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)
 
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

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 961 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 1001 of file z3py.py.

1001 def __eq__(self, other):
1002 """Return a Z3 expression that represents the constraint `self == other`.
1003
1004 If `other` is `None`, then this method simply returns `False`.
1005
1006 >>> a = Int('a')
1007 >>> b = Int('b')
1008 >>> a == b
1009 a == b
1010 >>> a is None
1011 False
1012 """
1013 if other is None:
1014 return False
1015 a, b = _coerce_exprs(self, other)
1016 return BoolRef(Z3_mk_eq(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
1017
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.
def Int(name, ctx=None)
Definition: z3py.py:3239

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

◆ __hash__()

def __hash__ (   self)
 Hash code. 

Reimplemented from AstRef.

Definition at line 1018 of file z3py.py.

1018 def __hash__(self):
1019 """ Hash code. """
1020 return AstRef.__hash__(self)
1021

◆ __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 1022 of file z3py.py.

1022 def __ne__(self, other):
1023 """Return a Z3 expression that represents the constraint `self != other`.
1024
1025 If `other` is `None`, then this method simply returns `True`.
1026
1027 >>> a = Int('a')
1028 >>> b = Int('b')
1029 >>> a != b
1030 a != b
1031 >>> a is not None
1032 True
1033 """
1034 if other is None:
1035 return True
1036 a, b = _coerce_exprs(self, other)
1037 _args, sz = _to_ast_array((a, b))
1038 return BoolRef(Z3_mk_distinct(self.ctx_ref(), 2, _args), self.ctx)
1039
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 1074 of file z3py.py.

1074 def arg(self, idx):
1075 """Return argument `idx` of the application `self`.
1076
1077 This method assumes that `self` is a function application with at least `idx+1` arguments.
1078
1079 >>> a = Int('a')
1080 >>> b = Int('b')
1081 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1082 >>> t = f(a, b, 0)
1083 >>> t.arg(0)
1084 a
1085 >>> t.arg(1)
1086 b
1087 >>> t.arg(2)
1088 0
1089 """
1090 if z3_debug():
1091 _z3_assert(is_app(self), "Z3 application expected")
1092 _z3_assert(idx < self.num_args(), "Invalid argument index")
1093 return _to_expr_ref(Z3_get_app_arg(self.ctx_ref(), self.as_ast(), idx), self.ctx)
1094
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.
def is_app(a)
Definition: z3py.py:1260
def z3_debug()
Definition: z3py.py:62
def Function(name, *sig)
Definition: z3py.py:863
def IntSort(ctx=None)
Definition: z3py.py:3129

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 972 of file z3py.py.

972 def as_ast(self):
973 return self.ast
974

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().

◆ 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 1095 of file z3py.py.

1095 def children(self):
1096 """Return a list containing the children of the given expression
1097
1098 >>> a = Int('a')
1099 >>> b = Int('b')
1100 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1101 >>> t = f(a, b, 0)
1102 >>> t.children()
1103 [a, b, 0]
1104 """
1105 if is_app(self):
1106 return [self.arg(i) for i in range(self.num_args())]
1107 else:
1108 return []
1109
expr range(expr const &lo, expr const &hi)
Definition: z3++.h:3946

◆ 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 1043 of file z3py.py.

1043 def decl(self):
1044 """Return the Z3 function declaration associated with a Z3 application.
1045
1046 >>> f = Function('f', IntSort(), IntSort())
1047 >>> a = Int('a')
1048 >>> t = f(a)
1049 >>> eq(t.decl(), f)
1050 True
1051 >>> (a + 1).decl()
1052 +
1053 """
1054 if z3_debug():
1055 _z3_assert(is_app(self), "Z3 application expected")
1056 return FuncDeclRef(Z3_get_app_decl(self.ctx_ref(), self.as_ast()), self.ctx)
1057
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.
def eq(a, b)
Definition: z3py.py:472

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

◆ from_string()

def from_string (   self,
  s 
)

Definition at line 1110 of file z3py.py.

1110 def from_string(self, s):
1111 pass
1112

◆ 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 975 of file z3py.py.

975 def get_id(self):
976 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
977
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 1058 of file z3py.py.

1058 def num_args(self):
1059 """Return the number of arguments of a Z3 application.
1060
1061 >>> a = Int('a')
1062 >>> b = Int('b')
1063 >>> (a + b).num_args()
1064 2
1065 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1066 >>> t = f(a, b, 0)
1067 >>> t.num_args()
1068 3
1069 """
1070 if z3_debug():
1071 _z3_assert(is_app(self), "Z3 application expected")
1072 return int(Z3_get_app_num_args(self.ctx_ref(), self.as_ast()))
1073
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 1040 of file z3py.py.

1040 def params(self):
1041 return self.decl().params()
1042

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

◆ serialize()

def serialize (   self)

Definition at line 1113 of file z3py.py.

1113 def serialize(self):
1114 s = Solver()
1115 f = Function('F', self.sort(), BoolSort(self.ctx))
1116 s.add(f(self))
1117 return s.sexpr()
1118
def BoolSort(ctx=None)
Definition: z3py.py:1682

◆ 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 978 of file z3py.py.

978 def sort(self):
979 """Return the sort of expression `self`.
980
981 >>> x = Int('x')
982 >>> (x + 1).sort()
983 Int
984 >>> y = Real('y')
985 >>> (x + y).sort()
986 Real
987 """
988 return _sort(self.ctx, self.as_ast())
989
def Real(name, ctx=None)
Definition: z3py.py:3292

Referenced by FPNumRef.as_string(), ArrayRef.domain(), ArrayRef.domain_n(), 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 990 of file z3py.py.

990 def sort_kind(self):
991 """Shorthand for `self.sort().kind()`.
992
993 >>> a = Array('a', IntSort(), IntSort())
994 >>> a.sort_kind() == Z3_ARRAY_SORT
995 True
996 >>> a.sort_kind() == Z3_INT_SORT
997 False
998 """
999 return self.sort().kind()
1000
def Array(name, *sorts)
Definition: z3py.py:4724