort(self):
1964  """Return the Boolean sort or sort of Lambda."""
1965  if self.is_lambda():
1966  return _sort(self.ctx, self.as_ast())
1967  return BoolSort(self.ctx)
1968 
def BoolSort(ctx=None)
Definition: z3py.py:1657

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 2096 of file z3py.py.

2096  def var_name(self, idx):
2097  """Return a string representing a name used when displaying the quantifier.
2098 
2099  >>> f = Function('f', IntSort(), IntSort(), IntSort())
2100  >>> x = Int('x')
2101  >>> y = Int('y')
2102  >>> q = ForAll([x, y], f(x, y) >= x)
2103  >>> q.var_name(0)
2104  'x'
2105  >>> q.var_name(1)
2106  'y'
2107  """
2108  if z3_debug():
2109  _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2110  return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
2111 
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 2112 of file z3py.py.

2112  def var_sort(self, idx):
2113  """Return the sort of a bound variable.
2114 
2115  >>> f = Function('f', IntSort(), RealSort(), IntSort())
2116  >>> x = Int('x')
2117  >>> y = Real('y')
2118  >>> q = ForAll([x, y], f(x, y) >= x)
2119  >>> q.var_sort(0)
2120  Int
2121  >>> q.var_sort(1)
2122  Real
2123  """
2124  if z3_debug():
2125  _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2126  return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
2127 
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 2019 of file z3py.py.

2019  def weight(self):
2020  """Return the weight annotation of `self`.
2021 
2022  >>> f = Function('f', IntSort(), IntSort())
2023  >>> x = Int('x')
2024  >>> q = ForAll(x, f(x) == 0)
2025  >>> q.weight()
2026  1
2027  >>> q = ForAll(x, f(x) == 0, weight=10)
2028  >>> q.weight()
2029  10
2030  """
2031  return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
2032 
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.