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	skolem_id (self)
def	qid (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	__add__ (self, other)
def	__radd__ (self, other)
def	__rmul__ (self, other)
def	__mul__ (self, other)
def	__and__ (self, other)
def	__or__ (self, other)
def	__xor__ (self, other)
def	__invert__ (self)
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)
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	__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 2028 of file z3py.py.

Member Function Documentation

__getitem__()

def __getitem__	(		self,
			arg
	)

Return the Z3 expression `self[arg]`.

Definition at line 2085 of file z3py.py.

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

as_ast()

def as_ast

(

self

)

Return a pointer to the corresponding C Z3_ast object.

Reimplemented from ExprRef.

Definition at line 2031 of file z3py.py.

    def as_ast(self):
        return self.ast
 

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 2156 of file z3py.py.

    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
        """
        return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
 

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 2211 of file z3py.py.

    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]
        """
        return [self.body()]
 
 

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 2034 of file z3py.py.

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

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 2057 of file z3py.py.

    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
        """
        return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
 

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 2043 of file z3py.py.

    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
        """
        return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
 

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 2071 of file z3py.py.

    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
        """
        return Z3_is_lambda(self.ctx_ref(), self.ast)
 

Referenced by QuantifierRef.__getitem__(), and QuantifierRef.sort().

no_pattern()

def no_pattern	(		self,
			idx
	)

Return a no-pattern.

Definition at line 2150 of file z3py.py.

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

num_no_patterns()

def num_no_patterns

(

self

)

Return the number of no-patterns.

Definition at line 2146 of file z3py.py.

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

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 2116 of file z3py.py.

    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
        """
        return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
 

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 2167 of file z3py.py.

    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
        """
        return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
 

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 2128 of file z3py.py.

    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))
        """
        if z3_debug():
            _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
        return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
 

qid()

def qid

(

self

)

Return the quantifier id of `self`.

Definition at line 2111 of file z3py.py.

    def qid(self):
        """Return the quantifier id of `self`.
        """
        return _symbol2py(self.ctx, Z3_get_quantifier_id(self.ctx_ref(), self.ast))
 

skolem_id()

def skolem_id

(

self

)

Return the skolem id of `self`.

Definition at line 2106 of file z3py.py.

    def skolem_id(self):
        """Return the skolem id of `self`.
        """
        return _symbol2py(self.ctx, Z3_get_quantifier_skolem_id(self.ctx_ref(), self.ast))
 

sort()

def sort

(

self

)

Return the Boolean sort or sort of Lambda.

Reimplemented from BoolRef.

Definition at line 2037 of file z3py.py.

    def sort(self):
        """Return the Boolean sort or sort of Lambda."""
        if self.is_lambda():
            return _sort(self.ctx, self.as_ast())
        return BoolSort(self.ctx)
 

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 2179 of file z3py.py.

    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'
        """
        if z3_debug():
            _z3_assert(idx < self.num_vars(), "Invalid variable idx")
        return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
 

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 2195 of file z3py.py.

    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
        """
        if z3_debug():
            _z3_assert(idx < self.num_vars(), "Invalid variable idx")
        return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
 

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 2092 of file z3py.py.

    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
        """
        return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))