Z3
Loading...
Searching...
No Matches
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 6457 of file z3py.py.

Constructor & Destructor Documentation

◆ __init__()

__init__ ( self,
m,
ctx )

Definition at line 6460 of file z3py.py.

6460 def __init__(self, m, ctx):
6461 assert ctx is not None
6462 self.model = m
6463 self.ctx = ctx
6464 Z3_model_inc_ref(self.ctx.ref(), self.model)
6465
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 6466 of file z3py.py.

6466 def __del__(self):
6467 if self.ctx.ref() is not None and Z3_model_dec_ref is not None:
6468 Z3_model_dec_ref(self.ctx.ref(), self.model)
6469
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 6796 of file z3py.py.

6796 def __copy__(self):
6797 return self.translate(self.ctx)
6798

◆ __deepcopy__()

__deepcopy__ ( self,
memo = {} )

Definition at line 6799 of file z3py.py.

6799 def __deepcopy__(self, memo={}):
6800 return self.translate(self.ctx)
6801
6802

◆ __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 6678 of file z3py.py.

6678 def __getitem__(self, idx):
6679 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned.
6680 If `idx` is a declaration, then the actual interpretation is returned.
6681
6682 The elements can be retrieved using position or the actual declaration.
6683
6684 >>> f = Function('f', IntSort(), IntSort())
6685 >>> x = Int('x')
6686 >>> s = Solver()
6687 >>> s.add(x > 0, x < 2, f(x) == 0)
6688 >>> s.check()
6689 sat
6690 >>> m = s.model()
6691 >>> len(m)
6692 2
6693 >>> m[0]
6694 x
6695 >>> m[1]
6696 f
6697 >>> m[x]
6698 1
6699 >>> m[f]
6700 [else -> 0]
6701 >>> for d in m: print("%s -> %s" % (d, m[d]))
6702 x -> 1
6703 f -> [else -> 0]
6704 """
6705 if _is_int(idx):
6706 if idx >= len(self):
6707 raise IndexError
6708 num_consts = Z3_model_get_num_consts(self.ctx.ref(), self.model)
6709 if (idx < num_consts):
6710 return FuncDeclRef(Z3_model_get_const_decl(self.ctx.ref(), self.model, idx), self.ctx)
6711 else:
6712 return FuncDeclRef(Z3_model_get_func_decl(self.ctx.ref(), self.model, idx - num_consts), self.ctx)
6713 if isinstance(idx, FuncDeclRef):
6714 return self.get_interp(idx)
6715 if is_const(idx):
6716 return self.get_interp(idx.decl())
6717 if isinstance(idx, SortRef):
6718 return self.get_universe(idx)
6719 if z3_debug():
6720 _z3_assert(False, "Integer, Z3 declaration, or Z3 constant expected")
6721 return None
6722
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 6534 of file z3py.py.

6534 def __len__(self):
6535 """Return the number of constant and function declarations in the model `self`.
6536
6537 >>> f = Function('f', IntSort(), IntSort())
6538 >>> x = Int('x')
6539 >>> s = Solver()
6540 >>> s.add(x > 0, f(x) != x)
6541 >>> s.check()
6542 sat
6543 >>> m = s.model()
6544 >>> len(m)
6545 2
6546 """
6547 num_consts = int(Z3_model_get_num_consts(self.ctx.ref(), self.model))
6548 num_funcs = int(Z3_model_get_num_funcs(self.ctx.ref(), self.model))
6549 return num_consts + num_funcs
6550
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 6470 of file z3py.py.

6470 def __repr__(self):
6471 return obj_to_string(self)
6472

◆ 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 6723 of file z3py.py.

6723 def decls(self):
6724 """Return a list with all symbols that have an interpretation in the model `self`.
6725 >>> f = Function('f', IntSort(), IntSort())
6726 >>> x = Int('x')
6727 >>> s = Solver()
6728 >>> s.add(x > 0, x < 2, f(x) == 0)
6729 >>> s.check()
6730 sat
6731 >>> m = s.model()
6732 >>> m.decls()
6733 [x, f]
6734 """
6735 r = []
6736 for i in range(Z3_model_get_num_consts(self.ctx.ref(), self.model)):
6737 r.append(FuncDeclRef(Z3_model_get_const_decl(self.ctx.ref(), self.model, i), self.ctx))
6738 for i in range(Z3_model_get_num_funcs(self.ctx.ref(), self.model)):
6739 r.append(FuncDeclRef(Z3_model_get_func_decl(self.ctx.ref(), self.model, i), self.ctx))
6740 return r
6741

◆ 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 6477 of file z3py.py.

6477 def eval(self, t, model_completion=False):
6478 """Evaluate the expression `t` in the model `self`.
6479 If `model_completion` is enabled, then a default interpretation is automatically added
6480 for symbols that do not have an interpretation in the model `self`.
6481
6482 >>> x = Int('x')
6483 >>> s = Solver()
6484 >>> s.add(x > 0, x < 2)
6485 >>> s.check()
6486 sat
6487 >>> m = s.model()
6488 >>> m.eval(x + 1)
6489 2
6490 >>> m.eval(x == 1)
6491 True
6492 >>> y = Int('y')
6493 >>> m.eval(y + x)
6494 1 + y
6495 >>> m.eval(y)
6496 y
6497 >>> m.eval(y, model_completion=True)
6498 0
6499 >>> # Now, m contains an interpretation for y
6500 >>> m.eval(y + x)
6501 1
6502 """
6503 r = (Ast * 1)()
6504 if Z3_model_eval(self.ctx.ref(), self.model, t.as_ast(), model_completion, r):
6505 return _to_expr_ref(r[0], self.ctx)
6506 raise Z3Exception("failed to evaluate expression in the model")
6507
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 6508 of file z3py.py.

6508 def evaluate(self, t, model_completion=False):
6509 """Alias for `eval`.
6510
6511 >>> x = Int('x')
6512 >>> s = Solver()
6513 >>> s.add(x > 0, x < 2)
6514 >>> s.check()
6515 sat
6516 >>> m = s.model()
6517 >>> m.evaluate(x + 1)
6518 2
6519 >>> m.evaluate(x == 1)
6520 True
6521 >>> y = Int('y')
6522 >>> m.evaluate(y + x)
6523 1 + y
6524 >>> m.evaluate(y)
6525 y
6526 >>> m.evaluate(y, model_completion=True)
6527 0
6528 >>> # Now, m contains an interpretation for y
6529 >>> m.evaluate(y + x)
6530 1
6531 """
6532 return self.eval(t, model_completion)
6533

◆ 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 6551 of file z3py.py.

6551 def get_interp(self, decl):
6552 """Return the interpretation for a given declaration or constant.
6553
6554 >>> f = Function('f', IntSort(), IntSort())
6555 >>> x = Int('x')
6556 >>> s = Solver()
6557 >>> s.add(x > 0, x < 2, f(x) == 0)
6558 >>> s.check()
6559 sat
6560 >>> m = s.model()
6561 >>> m[x]
6562 1
6563 >>> m[f]
6564 [else -> 0]
6565 """
6566 if z3_debug():
6567 _z3_assert(isinstance(decl, FuncDeclRef) or is_const(decl), "Z3 declaration expected")
6568 if is_const(decl):
6569 decl = decl.decl()
6570 try:
6571 if decl.arity() == 0:
6572 _r = Z3_model_get_const_interp(self.ctx.ref(), self.model, decl.ast)
6573 if _r.value is None:
6574 return None
6575 r = _to_expr_ref(_r, self.ctx)
6576 if is_as_array(r):
6577 fi = self.get_interp(get_as_array_func(r))
6578 if fi is None:
6579 return fi
6580 e = fi.else_value()
6581 if e is None:
6582 return fi
6583 if fi.arity() != 1:
6584 return fi
6585 srt = decl.range()
6586 dom = srt.domain()
6587 e = K(dom, e)
6588 i = 0
6589 sz = fi.num_entries()
6590 n = fi.arity()
6591 while i < sz:
6592 fe = fi.entry(i)
6593 e = Store(e, fe.arg_value(0), fe.value())
6594 i += 1
6595 return e
6596 else:
6597 return r
6598 else:
6599 return FuncInterp(Z3_model_get_func_interp(self.ctx.ref(), self.model, decl.ast), self.ctx)
6600 except Z3Exception:
6601 return None
6602
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 6618 of file z3py.py.

6618 def get_sort(self, idx):
6619 """Return the uninterpreted sort at position `idx` < self.num_sorts().
6620
6621 >>> A = DeclareSort('A')
6622 >>> B = DeclareSort('B')
6623 >>> a1, a2 = Consts('a1 a2', A)
6624 >>> b1, b2 = Consts('b1 b2', B)
6625 >>> s = Solver()
6626 >>> s.add(a1 != a2, b1 != b2)
6627 >>> s.check()
6628 sat
6629 >>> m = s.model()
6630 >>> m.num_sorts()
6631 2
6632 >>> m.get_sort(0)
6633 A
6634 >>> m.get_sort(1)
6635 B
6636 """
6637 if idx >= self.num_sorts():
6638 raise IndexError
6639 return _to_sort_ref(Z3_model_get_sort(self.ctx.ref(), self.model, idx), self.ctx)
6640
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 6658 of file z3py.py.

6658 def get_universe(self, s):
6659 """Return the interpretation for the uninterpreted sort `s` in the model `self`.
6660
6661 >>> A = DeclareSort('A')
6662 >>> a, b = Consts('a b', A)
6663 >>> s = Solver()
6664 >>> s.add(a != b)
6665 >>> s.check()
6666 sat
6667 >>> m = s.model()
6668 >>> m.get_universe(A)
6669 [A!val!1, A!val!0]
6670 """
6671 if z3_debug():
6672 _z3_assert(isinstance(s, SortRef), "Z3 sort expected")
6673 try:
6674 return AstVector(Z3_model_get_sort_universe(self.ctx.ref(), self.model, s.ast), self.ctx)
6675 except Z3Exception:
6676 return None
6677
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 6603 of file z3py.py.

6603 def num_sorts(self):
6604 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`.
6605
6606 >>> A = DeclareSort('A')
6607 >>> a, b = Consts('a b', A)
6608 >>> s = Solver()
6609 >>> s.add(a != b)
6610 >>> s.check()
6611 sat
6612 >>> m = s.model()
6613 >>> m.num_sorts()
6614 1
6615 """
6616 return int(Z3_model_get_num_sorts(self.ctx.ref(), self.model))
6617
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 6772 of file z3py.py.

6772 def project(self, vars, fml):
6773 """Perform model-based projection on fml with respect to vars.
6774 Assume that the model satisfies fml. Then compute a projection fml_p, such
6775 that vars do not occur free in fml_p, fml_p is true in the model and
6776 fml_p => exists vars . fml
6777 """
6778 ctx = self.ctx.ref()
6779 _vars = (Ast * len(vars))()
6780 for i in range(len(vars)):
6781 _vars[i] = vars[i].as_ast()
6782 return _to_expr_ref(Z3_qe_model_project(ctx, self.model, len(vars), _vars, fml.ast), self.ctx)
6783

◆ 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 6784 of file z3py.py.

6784 def project_with_witness(self, vars, fml):
6785 """Perform model-based projection, but also include realizer terms for the projected variables"""
6786 ctx = self.ctx.ref()
6787 _vars = (Ast * len(vars))()
6788 for i in range(len(vars)):
6789 _vars[i] = vars[i].as_ast()
6790 defs = AstMap()
6791 result = Z3_qe_model_project_with_witness(ctx, self.model, len(vars), _vars, fml.ast, defs.map)
6792 result = _to_expr_ref(result, self.ctx)
6793 return result, defs
6794
6795

◆ sexpr()

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

Definition at line 6473 of file z3py.py.

6473 def sexpr(self):
6474 """Return a textual representation of the s-expression representing the model."""
6475 return Z3_model_to_string(self.ctx.ref(), self.model)
6476
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 6641 of file z3py.py.

6641 def sorts(self):
6642 """Return all uninterpreted sorts that have an interpretation in the model `self`.
6643
6644 >>> A = DeclareSort('A')
6645 >>> B = DeclareSort('B')
6646 >>> a1, a2 = Consts('a1 a2', A)
6647 >>> b1, b2 = Consts('b1 b2', B)
6648 >>> s = Solver()
6649 >>> s.add(a1 != a2, b1 != b2)
6650 >>> s.check()
6651 sat
6652 >>> m = s.model()
6653 >>> m.sorts()
6654 [A, B]
6655 """
6656 return [self.get_sort(i) for i in range(self.num_sorts())]
6657

◆ translate()

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

Definition at line 6764 of file z3py.py.

6764 def translate(self, target):
6765 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
6766 """
6767 if z3_debug():
6768 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
6769 model = Z3_model_translate(self.ctx.ref(), self.model, target.ref())
6770 return ModelRef(model, target)
6771
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 6742 of file z3py.py.

6742 def update_value(self, x, value):
6743 """Update the interpretation of a constant"""
6744 if is_expr(x):
6745 x = x.decl()
6746 if is_func_decl(x) and x.arity() != 0 and isinstance(value, FuncInterp):
6747 fi1 = value.f
6748 fi2 = Z3_add_func_interp(x.ctx_ref(), self.model, x.ast, value.else_value().ast);
6749 fi2 = FuncInterp(fi2, x.ctx)
6750 for i in range(value.num_entries()):
6751 e = value.entry(i)
6752 n = Z3_func_entry_get_num_args(x.ctx_ref(), e.entry)
6753 v = AstVector()
6754 for j in range(n):
6755 v.push(e.arg_value(j))
6756 val = Z3_func_entry_get_value(x.ctx_ref(), e.entry)
6757 Z3_func_interp_add_entry(x.ctx_ref(), fi2.f, v.vector, val)
6758 return
6759 if not is_func_decl(x) or x.arity() != 0:
6760 raise Z3Exception("Expecting 0-ary function or constant expression")
6761 value = _py2expr(value)
6762 Z3_add_const_interp(x.ctx_ref(), self.model, x.ast, value.ast)
6763
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