ArithRef Class Reference

Inheritance diagram for ArithRef:

Public Member Functions
	sort (self)
	is_int (self)
	is_real (self)
	__add__ (self, other)
	__radd__ (self, other)
	__mul__ (self, other)
	__rmul__ (self, other)
	__sub__ (self, other)
	__rsub__ (self, other)
	__pow__ (self, other)
	__rpow__ (self, other)
	__div__ (self, other)
	__truediv__ (self, other)
	__rdiv__ (self, other)
	__rtruediv__ (self, other)
	__mod__ (self, other)
	__rmod__ (self, other)
	__neg__ (self)
	__pos__ (self)
	__le__ (self, other)
	__lt__ (self, other)
	__gt__ (self, other)
	__ge__ (self, other)
	__abs__ (self)
Public Member Functions inherited from ExprRef
	as_ast (self)
	get_id (self)
	sort_kind (self)
	__eq__ (self, other)
	__hash__ (self)
	__ne__ (self, other)
	params (self)
	decl (self)
	kind (self)
	num_args (self)
	arg (self, idx)
	children (self)
	update (self, *args)
	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)
	__nonzero__ (self)
	__bool__ (self)
	sexpr (self)
	ctx_ref (self)
	eq (self, other)
	translate (self, target)
	__copy__ (self)
	hash (self)
	py_value (self)
Public Member Functions inherited from Z3PPObject
	use_pp (self)

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

Additional Inherited Members
Protected Member Functions inherited from Z3PPObject
	_repr_html_ (self)

Detailed Description

Integer, Real, and Complex expressions.

Definition at line 2544 of file z3py.py.

Member Function Documentation

__abs__()

__abs__

(

self

)

Return an expression representing `abs(self)`.

>>> x = Int('x')
>>> abs(x)
If(x > 0, x, -x)
>>> eq(abs(x), Abs(x))
True

Definition at line 2828 of file z3py.py.

    def __abs__(self):
        """Return an expression representing `abs(self)`.
 
        >>> x = Int('x')
        >>> abs(x)
        If(x > 0, x, -x)
        >>> eq(abs(x), Abs(x))
        True
        """
        return Abs(self)
 
 

__add__()

__add__	(		self,
			other
	)

Create the Z3 expression `self + other`.

>>> x = Int('x')
>>> y = Int('y')
>>> x + y
x + y
>>> (x + y).sort()
Int

Definition at line 2582 of file z3py.py.

    def __add__(self, other):
        """Create the Z3 expression `self + other`.
 
        >>> x = Int('x')
        >>> y = Int('y')
        >>> x + y
        x + y
        >>> (x + y).sort()
        Int
        """
        a, b = _coerce_exprs(self, other)
        return _to_expr_ref(_mk_bin(Z3_mk_add, a, b), self.ctx)
 

__div__()

__div__	(		self,
			other
	)

Create the Z3 expression `other/self`.

>>> x = Int('x')
>>> y = Int('y')
>>> x/y
x/y
>>> (x/y).sort()
Int
>>> (x/y).sexpr()
'(div x y)'
>>> x = Real('x')
>>> y = Real('y')
>>> x/y
x/y
>>> (x/y).sort()
Real
>>> (x/y).sexpr()
'(/ x y)'

Definition at line 2681 of file z3py.py.

    def __div__(self, other):
        """Create the Z3 expression `other/self`.
 
        >>> x = Int('x')
        >>> y = Int('y')
        >>> x/y
        x/y
        >>> (x/y).sort()
        Int
        >>> (x/y).sexpr()
        '(div x y)'
        >>> x = Real('x')
        >>> y = Real('y')
        >>> x/y
        x/y
        >>> (x/y).sort()
        Real
        >>> (x/y).sexpr()
        '(/ x y)'
        """
        a, b = _coerce_exprs(self, other)
        return _to_expr_ref(Z3_mk_div(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
 

Referenced by ArithRef.__truediv__(), and BitVecRef.__truediv__().

__ge__()

__ge__	(		self,
			other
	)

Create the Z3 expression `other >= self`.

>>> x, y = Ints('x y')
>>> x >= y
x >= y
>>> y = Real('y')
>>> x >= y
ToReal(x) >= y

Definition at line 2815 of file z3py.py.

    def __ge__(self, other):
        """Create the Z3 expression `other >= self`.
 
        >>> x, y = Ints('x y')
        >>> x >= y
        x >= y
        >>> y = Real('y')
        >>> x >= y
        ToReal(x) >= y
        """
        a, b = _coerce_exprs(self, other)
        return BoolRef(Z3_mk_ge(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
 

__gt__()

__gt__	(		self,
			other
	)

Create the Z3 expression `other > self`.

>>> x, y = Ints('x y')
>>> x > y
x > y
>>> y = Real('y')
>>> x > y
ToReal(x) > y

Definition at line 2802 of file z3py.py.

    def __gt__(self, other):
        """Create the Z3 expression `other > self`.
 
        >>> x, y = Ints('x y')
        >>> x > y
        x > y
        >>> y = Real('y')
        >>> x > y
        ToReal(x) > y
        """
        a, b = _coerce_exprs(self, other)
        return BoolRef(Z3_mk_gt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
 

__le__()

__le__	(		self,
			other
	)

Create the Z3 expression `other <= self`.

>>> x, y = Ints('x y')
>>> x <= y
x <= y
>>> y = Real('y')
>>> x <= y
ToReal(x) <= y

Definition at line 2776 of file z3py.py.

    def __le__(self, other):
        """Create the Z3 expression `other <= self`.
 
        >>> x, y = Ints('x y')
        >>> x <= y
        x <= y
        >>> y = Real('y')
        >>> x <= y
        ToReal(x) <= y
        """
        a, b = _coerce_exprs(self, other)
        return BoolRef(Z3_mk_le(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
 

__lt__()

__lt__	(		self,
			other
	)

Create the Z3 expression `other < self`.

>>> x, y = Ints('x y')
>>> x < y
x < y
>>> y = Real('y')
>>> x < y
ToReal(x) < y

Definition at line 2789 of file z3py.py.

    def __lt__(self, other):
        """Create the Z3 expression `other < self`.
 
        >>> x, y = Ints('x y')
        >>> x < y
        x < y
        >>> y = Real('y')
        >>> x < y
        ToReal(x) < y
        """
        a, b = _coerce_exprs(self, other)
        return BoolRef(Z3_mk_lt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
 

__mod__()

__mod__	(		self,
			other
	)

Create the Z3 expression `other%self`.

>>> x = Int('x')
>>> y = Int('y')
>>> x % y
x%y
>>> simplify(IntVal(10) % IntVal(3))
1

Definition at line 2729 of file z3py.py.

    def __mod__(self, other):
        """Create the Z3 expression `other%self`.
 
        >>> x = Int('x')
        >>> y = Int('y')
        >>> x % y
        x%y
        >>> simplify(IntVal(10) % IntVal(3))
        1
        """
        a, b = _coerce_exprs(self, other)
        if z3_debug():
            _z3_assert(a.is_int(), "Z3 integer expression expected")
        return ArithRef(Z3_mk_mod(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
 

__mul__()

__mul__	(		self,
			other
	)

Create the Z3 expression `self * other`.

>>> x = Real('x')
>>> y = Real('y')
>>> x * y
x*y
>>> (x * y).sort()
Real

Definition at line 2605 of file z3py.py.

    def __mul__(self, other):
        """Create the Z3 expression `self * other`.
 
        >>> x = Real('x')
        >>> y = Real('y')
        >>> x * y
        x*y
        >>> (x * y).sort()
        Real
        """
        if isinstance(other, BoolRef):
            return If(other, self, 0)
        a, b = _coerce_exprs(self, other)
        return _to_expr_ref(_mk_bin(Z3_mk_mul, a, b), self.ctx)
 

__neg__()

__neg__

(

self

)

Return an expression representing `-self`.

>>> x = Int('x')
>>> -x
-x
>>> simplify(-(-x))
x

Definition at line 2756 of file z3py.py.

    def __neg__(self):
        """Return an expression representing `-self`.
 
        >>> x = Int('x')
        >>> -x
        -x
        >>> simplify(-(-x))
        x
        """
        return _to_expr_ref(Z3_mk_unary_minus(self.ctx_ref(), self.as_ast()), self.ctx)
 

__pos__()

__pos__

(

self

)

Return `self`.

>>> x = Int('x')
>>> +x
x

Definition at line 2767 of file z3py.py.

    def __pos__(self):
        """Return `self`.
 
        >>> x = Int('x')
        >>> +x
        x
        """
        return self
 

__pow__()

__pow__	(		self,
			other
	)

Create the Z3 expression `self**other` (** is the power operator).

>>> x = Real('x')
>>> x**3
x**3
>>> (x**3).sort()
Real
>>> simplify(IntVal(2)**8)
256

Definition at line 2653 of file z3py.py.

    def __pow__(self, other):
        """Create the Z3 expression `self**other` (** is the power operator).
 
        >>> x = Real('x')
        >>> x**3
        x**3
        >>> (x**3).sort()
        Real
        >>> simplify(IntVal(2)**8)
        256
        """
        a, b = _coerce_exprs(self, other)
        return ArithRef(Z3_mk_power(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
 

__radd__()

__radd__	(		self,
			other
	)

Create the Z3 expression `other + self`.

>>> x = Int('x')
>>> 10 + x
10 + x

Definition at line 2595 of file z3py.py.

    def __radd__(self, other):
        """Create the Z3 expression `other + self`.
 
        >>> x = Int('x')
        >>> 10 + x
        10 + x
        """
        a, b = _coerce_exprs(self, other)
        return _to_expr_ref(_mk_bin(Z3_mk_add, b, a), self.ctx)
 

__rdiv__()

__rdiv__	(		self,
			other
	)

Create the Z3 expression `other/self`.

>>> x = Int('x')
>>> 10/x
10/x
>>> (10/x).sexpr()
'(div 10 x)'
>>> x = Real('x')
>>> 10/x
10/x
>>> (10/x).sexpr()
'(/ 10.0 x)'

Definition at line 2708 of file z3py.py.

    def __rdiv__(self, other):
        """Create the Z3 expression `other/self`.
 
        >>> x = Int('x')
        >>> 10/x
        10/x
        >>> (10/x).sexpr()
        '(div 10 x)'
        >>> x = Real('x')
        >>> 10/x
        10/x
        >>> (10/x).sexpr()
        '(/ 10.0 x)'
        """
        a, b = _coerce_exprs(self, other)
        return _to_expr_ref(Z3_mk_div(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
 

Referenced by ArithRef.__rtruediv__(), and BitVecRef.__rtruediv__().

__rmod__()

__rmod__	(		self,
			other
	)

Create the Z3 expression `other%self`.

>>> x = Int('x')
>>> 10 % x
10%x

Definition at line 2744 of file z3py.py.

    def __rmod__(self, other):
        """Create the Z3 expression `other%self`.
 
        >>> x = Int('x')
        >>> 10 % x
        10%x
        """
        a, b = _coerce_exprs(self, other)
        if z3_debug():
            _z3_assert(a.is_int(), "Z3 integer expression expected")
        return ArithRef(Z3_mk_mod(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
 

__rmul__()

__rmul__	(		self,
			other
	)

Create the Z3 expression `other * self`.

>>> x = Real('x')
>>> 10 * x
10*x

Definition at line 2620 of file z3py.py.

    def __rmul__(self, other):
        """Create the Z3 expression `other * self`.
 
        >>> x = Real('x')
        >>> 10 * x
        10*x
        """
        a, b = _coerce_exprs(self, other)
        return _to_expr_ref(_mk_bin(Z3_mk_mul, b, a), self.ctx)
 

__rpow__()

__rpow__	(		self,
			other
	)

Create the Z3 expression `other**self` (** is the power operator).

>>> x = Real('x')
>>> 2**x
2**x
>>> (2**x).sort()
Real
>>> simplify(2**IntVal(8))
256

Definition at line 2667 of file z3py.py.

    def __rpow__(self, other):
        """Create the Z3 expression `other**self` (** is the power operator).
 
        >>> x = Real('x')
        >>> 2**x
        2**x
        >>> (2**x).sort()
        Real
        >>> simplify(2**IntVal(8))
        256
        """
        a, b = _coerce_exprs(self, other)
        return ArithRef(Z3_mk_power(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
 

__rsub__()

__rsub__	(		self,
			other
	)

Create the Z3 expression `other - self`.

>>> x = Int('x')
>>> 10 - x
10 - x

Definition at line 2643 of file z3py.py.

    def __rsub__(self, other):
        """Create the Z3 expression `other - self`.
 
        >>> x = Int('x')
        >>> 10 - x
        10 - x
        """
        a, b = _coerce_exprs(self, other)
        return _to_expr_ref(_mk_bin(Z3_mk_sub, b, a), self.ctx)
 

__rtruediv__()

__rtruediv__	(		self,
			other
	)

Create the Z3 expression `other/self`.

Definition at line 2725 of file z3py.py.

    def __rtruediv__(self, other):
        """Create the Z3 expression `other/self`."""
        return self.__rdiv__(other)
 

__sub__()

__sub__	(		self,
			other
	)

Create the Z3 expression `self - other`.

>>> x = Int('x')
>>> y = Int('y')
>>> x - y
x - y
>>> (x - y).sort()
Int

Definition at line 2630 of file z3py.py.

    def __sub__(self, other):
        """Create the Z3 expression `self - other`.
 
        >>> x = Int('x')
        >>> y = Int('y')
        >>> x - y
        x - y
        >>> (x - y).sort()
        Int
        """
        a, b = _coerce_exprs(self, other)
        return _to_expr_ref(_mk_bin(Z3_mk_sub, a, b), self.ctx)
 

__truediv__()

__truediv__	(		self,
			other
	)

Create the Z3 expression `other/self`.

Definition at line 2704 of file z3py.py.

    def __truediv__(self, other):
        """Create the Z3 expression `other/self`."""
        return self.__div__(other)
 

is_int()

is_int

(

self

)

Return `True` if `self` is an integer expression.

>>> x = Int('x')
>>> x.is_int()
True
>>> (x + 1).is_int()
True
>>> y = Real('y')
>>> (x + y).is_int()
False

Reimplemented in RatNumRef.

Definition at line 2557 of file z3py.py.

    def is_int(self):
        """Return `True` if `self` is an integer expression.
 
        >>> x = Int('x')
        >>> x.is_int()
        True
        >>> (x + 1).is_int()
        True
        >>> y = Real('y')
        >>> (x + y).is_int()
        False
        """
        return self.sort().is_int()
 

Referenced by IntNumRef.as_long(), ArithRef.is_int(), and ArithSortRef.subsort().

is_real()

is_real

(

self

)

Return `True` if `self` is an real expression.

>>> x = Real('x')
>>> x.is_real()
True
>>> (x + 1).is_real()
True

Reimplemented in RatNumRef.

Definition at line 2571 of file z3py.py.

    def is_real(self):
        """Return `True` if `self` is an real expression.
 
        >>> x = Real('x')
        >>> x.is_real()
        True
        >>> (x + 1).is_real()
        True
        """
        return self.sort().is_real()
 

Referenced by ArithRef.is_real().

sort()

sort

(

self

)

Return the sort (type) of the arithmetical expression `self`.

>>> Int('x').sort()
Int
>>> (Real('x') + 1).sort()
Real

Reimplemented from ExprRef.

Reimplemented in ComplexRef.

Definition at line 2547 of file z3py.py.

    def sort(self):
        """Return the sort (type) of the arithmetical expression `self`.
 
        >>> Int('x').sort()
        Int
        >>> (Real('x') + 1).sort()
        Real
        """
        return ArithSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
 

Referenced by ArrayRef.domain(), ArrayRef.domain_n(), ArithRef.is_int(), ArithRef.is_real(), ArrayRef.range(), BitVecRef.size(), and ExprRef.sort_kind().

Field Documentation

ctx

ctx

Definition at line 2555 of file z3py.py.

Referenced by ArithRef.__add__(), BitVecRef.__add__(), BitVecRef.__and__(), FuncDeclRef.__call__(), AstMap.__contains__(), AstRef.__copy__(), Goal.__copy__(), AstVector.__copy__(), FuncInterp.__copy__(), ModelRef.__copy__(), AstRef.__deepcopy__(), Datatype.__deepcopy__(), ParamsRef.__deepcopy__(), ParamDescrsRef.__deepcopy__(), Goal.__deepcopy__(), AstVector.__deepcopy__(), AstMap.__deepcopy__(), FuncEntry.__deepcopy__(), FuncInterp.__deepcopy__(), ModelRef.__deepcopy__(), Statistics.__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__(), ArithRef.__div__(), BitVecRef.__div__(), ExprRef.__eq__(), ArithRef.__ge__(), BitVecRef.__ge__(), AstVector.__getitem__(), ModelRef.__getitem__(), Statistics.__getitem__(), AstMap.__getitem__(), ArithRef.__gt__(), BitVecRef.__gt__(), BitVecRef.__invert__(), ArithRef.__le__(), BitVecRef.__le__(), AstVector.__len__(), AstMap.__len__(), ModelRef.__len__(), Statistics.__len__(), BitVecRef.__lshift__(), ArithRef.__lt__(), BitVecRef.__lt__(), ArithRef.__mod__(), BitVecRef.__mod__(), BoolRef.__mul__(), ArithRef.__mul__(), BitVecRef.__mul__(), ExprRef.__ne__(), ArithRef.__neg__(), BitVecRef.__neg__(), BitVecRef.__or__(), ArithRef.__pow__(), ArithRef.__radd__(), BitVecRef.__radd__(), BitVecRef.__rand__(), ArithRef.__rdiv__(), BitVecRef.__rdiv__(), ParamsRef.__repr__(), ParamDescrsRef.__repr__(), AstMap.__repr__(), Statistics.__repr__(), BitVecRef.__rlshift__(), ArithRef.__rmod__(), BitVecRef.__rmod__(), ArithRef.__rmul__(), BitVecRef.__rmul__(), BitVecRef.__ror__(), ArithRef.__rpow__(), BitVecRef.__rrshift__(), BitVecRef.__rshift__(), ArithRef.__rsub__(), BitVecRef.__rsub__(), BitVecRef.__rxor__(), AstVector.__setitem__(), AstMap.__setitem__(), ArithRef.__sub__(), BitVecRef.__sub__(), BitVecRef.__xor__(), DatatypeSortRef.accessor(), ExprRef.arg(), FuncEntry.arg_value(), FuncInterp.arity(), Goal.as_expr(), Solver.assert_and_track(), Goal.assert_exprs(), Solver.assert_exprs(), QuantifierRef.body(), FiniteSetSortRef.cast(), Solver.check(), Goal.convert_model(), AstRef.ctx_ref(), ExprRef.decl(), ModelRef.decls(), ArrayRef.default(), RatNumRef.denominator(), Goal.depth(), Goal.dimacs(), FuncDeclRef.domain(), ArraySortRef.domain_n(), FuncInterp.else_value(), FuncInterp.entry(), AstMap.erase(), ModelRef.eval(), Goal.get(), ParamDescrsRef.get_documentation(), ModelRef.get_interp(), Statistics.get_key_value(), ParamDescrsRef.get_kind(), ParamDescrsRef.get_name(), ModelRef.get_sort(), ModelRef.get_universe(), Goal.inconsistent(), AstMap.keys(), Statistics.keys(), Solver.model(), SortRef.name(), QuantifierRef.no_pattern(), FuncEntry.num_args(), FuncInterp.num_entries(), Solver.num_scopes(), ModelRef.num_sorts(), FuncDeclRef.params(), QuantifierRef.pattern(), AlgebraicNumRef.poly(), Solver.pop(), Goal.prec(), ModelRef.project(), ModelRef.project_with_witness(), Solver.push(), AstVector.push(), QuantifierRef.qid(), FuncDeclRef.range(), ArraySortRef.range(), DatatypeSortRef.recognizer(), Context.ref(), AstMap.reset(), Solver.reset(), AstVector.resize(), Solver.set(), ParamsRef.set(), Goal.sexpr(), AstVector.sexpr(), ModelRef.sexpr(), ParamDescrsRef.size(), Goal.size(), QuantifierRef.skolem_id(), AstVector.translate(), AstRef.translate(), Goal.translate(), ModelRef.translate(), ExprRef.update(), DatatypeRef.update_field(), ParamsRef.validate(), FuncEntry.value(), QuantifierRef.var_name(), and QuantifierRef.var_sort().