Z3
 
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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 (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
 
- Protected Member Functions inherited from Z3PPObject
def _repr_html_ (self)
 

Detailed Description

Integer and Real expressions.

Definition at line 2376 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 2414 of file z3py.py.

2414 def __add__(self, other):
2415 """Create the Z3 expression `self + other`.
2416
2417 >>> x = Int('x')
2418 >>> y = Int('y')
2419 >>> x + y
2420 x + y
2421 >>> (x + y).sort()
2422 Int
2423 """
2424 a, b = _coerce_exprs(self, other)
2425 return ArithRef(_mk_bin(Z3_mk_add, a, b), self.ctx)
2426

◆ __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 2513 of file z3py.py.

2513 def __div__(self, other):
2514 """Create the Z3 expression `other/self`.
2515
2516 >>> x = Int('x')
2517 >>> y = Int('y')
2518 >>> x/y
2519 x/y
2520 >>> (x/y).sort()
2521 Int
2522 >>> (x/y).sexpr()
2523 '(div x y)'
2524 >>> x = Real('x')
2525 >>> y = Real('y')
2526 >>> x/y
2527 x/y
2528 >>> (x/y).sort()
2529 Real
2530 >>> (x/y).sexpr()
2531 '(/ x y)'
2532 """
2533 a, b = _coerce_exprs(self, other)
2534 return ArithRef(Z3_mk_div(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2535
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 2647 of file z3py.py.

2647 def __ge__(self, other):
2648 """Create the Z3 expression `other >= self`.
2649
2650 >>> x, y = Ints('x y')
2651 >>> x >= y
2652 x >= y
2653 >>> y = Real('y')
2654 >>> x >= y
2655 ToReal(x) >= y
2656 """
2657 a, b = _coerce_exprs(self, other)
2658 return BoolRef(Z3_mk_ge(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2659
2660
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 2634 of file z3py.py.

2634 def __gt__(self, other):
2635 """Create the Z3 expression `other > self`.
2636
2637 >>> x, y = Ints('x y')
2638 >>> x > y
2639 x > y
2640 >>> y = Real('y')
2641 >>> x > y
2642 ToReal(x) > y
2643 """
2644 a, b = _coerce_exprs(self, other)
2645 return BoolRef(Z3_mk_gt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2646
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 2608 of file z3py.py.

2608 def __le__(self, other):
2609 """Create the Z3 expression `other <= self`.
2610
2611 >>> x, y = Ints('x y')
2612 >>> x <= y
2613 x <= y
2614 >>> y = Real('y')
2615 >>> x <= y
2616 ToReal(x) <= y
2617 """
2618 a, b = _coerce_exprs(self, other)
2619 return BoolRef(Z3_mk_le(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2620
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 2621 of file z3py.py.

2621 def __lt__(self, other):
2622 """Create the Z3 expression `other < self`.
2623
2624 >>> x, y = Ints('x y')
2625 >>> x < y
2626 x < y
2627 >>> y = Real('y')
2628 >>> x < y
2629 ToReal(x) < y
2630 """
2631 a, b = _coerce_exprs(self, other)
2632 return BoolRef(Z3_mk_lt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2633
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 2561 of file z3py.py.

2561 def __mod__(self, other):
2562 """Create the Z3 expression `other%self`.
2563
2564 >>> x = Int('x')
2565 >>> y = Int('y')
2566 >>> x % y
2567 x%y
2568 >>> simplify(IntVal(10) % IntVal(3))
2569 1
2570 """
2571 a, b = _coerce_exprs(self, other)
2572 if z3_debug():
2573 _z3_assert(a.is_int(), "Z3 integer expression expected")
2574 return ArithRef(Z3_mk_mod(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2575
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 2437 of file z3py.py.

2437 def __mul__(self, other):
2438 """Create the Z3 expression `self * other`.
2439
2440 >>> x = Real('x')
2441 >>> y = Real('y')
2442 >>> x * y
2443 x*y
2444 >>> (x * y).sort()
2445 Real
2446 """
2447 if isinstance(other, BoolRef):
2448 return If(other, self, 0)
2449 a, b = _coerce_exprs(self, other)
2450 return ArithRef(_mk_bin(Z3_mk_mul, a, b), self.ctx)
2451

◆ __neg__()

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

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

Definition at line 2588 of file z3py.py.

2588 def __neg__(self):
2589 """Return an expression representing `-self`.
2590
2591 >>> x = Int('x')
2592 >>> -x
2593 -x
2594 >>> simplify(-(-x))
2595 x
2596 """
2597 return ArithRef(Z3_mk_unary_minus(self.ctx_ref(), self.as_ast()), self.ctx)
2598
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 2599 of file z3py.py.

2599 def __pos__(self):
2600 """Return `self`.
2601
2602 >>> x = Int('x')
2603 >>> +x
2604 x
2605 """
2606 return self
2607

◆ __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 2485 of file z3py.py.

2485 def __pow__(self, other):
2486 """Create the Z3 expression `self**other` (** is the power operator).
2487
2488 >>> x = Real('x')
2489 >>> x**3
2490 x**3
2491 >>> (x**3).sort()
2492 Real
2493 >>> simplify(IntVal(2)**8)
2494 256
2495 """
2496 a, b = _coerce_exprs(self, other)
2497 return ArithRef(Z3_mk_power(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2498
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 2427 of file z3py.py.

2427 def __radd__(self, other):
2428 """Create the Z3 expression `other + self`.
2429
2430 >>> x = Int('x')
2431 >>> 10 + x
2432 10 + x
2433 """
2434 a, b = _coerce_exprs(self, other)
2435 return ArithRef(_mk_bin(Z3_mk_add, b, a), self.ctx)
2436

◆ __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 2540 of file z3py.py.

2540 def __rdiv__(self, other):
2541 """Create the Z3 expression `other/self`.
2542
2543 >>> x = Int('x')
2544 >>> 10/x
2545 10/x
2546 >>> (10/x).sexpr()
2547 '(div 10 x)'
2548 >>> x = Real('x')
2549 >>> 10/x
2550 10/x
2551 >>> (10/x).sexpr()
2552 '(/ 10.0 x)'
2553 """
2554 a, b = _coerce_exprs(self, other)
2555 return ArithRef(Z3_mk_div(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2556

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 2576 of file z3py.py.

2576 def __rmod__(self, other):
2577 """Create the Z3 expression `other%self`.
2578
2579 >>> x = Int('x')
2580 >>> 10 % x
2581 10%x
2582 """
2583 a, b = _coerce_exprs(self, other)
2584 if z3_debug():
2585 _z3_assert(a.is_int(), "Z3 integer expression expected")
2586 return ArithRef(Z3_mk_mod(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2587

◆ __rmul__()

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

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

Definition at line 2452 of file z3py.py.

2452 def __rmul__(self, other):
2453 """Create the Z3 expression `other * self`.
2454
2455 >>> x = Real('x')
2456 >>> 10 * x
2457 10*x
2458 """
2459 a, b = _coerce_exprs(self, other)
2460 return ArithRef(_mk_bin(Z3_mk_mul, b, a), self.ctx)
2461

◆ __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 2499 of file z3py.py.

2499 def __rpow__(self, other):
2500 """Create the Z3 expression `other**self` (** is the power operator).
2501
2502 >>> x = Real('x')
2503 >>> 2**x
2504 2**x
2505 >>> (2**x).sort()
2506 Real
2507 >>> simplify(2**IntVal(8))
2508 256
2509 """
2510 a, b = _coerce_exprs(self, other)
2511 return ArithRef(Z3_mk_power(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2512

◆ __rsub__()

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

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

Definition at line 2475 of file z3py.py.

2475 def __rsub__(self, other):
2476 """Create the Z3 expression `other - self`.
2477
2478 >>> x = Int('x')
2479 >>> 10 - x
2480 10 - x
2481 """
2482 a, b = _coerce_exprs(self, other)
2483 return ArithRef(_mk_bin(Z3_mk_sub, b, a), self.ctx)
2484

◆ __rtruediv__()

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

Definition at line 2557 of file z3py.py.

2557 def __rtruediv__(self, other):
2558 """Create the Z3 expression `other/self`."""
2559 return self.__rdiv__(other)
2560

◆ __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 2462 of file z3py.py.

2462 def __sub__(self, other):
2463 """Create the Z3 expression `self - other`.
2464
2465 >>> x = Int('x')
2466 >>> y = Int('y')
2467 >>> x - y
2468 x - y
2469 >>> (x - y).sort()
2470 Int
2471 """
2472 a, b = _coerce_exprs(self, other)
2473 return ArithRef(_mk_bin(Z3_mk_sub, a, b), self.ctx)
2474

◆ __truediv__()

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

Definition at line 2536 of file z3py.py.

2536 def __truediv__(self, other):
2537 """Create the Z3 expression `other/self`."""
2538 return self.__div__(other)
2539

◆ 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 2389 of file z3py.py.

2389 def is_int(self):
2390 """Return `True` if `self` is an integer expression.
2391
2392 >>> x = Int('x')
2393 >>> x.is_int()
2394 True
2395 >>> (x + 1).is_int()
2396 True
2397 >>> y = Real('y')
2398 >>> (x + y).is_int()
2399 False
2400 """
2401 return self.sort().is_int()
2402

Referenced by IntNumRef.as_long(), ArithRef.is_int(), 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 2403 of file z3py.py.

2403 def is_real(self):
2404 """Return `True` if `self` is an real expression.
2405
2406 >>> x = Real('x')
2407 >>> x.is_real()
2408 True
2409 >>> (x + 1).is_real()
2410 True
2411 """
2412 return self.sort().is_real()
2413

Referenced by ArithRef.is_real().

◆ 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 2379 of file z3py.py.

2379 def sort(self):
2380 """Return the sort (type) of the arithmetical expression `self`.
2381
2382 >>> Int('x').sort()
2383 Int
2384 >>> (Real('x') + 1).sort()
2385 Real
2386 """
2387 return ArithSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
2388
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.

Referenced by ArithRef.__add__(), ArithRef.__div__(), ArithRef.__mul__(), ArithRef.__pow__(), ArithRef.__rpow__(), ArithRef.__sub__(), FPNumRef.as_string(), ArrayRef.domain(), ArrayRef.domain_n(), FPRef.ebits(), ArithRef.is_int(), ArithRef.is_real(), ArrayRef.range(), FPRef.sbits(), BitVecRef.size(), ArithRef.sort(), and ExprRef.sort_kind().