Z3 |

Public Member Functions
ExprRef Class Reference

Expressions. More...

Inheritance diagram for ExprRef:

## Public Member Functions
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)
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

Expressions.

    Constraints, formulas and terms are expressions in Z3.

    Expressions are ASTs. Every expression has a sort.
    There are three main kinds of expressions:
    function applications, quantifiers and bounded variables.
    A constant is a function application with 0 arguments.
    For quantifier free problems, all expressions are
    function applications.

Definition at line 958 of file z3py.py.

## Member Function Documentation

## ◆ __eq__()

def __eq__ | ( |  | self,
|  |  | other
| ) |  |

    Return a Z3 expression that represents the constraint `self == other`.

    If `other` is `None`, then this method simply returns `False`.

    >>> a = Int('a')
    >>> b = Int('b')
    >>> a == b
    a == b
    >>> a is None
    False

Reimplemented from AstRef.

Definition at line 998 of file z3py.py.

998 def __eq__(self, other):
999 """Return a Z3 expression that represents the constraint `self == other`.
1000
1001 If `other` is `None`, then this method simply returns `False`.
1002
1003 >>> a = Int('a')
1004 >>> b = Int('b')
1005 >>> a == b
1006 a == b
1007 >>> a is None
1008 False
1009 """
1010 if other is None:
1011 return False
1012 a, b = _coerce_exprs(self, other)
1013 return BoolRef(Z3_mk_eq(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
1014
z3py.Int
def Int(name, ctx=None)
Definition: z3py.py:3210
Z3_mk_eq
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.

Referenced by CheckSatResult.__ne__(), and Probe.__ne__().

## ◆ __hash__()

def __hash__ | ( |  | self | ) |

     Hash code.

Reimplemented from AstRef.

Definition at line 1015 of file z3py.py.

1015 def __hash__(self):
1016 """ Hash code. """
1017 return AstRef.__hash__(self)
1018

## ◆ __ne__()

def __ne__ | ( |  | self,
|  |  | other
| ) |  |

    Return a Z3 expression that represents the constraint `self != other`.

    If `other` is `None`, then this method simply returns `True`.

    >>> a = Int('a')
    >>> b = Int('b')
    >>> a != b
    a != b
    >>> a is not None
    True

Definition at line 1019 of file z3py.py.

1019 def __ne__(self, other):
1020 """Return a Z3 expression that represents the constraint `self != other`.
1021
1022 If `other` is `None`, then this method simply returns `True`.
1023
1024 >>> a = Int('a')
1025 >>> b = Int('b')
1026 >>> a != b
1027 a != b
1028 >>> a is not None
1029 True
1030 """
1031 if other is None:
1032 return True
1033 a, b = _coerce_exprs(self, other)
1034 _args, sz = _to_ast_array((a, b))
1035 return BoolRef(Z3_mk_distinct(self.ctx_ref(), 2, _args), self.ctx)
1036
Z3_mk_distinct
Z3_ast Z3_API Z3_mk_distinct(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing distinct(args[0], ..., args[num_args-1]).

## ◆ arg()

def arg | ( |  | self,
|  |  | idx
| ) |  |

    Return argument `idx` of the application `self`.

    This method assumes that `self` is a function application with at least `idx+1` arguments.

    >>> a = Int('a')
    >>> b = Int('b')
    >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
    >>> t = f(a, b, 0)
    >>> t.arg(0)
    a
    >>> t.arg(1)
    b
    >>> t.arg(2)
    0

Definition at line 1071 of file z3py.py.

1071 def arg(self, idx):
1072 """Return argument `idx` of the application `self`.
1073
1074 This method assumes that `self` is a function application with at least `idx+1` arguments.
1075
1076 >>> a = Int('a')
1077 >>> b = Int('b')
1078 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1079 >>> t = f(a, b, 0)
1080 >>> t.arg(0)
1081 a
1082 >>> t.arg(1)
1083 b
1084 >>> t.arg(2)
1085 0
1086 """
1087 if z3_debug():
1088 _z3_assert(is_app(self), "Z3 application expected")
1089 _z3_assert(idx < self.num_args(), "Invalid argument index")
1090 return _to_expr_ref(Z3_get_app_arg(self.ctx_ref(), self.as_ast(), idx), self.ctx)
1091
z3py.z3_debug
def z3_debug()
Definition: z3py.py:64
z3py.IntSort
def IntSort(ctx=None)
Definition: z3py.py:3100
z3py.Function
def Function(name, *sig)
Definition: z3py.py:860
z3py.is_app
def is_app(a)
Definition: z3py.py:1233
Z3_get_app_arg
Z3_ast Z3_API Z3_get_app_arg(Z3_context c, Z3_app a, unsigned i)
Return the i-th argument of the given application.

Referenced by AstRef.__bool__(), and ExprRef.children().

## ◆ as_ast()

def as_ast | ( |  | self | ) |

    Return a pointer to the corresponding C Z3_ast object.

Reimplemented from AstRef.

Reimplemented in PatternRef, and QuantifierRef.

Definition at line 969 of file z3py.py.

969 def as_ast(self):
970 return self.ast
971

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().

## ◆ children()

def children | ( |  | self | ) |

    Return a list containing the children of the given expression

    >>> a = Int('a')
    >>> b = Int('b')
    >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
    >>> t = f(a, b, 0)
    >>> t.children()
    [a, b, 0]

Reimplemented in QuantifierRef.

Definition at line 1092 of file z3py.py.

1092 def children(self):
1093 """Return a list containing the children of the given expression
1094
1095 >>> a = Int('a')
1096 >>> b = Int('b')
1097 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1098 >>> t = f(a, b, 0)
1099 >>> t.children()
1100 [a, b, 0]
1101 """
1102 if is_app(self):
1103 return [self.arg(i) for i in range(self.num_args())]
1104 else:
1105 return []
1106
1107
z3::range
expr range(expr const &lo, expr const &hi)
Definition: z3++.h:3725

## ◆ decl()

def decl | ( |  | self | ) |

    Return the Z3 function declaration associated with a Z3 application.

    >>> f = Function('f', IntSort(), IntSort())
    >>> a = Int('a')
    >>> t = f(a)
    >>> eq(t.decl(), f)
    True
    >>> (a + 1).decl()
    +

Definition at line 1040 of file z3py.py.

1040 def decl(self):
1041 """Return the Z3 function declaration associated with a Z3 application.
1042
1043 >>> f = Function('f', IntSort(), IntSort())
1044 >>> a = Int('a')
1045 >>> t = f(a)
1046 >>> eq(t.decl(), f)
1047 True
1048 >>> (a + 1).decl()
1049 +
1050 """
1051 if z3_debug():
1052 _z3_assert(is_app(self), "Z3 application expected")
1053 return FuncDeclRef(Z3_get_app_decl(self.ctx_ref(), self.as_ast()), self.ctx)
1054
z3py.eq
def eq(a, b)
Definition: z3py.py:471
Z3_get_app_decl
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.

Referenced by ExprRef.decl(), and ExprRef.params().

## ◆ get_id()

def get_id | ( |  | self | ) |

    Return unique identifier for object. It can be used for hash-tables and maps.

Reimplemented from AstRef.

Reimplemented in PatternRef, and QuantifierRef.

Definition at line 972 of file z3py.py.

972 def get_id(self):
973 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
974
Z3_get_ast_id
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....

## ◆ num_args()

def num_args | ( |  | self | ) |

    Return the number of arguments of a Z3 application.

    >>> a = Int('a')
    >>> b = Int('b')
    >>> (a + b).num_args()
    2
    >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
    >>> t = f(a, b, 0)
    >>> t.num_args()
    3

Definition at line 1055 of file z3py.py.

1055 def num_args(self):
1056 """Return the number of arguments of a Z3 application.
1057
1058 >>> a = Int('a')
1059 >>> b = Int('b')
1060 >>> (a + b).num_args()
1061 2
1062 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1063 >>> t = f(a, b, 0)
1064 >>> t.num_args()
1065 3
1066 """
1067 if z3_debug():
1068 _z3_assert(is_app(self), "Z3 application expected")
1069 return int(Z3_get_app_num_args(self.ctx_ref(), self.as_ast()))
1070
Z3_get_app_num_args
unsigned Z3_API Z3_get_app_num_args(Z3_context c, Z3_app a)
Return the number of argument of an application. If t is an constant, then the number of arguments is...

Referenced by AstRef.__bool__(), ExprRef.arg(), FuncEntry.arg_value(), FuncEntry.as_list(), ExprRef.children(), and ExprRef.num_args().

## ◆ params()

def params | ( |  | self | ) |

Definition at line 1037 of file z3py.py.

1037 def params(self):
1038 return self.decl().params()
1039

Referenced by ParamsRef.__deepcopy__(), ParamsRef.__del__(), ParamsRef.__repr__(), ExprRef.params(), ParamsRef.set(), and ParamsRef.validate().

## ◆ sort()

def sort | ( |  | self | ) |

    Return the sort of expression `self`.

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

Reimplemented in BoolRef, QuantifierRef, ArithRef, BitVecRef, ArrayRef, DatatypeRef, FiniteDomainRef, FPRef, and SeqRef.

Definition at line 975 of file z3py.py.

975 def sort(self):
976 """Return the sort of expression `self`.
977
978 >>> x = Int('x')
979 >>> (x + 1).sort()
980 Int
981 >>> y = Real('y')
982 >>> (x + y).sort()
983 Real
984 """
985 return _sort(self.ctx, self.as_ast())
986
z3py.Real
def Real(name, ctx=None)
Definition: z3py.py:3263

Referenced by QuantifierRef.__getitem__(), FPNumRef.as_string(), ArrayRef.domain(), FPRef.ebits(), ArithRef.is_int(), ArithRef.is_real(), ArrayRef.range(), FPRef.sbits(), BitVecRef.size(), ExprRef.sort(), and ExprRef.sort_kind().

## ◆ sort_kind()

def sort_kind | ( |  | self | ) |

    Shorthand for `self.sort().kind()`.

    >>> a = Array('a', IntSort(), IntSort())
    >>> a.sort_kind() == Z3_ARRAY_SORT
    True
    >>> a.sort_kind() == Z3_INT_SORT
    False

Definition at line 987 of file z3py.py.

987 def sort_kind(self):
988 """Shorthand for `self.sort().kind()`.
989
990 >>> a = Array('a', IntSort(), IntSort())
991 >>> a.sort_kind() == Z3_ARRAY_SORT
992 True
993 >>> a.sort_kind() == Z3_INT_SORT
994 False
995 """
996 return self.sort().kind()
997
z3py.Array
def Array(name, dom, rng)
Definition: z3py.py:4678