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ModelRef Class Reference
+ Inheritance diagram for ModelRef:

Public Member Functions

 __init__ (self, m, ctx)
 
 __del__ (self)
 
 __repr__ (self)
 
 sexpr (self)
 
 eval (self, t, model_completion=False)
 
 evaluate (self, t, model_completion=False)
 
 __len__ (self)
 
 get_interp (self, decl)
 
 num_sorts (self)
 
 get_sort (self, idx)
 
 sorts (self)
 
 get_universe (self, s)
 
 __getitem__ (self, idx)
 
 decls (self)
 
 update_value (self, x, value)
 
 translate (self, target)
 
 project (self, vars, fml)
 
 project_with_witness (self, vars, fml)
 
 __copy__ (self)
 
 __deepcopy__ (self, memo={})
 
- Public Member Functions inherited from Z3PPObject
 use_pp (self)
 

Data Fields

 model = m
 
 ctx = ctx
 

Additional Inherited Members

- Protected Member Functions inherited from Z3PPObject
 _repr_html_ (self)
 

Detailed Description

Model/Solution of a satisfiability problem (aka system of constraints).

Definition at line 6448 of file z3py.py.

Constructor & Destructor Documentation

◆ __init__()

__init__ ( self,
m,
ctx )

Definition at line 6451 of file z3py.py.

6451 def __init__(self, m, ctx):
6452 assert ctx is not None
6453 self.model = m
6454 self.ctx = ctx
6455 Z3_model_inc_ref(self.ctx.ref(), self.model)
6456
void Z3_API Z3_model_inc_ref(Z3_context c, Z3_model m)
Increment the reference counter of the given model.

◆ __del__()

__del__ ( self)

Definition at line 6457 of file z3py.py.

6457 def __del__(self):
6458 if self.ctx.ref() is not None and Z3_model_dec_ref is not None:
6459 Z3_model_dec_ref(self.ctx.ref(), self.model)
6460
void Z3_API Z3_model_dec_ref(Z3_context c, Z3_model m)
Decrement the reference counter of the given model.

Member Function Documentation

◆ __copy__()

__copy__ ( self)

Definition at line 6787 of file z3py.py.

6787 def __copy__(self):
6788 return self.translate(self.ctx)
6789

◆ __deepcopy__()

__deepcopy__ ( self,
memo = {} )

Definition at line 6790 of file z3py.py.

6790 def __deepcopy__(self, memo={}):
6791 return self.translate(self.ctx)
6792
6793

◆ __getitem__()

__getitem__ ( self,
idx )
If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
If `idx` is a declaration, then the actual interpretation is returned.

The elements can be retrieved using position or the actual declaration.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> s = Solver()
>>> s.add(x > 0, x < 2, f(x) == 0)
>>> s.check()
sat
>>> m = s.model()
>>> len(m)
2
>>> m[0]
x
>>> m[1]
f
>>> m[x]
1
>>> m[f]
[else -> 0]
>>> for d in m: print("%s -> %s" % (d, m[d]))
x -> 1
f -> [else -> 0]

Definition at line 6669 of file z3py.py.

6669 def __getitem__(self, idx):
6670 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
6671 If `idx` is a declaration, then the actual interpretation is returned.
6672
6673 The elements can be retrieved using position or the actual declaration.
6674
6675 >>> f = Function('f', IntSort(), IntSort())
6676 >>> x = Int('x')
6677 >>> s = Solver()
6678 >>> s.add(x > 0, x < 2, f(x) == 0)
6679 >>> s.check()
6680 sat
6681 >>> m = s.model()
6682 >>> len(m)
6683 2
6684 >>> m[0]
6685 x
6686 >>> m[1]
6687 f
6688 >>> m[x]
6689 1
6690 >>> m[f]
6691 [else -> 0]
6692 >>> for d in m: print("%s -> %s" % (d, m[d]))
6693 x -> 1
6694 f -> [else -> 0]
6695 """
6696 if _is_int(idx):
6697 if idx >= len(self):
6698 raise IndexError
6699 num_consts = Z3_model_get_num_consts(self.ctx.ref(), self.model)
6700 if (idx < num_consts):
6701 return FuncDeclRef(Z3_model_get_const_decl(self.ctx.ref(), self.model, idx), self.ctx)
6702 else:
6703 return FuncDeclRef(Z3_model_get_func_decl(self.ctx.ref(), self.model, idx - num_consts), self.ctx)
6704 if isinstance(idx, FuncDeclRef):
6705 return self.get_interp(idx)
6706 if is_const(idx):
6707 return self.get_interp(idx.decl())
6708 if isinstance(idx, SortRef):
6709 return self.get_universe(idx)
6710 if z3_debug():
6711 _z3_assert(False, "Integer, Z3 declaration, or Z3 constant expected")
6712 return None
6713
Z3_func_decl Z3_API Z3_model_get_func_decl(Z3_context c, Z3_model m, unsigned i)
Return the declaration of the i-th function in the given model.
unsigned Z3_API Z3_model_get_num_consts(Z3_context c, Z3_model m)
Return the number of constants assigned by the given model.
Z3_func_decl Z3_API Z3_model_get_const_decl(Z3_context c, Z3_model m, unsigned i)
Return the i-th constant in the given model.

◆ __len__()

__len__ ( self)
Return the number of constant and function declarations in the model `self`.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> s = Solver()
>>> s.add(x > 0, f(x) != x)
>>> s.check()
sat
>>> m = s.model()
>>> len(m)
2

Definition at line 6525 of file z3py.py.

6525 def __len__(self):
6526 """Return the number of constant and function declarations in the model `self`.
6527
6528 >>> f = Function('f', IntSort(), IntSort())
6529 >>> x = Int('x')
6530 >>> s = Solver()
6531 >>> s.add(x > 0, f(x) != x)
6532 >>> s.check()
6533 sat
6534 >>> m = s.model()
6535 >>> len(m)
6536 2
6537 """
6538 num_consts = int(Z3_model_get_num_consts(self.ctx.ref(), self.model))
6539 num_funcs = int(Z3_model_get_num_funcs(self.ctx.ref(), self.model))
6540 return num_consts + num_funcs
6541
unsigned Z3_API Z3_model_get_num_funcs(Z3_context c, Z3_model m)
Return the number of function interpretations in the given model.

◆ __repr__()

__repr__ ( self)

Definition at line 6461 of file z3py.py.

6461 def __repr__(self):
6462 return obj_to_string(self)
6463

◆ decls()

decls ( self)
Return a list with all symbols that have an interpretation in the model `self`.
>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> s = Solver()
>>> s.add(x > 0, x < 2, f(x) == 0)
>>> s.check()
sat
>>> m = s.model()
>>> m.decls()
[x, f]

Definition at line 6714 of file z3py.py.

6714 def decls(self):
6715 """Return a list with all symbols that have an interpretation in the model `self`.
6716 >>> f = Function('f', IntSort(), IntSort())
6717 >>> x = Int('x')
6718 >>> s = Solver()
6719 >>> s.add(x > 0, x < 2, f(x) == 0)
6720 >>> s.check()
6721 sat
6722 >>> m = s.model()
6723 >>> m.decls()
6724 [x, f]
6725 """
6726 r = []
6727 for i in range(Z3_model_get_num_consts(self.ctx.ref(), self.model)):
6728 r.append(FuncDeclRef(Z3_model_get_const_decl(self.ctx.ref(), self.model, i), self.ctx))
6729 for i in range(Z3_model_get_num_funcs(self.ctx.ref(), self.model)):
6730 r.append(FuncDeclRef(Z3_model_get_func_decl(self.ctx.ref(), self.model, i), self.ctx))
6731 return r
6732

◆ eval()

eval ( self,
t,
model_completion = False )
Evaluate the expression `t` in the model `self`.
If `model_completion` is enabled, then a default interpretation is automatically added
for symbols that do not have an interpretation in the model `self`.

>>> x = Int('x')
>>> s = Solver()
>>> s.add(x > 0, x < 2)
>>> s.check()
sat
>>> m = s.model()
>>> m.eval(x + 1)
2
>>> m.eval(x == 1)
True
>>> y = Int('y')
>>> m.eval(y + x)
1 + y
>>> m.eval(y)
y
>>> m.eval(y, model_completion=True)
0
>>> # Now, m contains an interpretation for y
>>> m.eval(y + x)
1

Definition at line 6468 of file z3py.py.

6468 def eval(self, t, model_completion=False):
6469 """Evaluate the expression `t` in the model `self`.
6470 If `model_completion` is enabled, then a default interpretation is automatically added
6471 for symbols that do not have an interpretation in the model `self`.
6472
6473 >>> x = Int('x')
6474 >>> s = Solver()
6475 >>> s.add(x > 0, x < 2)
6476 >>> s.check()
6477 sat
6478 >>> m = s.model()
6479 >>> m.eval(x + 1)
6480 2
6481 >>> m.eval(x == 1)
6482 True
6483 >>> y = Int('y')
6484 >>> m.eval(y + x)
6485 1 + y
6486 >>> m.eval(y)
6487 y
6488 >>> m.eval(y, model_completion=True)
6489 0
6490 >>> # Now, m contains an interpretation for y
6491 >>> m.eval(y + x)
6492 1
6493 """
6494 r = (Ast * 1)()
6495 if Z3_model_eval(self.ctx.ref(), self.model, t.as_ast(), model_completion, r):
6496 return _to_expr_ref(r[0], self.ctx)
6497 raise Z3Exception("failed to evaluate expression in the model")
6498
bool Z3_API Z3_model_eval(Z3_context c, Z3_model m, Z3_ast t, bool model_completion, Z3_ast *v)
Evaluate the AST node t in the given model. Return true if succeeded, and store the result in v.

Referenced by evaluate().

◆ evaluate()

evaluate ( self,
t,
model_completion = False )
Alias for `eval`.

>>> x = Int('x')
>>> s = Solver()
>>> s.add(x > 0, x < 2)
>>> s.check()
sat
>>> m = s.model()
>>> m.evaluate(x + 1)
2
>>> m.evaluate(x == 1)
True
>>> y = Int('y')
>>> m.evaluate(y + x)
1 + y
>>> m.evaluate(y)
y
>>> m.evaluate(y, model_completion=True)
0
>>> # Now, m contains an interpretation for y
>>> m.evaluate(y + x)
1

Definition at line 6499 of file z3py.py.

6499 def evaluate(self, t, model_completion=False):
6500 """Alias for `eval`.
6501
6502 >>> x = Int('x')
6503 >>> s = Solver()
6504 >>> s.add(x > 0, x < 2)
6505 >>> s.check()
6506 sat
6507 >>> m = s.model()
6508 >>> m.evaluate(x + 1)
6509 2
6510 >>> m.evaluate(x == 1)
6511 True
6512 >>> y = Int('y')
6513 >>> m.evaluate(y + x)
6514 1 + y
6515 >>> m.evaluate(y)
6516 y
6517 >>> m.evaluate(y, model_completion=True)
6518 0
6519 >>> # Now, m contains an interpretation for y
6520 >>> m.evaluate(y + x)
6521 1
6522 """
6523 return self.eval(t, model_completion)
6524

◆ get_interp()

get_interp ( self,
decl )
Return the interpretation for a given declaration or constant.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> s = Solver()
>>> s.add(x > 0, x < 2, f(x) == 0)
>>> s.check()
sat
>>> m = s.model()
>>> m[x]
1
>>> m[f]
[else -> 0]

Definition at line 6542 of file z3py.py.

6542 def get_interp(self, decl):
6543 """Return the interpretation for a given declaration or constant.
6544
6545 >>> f = Function('f', IntSort(), IntSort())
6546 >>> x = Int('x')
6547 >>> s = Solver()
6548 >>> s.add(x > 0, x < 2, f(x) == 0)
6549 >>> s.check()
6550 sat
6551 >>> m = s.model()
6552 >>> m[x]
6553 1
6554 >>> m[f]
6555 [else -> 0]
6556 """
6557 if z3_debug():
6558 _z3_assert(isinstance(decl, FuncDeclRef) or is_const(decl), "Z3 declaration expected")
6559 if is_const(decl):
6560 decl = decl.decl()
6561 try:
6562 if decl.arity() == 0:
6563 _r = Z3_model_get_const_interp(self.ctx.ref(), self.model, decl.ast)
6564 if _r.value is None:
6565 return None
6566 r = _to_expr_ref(_r, self.ctx)
6567 if is_as_array(r):
6568 fi = self.get_interp(get_as_array_func(r))
6569 if fi is None:
6570 return fi
6571 e = fi.else_value()
6572 if e is None:
6573 return fi
6574 if fi.arity() != 1:
6575 return fi
6576 srt = decl.range()
6577 dom = srt.domain()
6578 e = K(dom, e)
6579 i = 0
6580 sz = fi.num_entries()
6581 n = fi.arity()
6582 while i < sz:
6583 fe = fi.entry(i)
6584 e = Store(e, fe.arg_value(0), fe.value())
6585 i += 1
6586 return e
6587 else:
6588 return r
6589 else:
6590 return FuncInterp(Z3_model_get_func_interp(self.ctx.ref(), self.model, decl.ast), self.ctx)
6591 except Z3Exception:
6592 return None
6593
Z3_ast Z3_API Z3_model_get_const_interp(Z3_context c, Z3_model m, Z3_func_decl a)
Return the interpretation (i.e., assignment) of constant a in the model m. Return NULL,...
Z3_func_interp Z3_API Z3_model_get_func_interp(Z3_context c, Z3_model m, Z3_func_decl f)
Return the interpretation of the function f in the model m. Return NULL, if the model does not assign...

Referenced by __getitem__(), and get_interp().

◆ get_sort()

get_sort ( self,
idx )
Return the uninterpreted sort at position `idx` < self.num_sorts().

>>> A = DeclareSort('A')
>>> B = DeclareSort('B')
>>> a1, a2 = Consts('a1 a2', A)
>>> b1, b2 = Consts('b1 b2', B)
>>> s = Solver()
>>> s.add(a1 != a2, b1 != b2)
>>> s.check()
sat
>>> m = s.model()
>>> m.num_sorts()
2
>>> m.get_sort(0)
A
>>> m.get_sort(1)
B

Definition at line 6609 of file z3py.py.

6609 def get_sort(self, idx):
6610 """Return the uninterpreted sort at position `idx` < self.num_sorts().
6611
6612 >>> A = DeclareSort('A')
6613 >>> B = DeclareSort('B')
6614 >>> a1, a2 = Consts('a1 a2', A)
6615 >>> b1, b2 = Consts('b1 b2', B)
6616 >>> s = Solver()
6617 >>> s.add(a1 != a2, b1 != b2)
6618 >>> s.check()
6619 sat
6620 >>> m = s.model()
6621 >>> m.num_sorts()
6622 2
6623 >>> m.get_sort(0)
6624 A
6625 >>> m.get_sort(1)
6626 B
6627 """
6628 if idx >= self.num_sorts():
6629 raise IndexError
6630 return _to_sort_ref(Z3_model_get_sort(self.ctx.ref(), self.model, idx), self.ctx)
6631
Z3_sort Z3_API Z3_model_get_sort(Z3_context c, Z3_model m, unsigned i)
Return a uninterpreted sort that m assigns an interpretation.

Referenced by sorts().

◆ get_universe()

get_universe ( self,
s )
Return the interpretation for the uninterpreted sort `s` in the model `self`.

>>> A = DeclareSort('A')
>>> a, b = Consts('a b', A)
>>> s = Solver()
>>> s.add(a != b)
>>> s.check()
sat
>>> m = s.model()
>>> m.get_universe(A)
[A!val!1, A!val!0]

Definition at line 6649 of file z3py.py.

6649 def get_universe(self, s):
6650 """Return the interpretation for the uninterpreted sort `s` in the model `self`.
6651
6652 >>> A = DeclareSort('A')
6653 >>> a, b = Consts('a b', A)
6654 >>> s = Solver()
6655 >>> s.add(a != b)
6656 >>> s.check()
6657 sat
6658 >>> m = s.model()
6659 >>> m.get_universe(A)
6660 [A!val!1, A!val!0]
6661 """
6662 if z3_debug():
6663 _z3_assert(isinstance(s, SortRef), "Z3 sort expected")
6664 try:
6665 return AstVector(Z3_model_get_sort_universe(self.ctx.ref(), self.model, s.ast), self.ctx)
6666 except Z3Exception:
6667 return None
6668
Z3_ast_vector Z3_API Z3_model_get_sort_universe(Z3_context c, Z3_model m, Z3_sort s)
Return the finite set of distinct values that represent the interpretation for sort s.

Referenced by __getitem__().

◆ num_sorts()

num_sorts ( self)
Return the number of uninterpreted sorts that contain an interpretation in the model `self`.

>>> A = DeclareSort('A')
>>> a, b = Consts('a b', A)
>>> s = Solver()
>>> s.add(a != b)
>>> s.check()
sat
>>> m = s.model()
>>> m.num_sorts()
1

Definition at line 6594 of file z3py.py.

6594 def num_sorts(self):
6595 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`.
6596
6597 >>> A = DeclareSort('A')
6598 >>> a, b = Consts('a b', A)
6599 >>> s = Solver()
6600 >>> s.add(a != b)
6601 >>> s.check()
6602 sat
6603 >>> m = s.model()
6604 >>> m.num_sorts()
6605 1
6606 """
6607 return int(Z3_model_get_num_sorts(self.ctx.ref(), self.model))
6608
unsigned Z3_API Z3_model_get_num_sorts(Z3_context c, Z3_model m)
Return the number of uninterpreted sorts that m assigns an interpretation to.

Referenced by get_sort(), and sorts().

◆ project()

project ( self,
vars,
fml )
Perform model-based projection on fml with respect to vars.
Assume that the model satisfies fml. Then compute a projection fml_p, such
that vars do not occur free in fml_p, fml_p is true in the model and
fml_p => exists vars . fml

Definition at line 6763 of file z3py.py.

6763 def project(self, vars, fml):
6764 """Perform model-based projection on fml with respect to vars.
6765 Assume that the model satisfies fml. Then compute a projection fml_p, such
6766 that vars do not occur free in fml_p, fml_p is true in the model and
6767 fml_p => exists vars . fml
6768 """
6769 ctx = self.ctx.ref()
6770 _vars = (Ast * len(vars))()
6771 for i in range(len(vars)):
6772 _vars[i] = vars[i].as_ast()
6773 return _to_expr_ref(Z3_qe_model_project(ctx, self.model, len(vars), _vars, fml.ast), self.ctx)
6774

◆ project_with_witness()

project_with_witness ( self,
vars,
fml )
Perform model-based projection, but also include realizer terms for the projected variables

Definition at line 6775 of file z3py.py.

6775 def project_with_witness(self, vars, fml):
6776 """Perform model-based projection, but also include realizer terms for the projected variables"""
6777 ctx = self.ctx.ref()
6778 _vars = (Ast * len(vars))()
6779 for i in range(len(vars)):
6780 _vars[i] = vars[i].as_ast()
6781 defs = AstMap()
6782 result = Z3_qe_model_project_with_witness(ctx, self.model, len(vars), _vars, fml.ast, defs.map)
6783 result = _to_expr_ref(result, self.ctx)
6784 return result, defs
6785
6786

◆ sexpr()

sexpr ( self)
Return a textual representation of the s-expression representing the model.

Definition at line 6464 of file z3py.py.

6464 def sexpr(self):
6465 """Return a textual representation of the s-expression representing the model."""
6466 return Z3_model_to_string(self.ctx.ref(), self.model)
6467
Z3_string Z3_API Z3_model_to_string(Z3_context c, Z3_model m)
Convert the given model into a string.

◆ sorts()

sorts ( self)
Return all uninterpreted sorts that have an interpretation in the model `self`.

>>> A = DeclareSort('A')
>>> B = DeclareSort('B')
>>> a1, a2 = Consts('a1 a2', A)
>>> b1, b2 = Consts('b1 b2', B)
>>> s = Solver()
>>> s.add(a1 != a2, b1 != b2)
>>> s.check()
sat
>>> m = s.model()
>>> m.sorts()
[A, B]

Definition at line 6632 of file z3py.py.

6632 def sorts(self):
6633 """Return all uninterpreted sorts that have an interpretation in the model `self`.
6634
6635 >>> A = DeclareSort('A')
6636 >>> B = DeclareSort('B')
6637 >>> a1, a2 = Consts('a1 a2', A)
6638 >>> b1, b2 = Consts('b1 b2', B)
6639 >>> s = Solver()
6640 >>> s.add(a1 != a2, b1 != b2)
6641 >>> s.check()
6642 sat
6643 >>> m = s.model()
6644 >>> m.sorts()
6645 [A, B]
6646 """
6647 return [self.get_sort(i) for i in range(self.num_sorts())]
6648

◆ translate()

translate ( self,
target )
Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.

Definition at line 6755 of file z3py.py.

6755 def translate(self, target):
6756 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
6757 """
6758 if z3_debug():
6759 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
6760 model = Z3_model_translate(self.ctx.ref(), self.model, target.ref())
6761 return ModelRef(model, target)
6762
Z3_model Z3_API Z3_model_translate(Z3_context c, Z3_model m, Z3_context dst)
translate model from context c to context dst.

Referenced by __copy__(), and __deepcopy__().

◆ update_value()

update_value ( self,
x,
value )
Update the interpretation of a constant

Definition at line 6733 of file z3py.py.

6733 def update_value(self, x, value):
6734 """Update the interpretation of a constant"""
6735 if is_expr(x):
6736 x = x.decl()
6737 if is_func_decl(x) and x.arity() != 0 and isinstance(value, FuncInterp):
6738 fi1 = value.f
6739 fi2 = Z3_add_func_interp(x.ctx_ref(), self.model, x.ast, value.else_value().ast);
6740 fi2 = FuncInterp(fi2, x.ctx)
6741 for i in range(value.num_entries()):
6742 e = value.entry(i)
6743 n = Z3_func_entry_get_num_args(x.ctx_ref(), e.entry)
6744 v = AstVector()
6745 for j in range(n):
6746 v.push(e.arg_value(j))
6747 val = Z3_func_entry_get_value(x.ctx_ref(), e.entry)
6748 Z3_func_interp_add_entry(x.ctx_ref(), fi2.f, v.vector, val)
6749 return
6750 if not is_func_decl(x) or x.arity() != 0:
6751 raise Z3Exception("Expecting 0-ary function or constant expression")
6752 value = _py2expr(value)
6753 Z3_add_const_interp(x.ctx_ref(), self.model, x.ast, value.ast)
6754
Z3_func_interp Z3_API Z3_add_func_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast default_value)
Create a fresh func_interp object, add it to a model for a specified function. It has reference count...
unsigned Z3_API Z3_func_entry_get_num_args(Z3_context c, Z3_func_entry e)
Return the number of arguments in a Z3_func_entry object.
Z3_ast Z3_API Z3_func_entry_get_value(Z3_context c, Z3_func_entry e)
Return the value of this point.
void Z3_API Z3_add_const_interp(Z3_context c, Z3_model m, Z3_func_decl f, Z3_ast a)
Add a constant interpretation.
void Z3_API Z3_func_interp_add_entry(Z3_context c, Z3_func_interp fi, Z3_ast_vector args, Z3_ast value)
add a function entry to a function interpretation.

Field Documentation

◆ ctx

◆ model