Z3
Public Member Functions
ArithRef Class Reference
+ Inheritance diagram for ArithRef:

Public Member Functions

def sort (self)
 
def is_int (self)
 
def is_real (self)
 
def __add__ (self, other)
 
def __radd__ (self, other)
 
def __mul__ (self, other)
 
def __rmul__ (self, other)
 
def __sub__ (self, other)
 
def __rsub__ (self, other)
 
def __pow__ (self, other)
 
def __rpow__ (self, other)
 
def __div__ (self, other)
 
def __truediv__ (self, other)
 
def __rdiv__ (self, other)
 
def __rtruediv__ (self, other)
 
def __mod__ (self, other)
 
def __rmod__ (self, other)
 
def __neg__ (self)
 
def __pos__ (self)
 
def __le__ (self, other)
 
def __lt__ (self, other)
 
def __gt__ (self, other)
 
def __ge__ (self, other)
 
- Public Member Functions inherited from ExprRef
def as_ast (self)
 
def get_id (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 __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

Integer and Real expressions.

Definition at line 2342 of file z3py.py.

Member Function Documentation

◆ __add__()

def __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 2380 of file z3py.py.

2380  def __add__(self, other):
2381  """Create the Z3 expression `self + other`.
2382 
2383  >>> x = Int('x')
2384  >>> y = Int('y')
2385  >>> x + y
2386  x + y
2387  >>> (x + y).sort()
2388  Int
2389  """
2390  a, b = _coerce_exprs(self, other)
2391  return ArithRef(_mk_bin(Z3_mk_add, a, b), self.ctx)
2392 

◆ __div__()

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)'

Definition at line 2479 of file z3py.py.

2479  def __div__(self, other):
2480  """Create the Z3 expression `other/self`.
2481 
2482  >>> x = Int('x')
2483  >>> y = Int('y')
2484  >>> x/y
2485  x/y
2486  >>> (x/y).sort()
2487  Int
2488  >>> (x/y).sexpr()
2489  '(div x y)'
2490  >>> x = Real('x')
2491  >>> y = Real('y')
2492  >>> x/y
2493  x/y
2494  >>> (x/y).sort()
2495  Real
2496  >>> (x/y).sexpr()
2497  '(/ x y)'
2498  """
2499  a, b = _coerce_exprs(self, other)
2500  return ArithRef(Z3_mk_div(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2501 
Z3_ast Z3_API Z3_mk_div(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 div arg2.

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

◆ __ge__()

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

Definition at line 2613 of file z3py.py.

2613  def __ge__(self, other):
2614  """Create the Z3 expression `other >= self`.
2615 
2616  >>> x, y = Ints('x y')
2617  >>> x >= y
2618  x >= y
2619  >>> y = Real('y')
2620  >>> x >= y
2621  ToReal(x) >= y
2622  """
2623  a, b = _coerce_exprs(self, other)
2624  return BoolRef(Z3_mk_ge(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2625 
2626 
Z3_ast Z3_API Z3_mk_ge(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than or equal to.

◆ __gt__()

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

Definition at line 2600 of file z3py.py.

2600  def __gt__(self, other):
2601  """Create the Z3 expression `other > self`.
2602 
2603  >>> x, y = Ints('x y')
2604  >>> x > y
2605  x > y
2606  >>> y = Real('y')
2607  >>> x > y
2608  ToReal(x) > y
2609  """
2610  a, b = _coerce_exprs(self, other)
2611  return BoolRef(Z3_mk_gt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2612 
Z3_ast Z3_API Z3_mk_gt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create greater than.

◆ __le__()

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

Definition at line 2574 of file z3py.py.

2574  def __le__(self, other):
2575  """Create the Z3 expression `other <= self`.
2576 
2577  >>> x, y = Ints('x y')
2578  >>> x <= y
2579  x <= y
2580  >>> y = Real('y')
2581  >>> x <= y
2582  ToReal(x) <= y
2583  """
2584  a, b = _coerce_exprs(self, other)
2585  return BoolRef(Z3_mk_le(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2586 
Z3_ast Z3_API Z3_mk_le(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than or equal to.

◆ __lt__()

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

Definition at line 2587 of file z3py.py.

2587  def __lt__(self, other):
2588  """Create the Z3 expression `other < self`.
2589 
2590  >>> x, y = Ints('x y')
2591  >>> x < y
2592  x < y
2593  >>> y = Real('y')
2594  >>> x < y
2595  ToReal(x) < y
2596  """
2597  a, b = _coerce_exprs(self, other)
2598  return BoolRef(Z3_mk_lt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2599 
Z3_ast Z3_API Z3_mk_lt(Z3_context c, Z3_ast t1, Z3_ast t2)
Create less than.

◆ __mod__()

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

Definition at line 2527 of file z3py.py.

2527  def __mod__(self, other):
2528  """Create the Z3 expression `other%self`.
2529 
2530  >>> x = Int('x')
2531  >>> y = Int('y')
2532  >>> x % y
2533  x%y
2534  >>> simplify(IntVal(10) % IntVal(3))
2535  1
2536  """
2537  a, b = _coerce_exprs(self, other)
2538  if z3_debug():
2539  _z3_assert(a.is_int(), "Z3 integer expression expected")
2540  return ArithRef(Z3_mk_mod(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2541 
def z3_debug()
Definition: z3py.py:64
Z3_ast Z3_API Z3_mk_mod(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 mod arg2.

◆ __mul__()

def __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 2403 of file z3py.py.

2403  def __mul__(self, other):
2404  """Create the Z3 expression `self * other`.
2405 
2406  >>> x = Real('x')
2407  >>> y = Real('y')
2408  >>> x * y
2409  x*y
2410  >>> (x * y).sort()
2411  Real
2412  """
2413  if isinstance(other, BoolRef):
2414  return If(other, self, 0)
2415  a, b = _coerce_exprs(self, other)
2416  return ArithRef(_mk_bin(Z3_mk_mul, a, b), self.ctx)
2417 
def If(a, b, c, ctx=None)
Definition: z3py.py:1349

◆ __neg__()

def __neg__ (   self)
Return an expression representing `-self`.

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

Definition at line 2554 of file z3py.py.

2554  def __neg__(self):
2555  """Return an expression representing `-self`.
2556 
2557  >>> x = Int('x')
2558  >>> -x
2559  -x
2560  >>> simplify(-(-x))
2561  x
2562  """
2563  return ArithRef(Z3_mk_unary_minus(self.ctx_ref(), self.as_ast()), self.ctx)
2564 
Z3_ast Z3_API Z3_mk_unary_minus(Z3_context c, Z3_ast arg)
Create an AST node representing - arg.

◆ __pos__()

def __pos__ (   self)
Return `self`.

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

Definition at line 2565 of file z3py.py.

2565  def __pos__(self):
2566  """Return `self`.
2567 
2568  >>> x = Int('x')
2569  >>> +x
2570  x
2571  """
2572  return self
2573 

◆ __pow__()

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

Definition at line 2451 of file z3py.py.

2451  def __pow__(self, other):
2452  """Create the Z3 expression `self**other` (** is the power operator).
2453 
2454  >>> x = Real('x')
2455  >>> x**3
2456  x**3
2457  >>> (x**3).sort()
2458  Real
2459  >>> simplify(IntVal(2)**8)
2460  256
2461  """
2462  a, b = _coerce_exprs(self, other)
2463  return ArithRef(Z3_mk_power(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2464 
Z3_ast Z3_API Z3_mk_power(Z3_context c, Z3_ast arg1, Z3_ast arg2)
Create an AST node representing arg1 ^ arg2.

◆ __radd__()

def __radd__ (   self,
  other 
)
Create the Z3 expression `other + self`.

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

Definition at line 2393 of file z3py.py.

2393  def __radd__(self, other):
2394  """Create the Z3 expression `other + self`.
2395 
2396  >>> x = Int('x')
2397  >>> 10 + x
2398  10 + x
2399  """
2400  a, b = _coerce_exprs(self, other)
2401  return ArithRef(_mk_bin(Z3_mk_add, b, a), self.ctx)
2402 

◆ __rdiv__()

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)'

Definition at line 2506 of file z3py.py.

2506  def __rdiv__(self, other):
2507  """Create the Z3 expression `other/self`.
2508 
2509  >>> x = Int('x')
2510  >>> 10/x
2511  10/x
2512  >>> (10/x).sexpr()
2513  '(div 10 x)'
2514  >>> x = Real('x')
2515  >>> 10/x
2516  10/x
2517  >>> (10/x).sexpr()
2518  '(/ 10.0 x)'
2519  """
2520  a, b = _coerce_exprs(self, other)
2521  return ArithRef(Z3_mk_div(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2522 

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

◆ __rmod__()

def __rmod__ (   self,
  other 
)
Create the Z3 expression `other%self`.

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

Definition at line 2542 of file z3py.py.

2542  def __rmod__(self, other):
2543  """Create the Z3 expression `other%self`.
2544 
2545  >>> x = Int('x')
2546  >>> 10 % x
2547  10%x
2548  """
2549  a, b = _coerce_exprs(self, other)
2550  if z3_debug():
2551  _z3_assert(a.is_int(), "Z3 integer expression expected")
2552  return ArithRef(Z3_mk_mod(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2553 

◆ __rmul__()

def __rmul__ (   self,
  other 
)
Create the Z3 expression `other * self`.

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

Definition at line 2418 of file z3py.py.

2418  def __rmul__(self, other):
2419  """Create the Z3 expression `other * self`.
2420 
2421  >>> x = Real('x')
2422  >>> 10 * x
2423  10*x
2424  """
2425  a, b = _coerce_exprs(self, other)
2426  return ArithRef(_mk_bin(Z3_mk_mul, b, a), self.ctx)
2427 

◆ __rpow__()

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

Definition at line 2465 of file z3py.py.

2465  def __rpow__(self, other):
2466  """Create the Z3 expression `other**self` (** is the power operator).
2467 
2468  >>> x = Real('x')
2469  >>> 2**x
2470  2**x
2471  >>> (2**x).sort()
2472  Real
2473  >>> simplify(2**IntVal(8))
2474  256
2475  """
2476  a, b = _coerce_exprs(self, other)
2477  return ArithRef(Z3_mk_power(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2478 

◆ __rsub__()

def __rsub__ (   self,
  other 
)
Create the Z3 expression `other - self`.

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

Definition at line 2441 of file z3py.py.

2441  def __rsub__(self, other):
2442  """Create the Z3 expression `other - self`.
2443 
2444  >>> x = Int('x')
2445  >>> 10 - x
2446  10 - x
2447  """
2448  a, b = _coerce_exprs(self, other)
2449  return ArithRef(_mk_bin(Z3_mk_sub, b, a), self.ctx)
2450 

◆ __rtruediv__()

def __rtruediv__ (   self,
  other 
)
Create the Z3 expression `other/self`.

Definition at line 2523 of file z3py.py.

2523  def __rtruediv__(self, other):
2524  """Create the Z3 expression `other/self`."""
2525  return self.__rdiv__(other)
2526 

◆ __sub__()

def __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 2428 of file z3py.py.

2428  def __sub__(self, other):
2429  """Create the Z3 expression `self - other`.
2430 
2431  >>> x = Int('x')
2432  >>> y = Int('y')
2433  >>> x - y
2434  x - y
2435  >>> (x - y).sort()
2436  Int
2437  """
2438  a, b = _coerce_exprs(self, other)
2439  return ArithRef(_mk_bin(Z3_mk_sub, a, b), self.ctx)
2440 

◆ __truediv__()

def __truediv__ (   self,
  other 
)
Create the Z3 expression `other/self`.

Definition at line 2502 of file z3py.py.

2502  def __truediv__(self, other):
2503  """Create the Z3 expression `other/self`."""
2504  return self.__div__(other)
2505 

◆ is_int()

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

Reimplemented in RatNumRef.

Definition at line 2355 of file z3py.py.

2355  def is_int(self):
2356  """Return `True` if `self` is an integer expression.
2357 
2358  >>> x = Int('x')
2359  >>> x.is_int()
2360  True
2361  >>> (x + 1).is_int()
2362  True
2363  >>> y = Real('y')
2364  >>> (x + y).is_int()
2365  False
2366  """
2367  return self.sort().is_int()
2368 
def is_int(a)
Definition: z3py.py:2648

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

◆ is_real()

def 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 2369 of file z3py.py.

2369  def is_real(self):
2370  """Return `True` if `self` is an real expression.
2371 
2372  >>> x = Real('x')
2373  >>> x.is_real()
2374  True
2375  >>> (x + 1).is_real()
2376  True
2377  """
2378  return self.sort().is_real()
2379 
def is_real(a)
Definition: z3py.py:2667

◆ sort()

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

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

Reimplemented from ExprRef.

Definition at line 2345 of file z3py.py.

2345  def sort(self):
2346  """Return the sort (type) of the arithmetical expression `self`.
2347 
2348  >>> Int('x').sort()
2349  Int
2350  >>> (Real('x') + 1).sort()
2351  Real
2352  """
2353  return ArithSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
2354 
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.

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