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Public Member Functions | Data Fields
QuantifierRef Class Reference

Quantifiers. More...

+ Inheritance diagram for QuantifierRef:

Public Member Functions

 as_ast (self)
 
 get_id (self)
 
 sort (self)
 
 is_forall (self)
 
 is_exists (self)
 
 is_lambda (self)
 
 __getitem__ (self, arg)
 
 weight (self)
 
 num_patterns (self)
 
 pattern (self, idx)
 
 num_no_patterns (self)
 
 no_pattern (self, idx)
 
 body (self)
 
 num_vars (self)
 
 var_name (self, idx)
 
 var_sort (self, idx)
 
 children (self)
 
- Public Member Functions inherited from BoolRef
 sort (self)
 
 __rmul__ (self, other)
 
 __mul__ (self, other)
 
- Public Member Functions inherited from ExprRef
 as_ast (self)
 
 get_id (self)
 
 sort (self)
 
 sort_kind (self)
 
 __eq__ (self, other)
 
 __hash__ (self)
 
 __ne__ (self, other)
 
 params (self)
 
 decl (self)
 
 num_args (self)
 
 arg (self, idx)
 
 children (self)
 
 from_string (self, s)
 
 serialize (self)
 
- Public Member Functions inherited from AstRef
 __init__ (self, ast, ctx=None)
 
 __del__ (self)
 
 __deepcopy__ (self, memo={})
 
 __str__ (self)
 
 __repr__ (self)
 
 __eq__ (self, other)
 
 __hash__ (self)
 
 __nonzero__ (self)
 
 __bool__ (self)
 
 sexpr (self)
 
 as_ast (self)
 
 get_id (self)
 
 ctx_ref (self)
 
 eq (self, other)
 
 translate (self, target)
 
 __copy__ (self)
 
 hash (self)
 
- Public Member Functions inherited from Z3PPObject
 use_pp (self)
 

Data Fields

 ctx
 
 ast
 
- Data Fields inherited from BoolRef
 ctx
 
- Data Fields inherited from ExprRef
 ctx
 
- Data Fields inherited from AstRef
 ast
 
 ctx
 

Additional Inherited Members

- Protected Member Functions inherited from Z3PPObject
 _repr_html_ (self)
 

Detailed Description

Quantifiers.

Universally and Existentially quantified formulas.

Definition at line 1984 of file z3py.py.

Member Function Documentation

◆ __getitem__()

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

Definition at line 2041 of file z3py.py.

2041 def __getitem__(self, arg):
2042 """Return the Z3 expression `self[arg]`.
2043 """
2044 if z3_debug():
2045 _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
2046 return _array_select(self, arg)
2047

◆ as_ast()

as_ast (   self)

◆ body()

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 2102 of file z3py.py.

2102 def body(self):
2103 """Return the expression being quantified.
2104
2105 >>> f = Function('f', IntSort(), IntSort())
2106 >>> x = Int('x')
2107 >>> q = ForAll(x, f(x) == 0)
2108 >>> q.body()
2109 f(Var(0)) == 0
2110 """
2111 return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
2112
Z3_ast Z3_API Z3_get_quantifier_body(Z3_context c, Z3_ast a)
Return body of quantifier.

Referenced by QuantifierRef.children().

◆ children()

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 2157 of file z3py.py.

2157 def children(self):
2158 """Return a list containing a single element self.body()
2159
2160 >>> f = Function('f', IntSort(), IntSort())
2161 >>> x = Int('x')
2162 >>> q = ForAll(x, f(x) == 0)
2163 >>> q.children()
2164 [f(Var(0)) == 0]
2165 """
2166 return [self.body()]
2167
2168

◆ get_id()

get_id (   self)
Return unique identifier for object. It can be used for hash-tables and maps.

Reimplemented from ExprRef.

Definition at line 1990 of file z3py.py.

1990 def get_id(self):
1991 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1992
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()

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 2013 of file z3py.py.

2013 def is_exists(self):
2014 """Return `True` if `self` is an existential quantifier.
2015
2016 >>> f = Function('f', IntSort(), IntSort())
2017 >>> x = Int('x')
2018 >>> q = ForAll(x, f(x) == 0)
2019 >>> q.is_exists()
2020 False
2021 >>> q = Exists(x, f(x) != 0)
2022 >>> q.is_exists()
2023 True
2024 """
2025 return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
2026
bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a)
Determine if ast is an existential quantifier.

◆ is_forall()

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 1999 of file z3py.py.

1999 def is_forall(self):
2000 """Return `True` if `self` is a universal quantifier.
2001
2002 >>> f = Function('f', IntSort(), IntSort())
2003 >>> x = Int('x')
2004 >>> q = ForAll(x, f(x) == 0)
2005 >>> q.is_forall()
2006 True
2007 >>> q = Exists(x, f(x) != 0)
2008 >>> q.is_forall()
2009 False
2010 """
2011 return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
2012
bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a)
Determine if an ast is a universal quantifier.

◆ is_lambda()

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 2027 of file z3py.py.

2027 def is_lambda(self):
2028 """Return `True` if `self` is a lambda expression.
2029
2030 >>> f = Function('f', IntSort(), IntSort())
2031 >>> x = Int('x')
2032 >>> q = Lambda(x, f(x))
2033 >>> q.is_lambda()
2034 True
2035 >>> q = Exists(x, f(x) != 0)
2036 >>> q.is_lambda()
2037 False
2038 """
2039 return Z3_is_lambda(self.ctx_ref(), self.ast)
2040
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()

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

Definition at line 2096 of file z3py.py.

2096 def no_pattern(self, idx):
2097 """Return a no-pattern."""
2098 if z3_debug():
2099 _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
2100 return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2101
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()

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

Definition at line 2092 of file z3py.py.

2092 def num_no_patterns(self):
2093 """Return the number of no-patterns."""
2094 return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
2095
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()

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 2062 of file z3py.py.

2062 def num_patterns(self):
2063 """Return the number of patterns (i.e., quantifier instantiation hints) in `self`.
2064
2065 >>> f = Function('f', IntSort(), IntSort())
2066 >>> g = Function('g', IntSort(), IntSort())
2067 >>> x = Int('x')
2068 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2069 >>> q.num_patterns()
2070 2
2071 """
2072 return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
2073
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()

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 2113 of file z3py.py.

2113 def num_vars(self):
2114 """Return the number of variables bounded by this quantifier.
2115
2116 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2117 >>> x = Int('x')
2118 >>> y = Int('y')
2119 >>> q = ForAll([x, y], f(x, y) >= x)
2120 >>> q.num_vars()
2121 2
2122 """
2123 return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
2124
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()

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 2074 of file z3py.py.

2074 def pattern(self, idx):
2075 """Return a pattern (i.e., quantifier instantiation hints) in `self`.
2076
2077 >>> f = Function('f', IntSort(), IntSort())
2078 >>> g = Function('g', IntSort(), IntSort())
2079 >>> x = Int('x')
2080 >>> q = ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2081 >>> q.num_patterns()
2082 2
2083 >>> q.pattern(0)
2084 f(Var(0))
2085 >>> q.pattern(1)
2086 g(Var(0))
2087 """
2088 if z3_debug():
2089 _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
2090 return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2091
Z3_pattern Z3_API Z3_get_quantifier_pattern_ast(Z3_context c, Z3_ast a, unsigned i)
Return i'th pattern.

◆ sort()

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

Reimplemented from BoolRef.

Definition at line 1993 of file z3py.py.

1993 def sort(self):
1994 """Return the Boolean sort or sort of Lambda."""
1995 if self.is_lambda():
1996 return _sort(self.ctx, self.as_ast())
1997 return BoolSort(self.ctx)
1998

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()

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 2125 of file z3py.py.

2125 def var_name(self, idx):
2126 """Return a string representing a name used when displaying the quantifier.
2127
2128 >>> f = Function('f', IntSort(), IntSort(), IntSort())
2129 >>> x = Int('x')
2130 >>> y = Int('y')
2131 >>> q = ForAll([x, y], f(x, y) >= x)
2132 >>> q.var_name(0)
2133 'x'
2134 >>> q.var_name(1)
2135 'y'
2136 """
2137 if z3_debug():
2138 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2139 return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
2140
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()

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 2141 of file z3py.py.

2141 def var_sort(self, idx):
2142 """Return the sort of a bound variable.
2143
2144 >>> f = Function('f', IntSort(), RealSort(), IntSort())
2145 >>> x = Int('x')
2146 >>> y = Real('y')
2147 >>> q = ForAll([x, y], f(x, y) >= x)
2148 >>> q.var_sort(0)
2149 Int
2150 >>> q.var_sort(1)
2151 Real
2152 """
2153 if z3_debug():
2154 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2155 return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
2156
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()

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 2048 of file z3py.py.

2048 def weight(self):
2049 """Return the weight annotation of `self`.
2050
2051 >>> f = Function('f', IntSort(), IntSort())
2052 >>> x = Int('x')
2053 >>> q = ForAll(x, f(x) == 0)
2054 >>> q.weight()
2055 1
2056 >>> q = ForAll(x, f(x) == 0, weight=10)
2057 >>> q.weight()
2058 10
2059 """
2060 return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
2061
unsigned Z3_API Z3_get_quantifier_weight(Z3_context c, Z3_ast a)
Obtain weight of quantifier.

Field Documentation

◆ ast

ast

◆ ctx

ctx

Definition at line 1996 of file z3py.py.

Referenced by ArithRef.__add__(), BitVecRef.__add__(), FPRef.__add__(), BitVecRef.__and__(), FuncDeclRef.__call__(), Probe.__call__(), AstMap.__contains__(), AstRef.__copy__(), Goal.__copy__(), AstVector.__copy__(), FuncInterp.__copy__(), ModelRef.__copy__(), Solver.__copy__(), AstRef.__deepcopy__(), Datatype.__deepcopy__(), ParamsRef.__deepcopy__(), ParamDescrsRef.__deepcopy__(), Goal.__deepcopy__(), AstVector.__deepcopy__(), AstMap.__deepcopy__(), FuncEntry.__deepcopy__(), FuncInterp.__deepcopy__(), ModelRef.__deepcopy__(), Statistics.__deepcopy__(), Solver.__deepcopy__(), Fixedpoint.__deepcopy__(), Optimize.__deepcopy__(), ApplyResult.__deepcopy__(), Simplifier.__deepcopy__(), Tactic.__deepcopy__(), Probe.__deepcopy__(), Context.__del__(), AstRef.__del__(), ScopedConstructor.__del__(), ScopedConstructorList.__del__(), ParamsRef.__del__(), ParamDescrsRef.__del__(), Goal.__del__(), AstVector.__del__(), AstMap.__del__(), FuncEntry.__del__(), FuncInterp.__del__(), ModelRef.__del__(), Statistics.__del__(), Solver.__del__(), Fixedpoint.__del__(), Optimize.__del__(), ApplyResult.__del__(), Simplifier.__del__(), Tactic.__del__(), Probe.__del__(), ParserContext.__del__(), ArithRef.__div__(), BitVecRef.__div__(), FPRef.__div__(), ExprRef.__eq__(), Probe.__eq__(), ArithRef.__ge__(), BitVecRef.__ge__(), Probe.__ge__(), FPRef.__ge__(), SeqRef.__ge__(), AstVector.__getitem__(), SeqRef.__getitem__(), ModelRef.__getitem__(), Statistics.__getitem__(), ApplyResult.__getitem__(), AstMap.__getitem__(), ArithRef.__gt__(), BitVecRef.__gt__(), Probe.__gt__(), FPRef.__gt__(), SeqRef.__gt__(), BitVecRef.__invert__(), ArithRef.__le__(), BitVecRef.__le__(), Probe.__le__(), FPRef.__le__(), SeqRef.__le__(), CharRef.__le__(), AstVector.__len__(), AstMap.__len__(), ModelRef.__len__(), Statistics.__len__(), ApplyResult.__len__(), BitVecRef.__lshift__(), ArithRef.__lt__(), BitVecRef.__lt__(), Probe.__lt__(), FPRef.__lt__(), SeqRef.__lt__(), ArithRef.__mod__(), BitVecRef.__mod__(), BoolRef.__mul__(), ArithRef.__mul__(), BitVecRef.__mul__(), FPRef.__mul__(), ExprRef.__ne__(), Probe.__ne__(), ArithRef.__neg__(), BitVecRef.__neg__(), BitVecRef.__or__(), ArithRef.__pow__(), ArithRef.__radd__(), BitVecRef.__radd__(), FPRef.__radd__(), BitVecRef.__rand__(), ArithRef.__rdiv__(), BitVecRef.__rdiv__(), FPRef.__rdiv__(), ParamsRef.__repr__(), ParamDescrsRef.__repr__(), AstMap.__repr__(), Statistics.__repr__(), BitVecRef.__rlshift__(), ArithRef.__rmod__(), BitVecRef.__rmod__(), ArithRef.__rmul__(), BitVecRef.__rmul__(), FPRef.__rmul__(), BitVecRef.__ror__(), ArithRef.__rpow__(), BitVecRef.__rrshift__(), BitVecRef.__rshift__(), ArithRef.__rsub__(), BitVecRef.__rsub__(), FPRef.__rsub__(), BitVecRef.__rxor__(), AstVector.__setitem__(), AstMap.__setitem__(), ArithRef.__sub__(), BitVecRef.__sub__(), FPRef.__sub__(), BitVecRef.__xor__(), DatatypeSortRef.accessor(), Simplifier.add(), Fixedpoint.add_cover(), ParserContext.add_decl(), Fixedpoint.add_rule(), Optimize.add_soft(), ParserContext.add_sort(), Tactic.apply(), ExprRef.arg(), FuncEntry.arg_value(), FuncInterp.arity(), Goal.as_expr(), ApplyResult.as_expr(), FPNumRef.as_string(), Solver.assert_and_track(), Optimize.assert_and_track(), Goal.assert_exprs(), Solver.assert_exprs(), Fixedpoint.assert_exprs(), Optimize.assert_exprs(), Solver.assertions(), Optimize.assertions(), SeqRef.at(), QuantifierRef.body(), Solver.check(), Optimize.check(), UserPropagateBase.conflict(), Solver.consequences(), Goal.convert_model(), AstRef.ctx_ref(), UserPropagateBase.ctx_ref(), ExprRef.decl(), ModelRef.decls(), ArrayRef.default(), RatNumRef.denominator(), Goal.depth(), Goal.dimacs(), Solver.dimacs(), FuncDeclRef.domain(), ArraySortRef.domain_n(), FuncInterp.else_value(), FuncInterp.entry(), AstMap.erase(), ModelRef.eval(), FPNumRef.exponent(), FPNumRef.exponent_as_bv(), FPNumRef.exponent_as_long(), Solver.from_file(), Optimize.from_file(), Solver.from_string(), Optimize.from_string(), ParserContext.from_string(), Goal.get(), Fixedpoint.get_answer(), Fixedpoint.get_assertions(), Fixedpoint.get_cover_delta(), ParamDescrsRef.get_documentation(), Fixedpoint.get_ground_sat_answer(), ModelRef.get_interp(), Statistics.get_key_value(), ParamDescrsRef.get_kind(), ParamDescrsRef.get_name(), Fixedpoint.get_num_levels(), Fixedpoint.get_rule_names_along_trace(), Fixedpoint.get_rules(), Fixedpoint.get_rules_along_trace(), ModelRef.get_sort(), ModelRef.get_universe(), Solver.help(), Fixedpoint.help(), Optimize.help(), Simplifier.help(), Tactic.help(), Solver.import_model_converter(), Goal.inconsistent(), CharRef.is_digit(), FPNumRef.isInf(), FPNumRef.isNaN(), FPNumRef.isNegative(), FPNumRef.isNormal(), FPNumRef.isPositive(), FPNumRef.isSubnormal(), FPNumRef.isZero(), AstMap.keys(), Statistics.keys(), Optimize.maximize(), Optimize.minimize(), Solver.model(), Optimize.model(), SortRef.name(), Solver.next(), QuantifierRef.no_pattern(), Solver.non_units(), FuncEntry.num_args(), FuncInterp.num_entries(), Solver.num_scopes(), ModelRef.num_sorts(), Optimize.objectives(), Solver.param_descrs(), Fixedpoint.param_descrs(), Optimize.param_descrs(), Simplifier.param_descrs(), Tactic.param_descrs(), FuncDeclRef.params(), Fixedpoint.parse_file(), Fixedpoint.parse_string(), QuantifierRef.pattern(), AlgebraicNumRef.poly(), Optimize.pop(), Solver.pop(), Goal.prec(), Solver.proof(), Solver.push(), Optimize.push(), AstVector.push(), Fixedpoint.query(), Fixedpoint.query_from_lvl(), FuncDeclRef.range(), ArraySortRef.range(), Solver.reason_unknown(), Fixedpoint.reason_unknown(), Optimize.reason_unknown(), DatatypeSortRef.recognizer(), Context.ref(), Fixedpoint.register_relation(), AstMap.reset(), Solver.reset(), AstVector.resize(), Solver.root(), Solver.set(), Fixedpoint.set(), Optimize.set(), ParamsRef.set(), Optimize.set_on_model(), Fixedpoint.set_predicate_representation(), Goal.sexpr(), AstVector.sexpr(), ModelRef.sexpr(), Solver.sexpr(), Fixedpoint.sexpr(), Optimize.sexpr(), ApplyResult.sexpr(), FPNumRef.sign(), FPNumRef.significand(), FPNumRef.significand_as_bv(), FPNumRef.significand_as_long(), ParamDescrsRef.size(), Goal.size(), Tactic.solver(), Solver.statistics(), Fixedpoint.statistics(), Optimize.statistics(), CharRef.to_bv(), CharRef.to_int(), Solver.to_smt2(), Fixedpoint.to_string(), Solver.trail(), Solver.trail_levels(), AstVector.translate(), AstRef.translate(), Goal.translate(), ModelRef.translate(), Solver.translate(), Solver.units(), Solver.unsat_core(), Optimize.unsat_core(), Fixedpoint.update_rule(), Simplifier.using_params(), ParamsRef.validate(), FuncEntry.value(), QuantifierRef.var_name(), and QuantifierRef.var_sort().