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 (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

Integer and Real expressions.

Definition at line 2193 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 2231 of file z3py.py.

2231 def __add__(self, other):
2232 """Create the Z3 expression `self + other`.
2233
2234 >>> x = Int('x')
2235 >>> y = Int('y')
2236 >>> x + y
2237 x + y
2238 >>> (x + y).sort()
2239 Int
2240 """
2241 a, b = _coerce_exprs(self, other)
2242 return ArithRef(_mk_bin(Z3_mk_add, a, b), self.ctx)
2243
def Int(name, ctx=None)
Definition: z3py.py:3010

◆ __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 2330 of file z3py.py.

2330 def __div__(self, other):
2331 """Create the Z3 expression `other/self`.
2332
2333 >>> x = Int('x')
2334 >>> y = Int('y')
2335 >>> x/y
2336 x/y
2337 >>> (x/y).sort()
2338 Int
2339 >>> (x/y).sexpr()
2340 '(div x y)'
2341 >>> x = Real('x')
2342 >>> y = Real('y')
2343 >>> x/y
2344 x/y
2345 >>> (x/y).sort()
2346 Real
2347 >>> (x/y).sexpr()
2348 '(/ x y)'
2349 """
2350 a, b = _coerce_exprs(self, other)
2351 return ArithRef(Z3_mk_div(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2352
def Real(name, ctx=None)
Definition: z3py.py:3058
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 2464 of file z3py.py.

2464 def __ge__(self, other):
2465 """Create the Z3 expression `other >= self`.
2466
2467 >>> x, y = Ints('x y')
2468 >>> x >= y
2469 x >= y
2470 >>> y = Real('y')
2471 >>> x >= y
2472 ToReal(x) >= y
2473 """
2474 a, b = _coerce_exprs(self, other)
2475 return BoolRef(Z3_mk_ge(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2476
def ToReal(a)
Definition: z3py.py:3110
def Ints(names, ctx=None)
Definition: z3py.py:3022
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 2451 of file z3py.py.

2451 def __gt__(self, other):
2452 """Create the Z3 expression `other > self`.
2453
2454 >>> x, y = Ints('x y')
2455 >>> x > y
2456 x > y
2457 >>> y = Real('y')
2458 >>> x > y
2459 ToReal(x) > y
2460 """
2461 a, b = _coerce_exprs(self, other)
2462 return BoolRef(Z3_mk_gt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2463
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 2425 of file z3py.py.

2425 def __le__(self, other):
2426 """Create the Z3 expression `other <= self`.
2427
2428 >>> x, y = Ints('x y')
2429 >>> x <= y
2430 x <= y
2431 >>> y = Real('y')
2432 >>> x <= y
2433 ToReal(x) <= y
2434 """
2435 a, b = _coerce_exprs(self, other)
2436 return BoolRef(Z3_mk_le(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2437
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 2438 of file z3py.py.

2438 def __lt__(self, other):
2439 """Create the Z3 expression `other < self`.
2440
2441 >>> x, y = Ints('x y')
2442 >>> x < y
2443 x < y
2444 >>> y = Real('y')
2445 >>> x < y
2446 ToReal(x) < y
2447 """
2448 a, b = _coerce_exprs(self, other)
2449 return BoolRef(Z3_mk_lt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2450
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 2378 of file z3py.py.

2378 def __mod__(self, other):
2379 """Create the Z3 expression `other%self`.
2380
2381 >>> x = Int('x')
2382 >>> y = Int('y')
2383 >>> x % y
2384 x%y
2385 >>> simplify(IntVal(10) % IntVal(3))
2386 1
2387 """
2388 a, b = _coerce_exprs(self, other)
2389 if z3_debug():
2390 _z3_assert(a.is_int(), "Z3 integer expression expected")
2391 return ArithRef(Z3_mk_mod(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2392
def z3_debug()
Definition: z3py.py:56
def simplify(a, *arguments, **keywords)
Utils.
Definition: z3py.py:8182
def IntVal(val, ctx=None)
Definition: z3py.py:2954
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 2254 of file z3py.py.

2254 def __mul__(self, other):
2255 """Create the Z3 expression `self * other`.
2256
2257 >>> x = Real('x')
2258 >>> y = Real('y')
2259 >>> x * y
2260 x*y
2261 >>> (x * y).sort()
2262 Real
2263 """
2264 if isinstance(other, BoolRef):
2265 return If(other, self, 0)
2266 a, b = _coerce_exprs(self, other)
2267 return ArithRef(_mk_bin(Z3_mk_mul, a, b), self.ctx)
2268
def If(a, b, c, ctx=None)
Definition: z3py.py:1248

◆ __neg__()

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

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

Definition at line 2405 of file z3py.py.

2405 def __neg__(self):
2406 """Return an expression representing `-self`.
2407
2408 >>> x = Int('x')
2409 >>> -x
2410 -x
2411 >>> simplify(-(-x))
2412 x
2413 """
2414 return ArithRef(Z3_mk_unary_minus(self.ctx_ref(), self.as_ast()), self.ctx)
2415
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 2416 of file z3py.py.

2416 def __pos__(self):
2417 """Return `self`.
2418
2419 >>> x = Int('x')
2420 >>> +x
2421 x
2422 """
2423 return self
2424

◆ __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 2302 of file z3py.py.

2302 def __pow__(self, other):
2303 """Create the Z3 expression `self**other` (** is the power operator).
2304
2305 >>> x = Real('x')
2306 >>> x**3
2307 x**3
2308 >>> (x**3).sort()
2309 Real
2310 >>> simplify(IntVal(2)**8)
2311 256
2312 """
2313 a, b = _coerce_exprs(self, other)
2314 return ArithRef(Z3_mk_power(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2315
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 2244 of file z3py.py.

2244 def __radd__(self, other):
2245 """Create the Z3 expression `other + self`.
2246
2247 >>> x = Int('x')
2248 >>> 10 + x
2249 10 + x
2250 """
2251 a, b = _coerce_exprs(self, other)
2252 return ArithRef(_mk_bin(Z3_mk_add, b, a), self.ctx)
2253

◆ __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 2357 of file z3py.py.

2357 def __rdiv__(self, other):
2358 """Create the Z3 expression `other/self`.
2359
2360 >>> x = Int('x')
2361 >>> 10/x
2362 10/x
2363 >>> (10/x).sexpr()
2364 '(div 10 x)'
2365 >>> x = Real('x')
2366 >>> 10/x
2367 10/x
2368 >>> (10/x).sexpr()
2369 '(/ 10.0 x)'
2370 """
2371 a, b = _coerce_exprs(self, other)
2372 return ArithRef(Z3_mk_div(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2373

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 2393 of file z3py.py.

2393 def __rmod__(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 if z3_debug():
2402 _z3_assert(a.is_int(), "Z3 integer expression expected")
2403 return ArithRef(Z3_mk_mod(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2404

◆ __rmul__()

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

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

Definition at line 2269 of file z3py.py.

2269 def __rmul__(self, other):
2270 """Create the Z3 expression `other * self`.
2271
2272 >>> x = Real('x')
2273 >>> 10 * x
2274 10*x
2275 """
2276 a, b = _coerce_exprs(self, other)
2277 return ArithRef(_mk_bin(Z3_mk_mul, b, a), self.ctx)
2278

◆ __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 2316 of file z3py.py.

2316 def __rpow__(self, other):
2317 """Create the Z3 expression `other**self` (** is the power operator).
2318
2319 >>> x = Real('x')
2320 >>> 2**x
2321 2**x
2322 >>> (2**x).sort()
2323 Real
2324 >>> simplify(2**IntVal(8))
2325 256
2326 """
2327 a, b = _coerce_exprs(self, other)
2328 return ArithRef(Z3_mk_power(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2329

◆ __rsub__()

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

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

Definition at line 2292 of file z3py.py.

2292 def __rsub__(self, other):
2293 """Create the Z3 expression `other - self`.
2294
2295 >>> x = Int('x')
2296 >>> 10 - x
2297 10 - x
2298 """
2299 a, b = _coerce_exprs(self, other)
2300 return ArithRef(_mk_bin(Z3_mk_sub, b, a), self.ctx)
2301

◆ __rtruediv__()

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

Definition at line 2374 of file z3py.py.

2374 def __rtruediv__(self, other):
2375 """Create the Z3 expression `other/self`."""
2376 return self.__rdiv__(other)
2377

◆ __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 2279 of file z3py.py.

2279 def __sub__(self, other):
2280 """Create the Z3 expression `self - other`.
2281
2282 >>> x = Int('x')
2283 >>> y = Int('y')
2284 >>> x - y
2285 x - y
2286 >>> (x - y).sort()
2287 Int
2288 """
2289 a, b = _coerce_exprs(self, other)
2290 return ArithRef(_mk_bin(Z3_mk_sub, a, b), self.ctx)
2291

◆ __truediv__()

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

Definition at line 2353 of file z3py.py.

2353 def __truediv__(self, other):
2354 """Create the Z3 expression `other/self`."""
2355 return self.__div__(other)
2356

◆ 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 2206 of file z3py.py.

2206 def is_int(self):
2207 """Return `True` if `self` is an integer expression.
2208
2209 >>> x = Int('x')
2210 >>> x.is_int()
2211 True
2212 >>> (x + 1).is_int()
2213 True
2214 >>> y = Real('y')
2215 >>> (x + y).is_int()
2216 False
2217 """
2218 return self.sort().is_int()
2219
def is_int(a)
Definition: z3py.py:2497

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 2220 of file z3py.py.

2220 def is_real(self):
2221 """Return `True` if `self` is an real expression.
2222
2223 >>> x = Real('x')
2224 >>> x.is_real()
2225 True
2226 >>> (x + 1).is_real()
2227 True
2228 """
2229 return self.sort().is_real()
2230
def is_real(a)
Definition: z3py.py:2515

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 2196 of file z3py.py.

2196 def sort(self):
2197 """Return the sort (type) of the arithmetical expression `self`.
2198
2199 >>> Int('x').sort()
2200 Int
2201 >>> (Real('x') + 1).sort()
2202 Real
2203 """
2204 return ArithSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
2205
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__(), QuantifierRef.__getitem__(), ArithRef.__mul__(), ArithRef.__pow__(), ArithRef.__rpow__(), ArithRef.__sub__(), FPNumRef.as_string(), ArrayRef.domain(), FPRef.ebits(), ArithRef.is_int(), ArithRef.is_real(), ArrayRef.range(), FPRef.sbits(), BitVecRef.size(), ArithRef.sort(), and ExprRef.sort_kind().