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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)
 
def from_string (self, s)
 
def serialize (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 1979 of file z3py.py.

Member Function Documentation

◆ __getitem__()

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

Definition at line 2036 of file z3py.py.

2036 def __getitem__(self, arg):
2037 """Return the Z3 expression `self[arg]`.
2038 """
2039 if z3_debug():
2040 _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
2041 return _array_select(self, arg)
2042

◆ as_ast()

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

Reimplemented from ExprRef.

Definition at line 1982 of file z3py.py.

1982 def as_ast(self):
1983 return self.ast
1984

Referenced by AstRef.__del__(), SeqRef.__ge__(), SeqRef.__getitem__(), SeqRef.__gt__(), BitVecRef.__invert__(), SeqRef.__le__(), CharRef.__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(), CharRef.is_digit(), 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(), CharRef.to_bv(), CharRef.to_int(), 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 2097 of file z3py.py.

2097 def body(self):
2098 """Return the expression being quantified.
2099
2100 >>> f = Function('f', IntSort(), IntSort())
2101 >>> x = Int('x')
2102 >>> q = ForAll(x, f(x) == 0)
2103 >>> q.body()
2104 f(Var(0)) == 0
2105 """
2106 return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
2107
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 2152 of file z3py.py.

2152 def children(self):
2153 """Return a list containing a single element self.body()
2154
2155 >>> f = Function('f', IntSort(), IntSort())
2156 >>> x = Int('x')
2157 >>> q = ForAll(x, f(x) == 0)
2158 >>> q.children()
2159 [f(Var(0)) == 0]
2160 """
2161 return [self.body()]
2162
2163

◆ 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 1985 of file z3py.py.

1985 def get_id(self):
1986 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1987
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 2008 of file z3py.py.

2008 def is_exists(self):
2009 """Return `True` if `self` is an existential quantifier.
2010
2011 >>> f = Function('f', IntSort(), IntSort())
2012 >>> x = Int('x')
2013 >>> q = ForAll(x, f(x) == 0)
2014 >>> q.is_exists()
2015 False
2016 >>> q = Exists(x, f(x) != 0)
2017 >>> q.is_exists()
2018 True
2019 """
2020 return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
2021
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 1994 of file z3py.py.

1994 def is_forall(self):
1995 """Return `True` if `self` is a universal quantifier.
1996
1997 >>> f = Function('f', IntSort(), IntSort())
1998 >>> x = Int('x')
1999 >>> q = ForAll(x, f(x) == 0)
2000 >>> q.is_forall()
2001 True
2002 >>> q = Exists(x, f(x) != 0)
2003 >>> q.is_forall()
2004 False
2005 """
2006 return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
2007
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 2022 of file z3py.py.

2022 def is_lambda(self):
2023 """Return `True` if `self` is a lambda expression.
2024
2025 >>> f = Function('f', IntSort(), IntSort())
2026 >>> x = Int('x')
2027 >>> q = Lambda(x, f(x))
2028 >>> q.is_lambda()
2029 True
2030 >>> q = Exists(x, f(x) != 0)
2031 >>> q.is_lambda()
2032 False
2033 """
2034 return Z3_is_lambda(self.ctx_ref(), self.ast)
2035
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 2091 of file z3py.py.

2091 def no_pattern(self, idx):
2092 """Return a no-pattern."""
2093 if z3_debug():
2094 _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
2095 return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2096
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 2087 of file z3py.py.

2087 def num_no_patterns(self):
2088 """Return the number of no-patterns."""
2089 return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
2090
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 2057 of file z3py.py.

2057 def num_patterns(self):
2058 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2059
2060 >>> f = Function('f', IntSort(), IntSort())
2061 >>> g = Function('g', IntSort(), IntSort())
2062 >>> x = Int('x')
2063 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2064 >>> q.num_patterns()
2065 2
2066 """
2067 return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
2068
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 2108 of file z3py.py.

2108 def num_vars(self):
2109 """Return the number of variables bounded by this quantifier.
2110
2111 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2112 >>> x = Int('x')
2113 >>> y = Int('y')
2114 >>> q = ForAll([x, y], f(x, y) >= x)
2115 >>> q.num_vars()
2116 2
2117 """
2118 return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
2119
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 2069 of file z3py.py.

2069 def pattern(self, idx):
2070 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2071
2072 >>> f = Function('f', IntSort(), IntSort())
2073 >>> g = Function('g', IntSort(), IntSort())
2074 >>> x = Int('x')
2075 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2076 >>> q.num_patterns()
2077 2
2078 >>> q.pattern(0)
2079 f(Var(0))
2080 >>> q.pattern(1)
2081 g(Var(0))
2082 """
2083 if z3_debug():
2084 _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
2085 return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2086
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 1988 of file z3py.py.

1988 def sort(self):
1989 """Return the Boolean sort or sort of Lambda."""
1990 if self.is_lambda():
1991 return _sort(self.ctx, self.as_ast())
1992 return BoolSort(self.ctx)
1993

Referenced by FPNumRef.as_string(), ArrayRef.domain(), ArrayRef.domain_n(), 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 2120 of file z3py.py.

2120 def var_name(self, idx):
2121 """Return a string representing a name used when displaying the quantifier.
2122
2123 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2124 >>> x = Int('x')
2125 >>> y = Int('y')
2126 >>> q = ForAll([x, y], f(x, y) >= x)
2127 >>> q.var_name(0)
2128 'x'
2129 >>> q.var_name(1)
2130 'y'
2131 """
2132 if z3_debug():
2133 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2134 return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
2135
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 2136 of file z3py.py.

2136 def var_sort(self, idx):
2137 """Return the sort of a bound variable.
2138
2139 >>> f = Function('f', IntSort(), RealSort(), IntSort())
2140 >>> x = Int('x')
2141 >>> y = Real('y')
2142 >>> q = ForAll([x, y], f(x, y) >= x)
2143 >>> q.var_sort(0)
2144 Int
2145 >>> q.var_sort(1)
2146 Real
2147 """
2148 if z3_debug():
2149 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2150 return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
2151
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 2043 of file z3py.py.

2043 def weight(self):
2044 """Return the weight annotation of `self`.
2045
2046 >>> f = Function('f', IntSort(), IntSort())
2047 >>> x = Int('x')
2048 >>> q = ForAll(x, f(x) == 0)
2049 >>> q.weight()
2050 1
2051 >>> q = ForAll(x, f(x) == 0, weight=10)
2052 >>> q.weight()
2053 10
2054 """
2055 return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
2056
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.