Model/Solution of a satisfiability problem (aka system of constraints).
Definition at line 6413 of file z3py.py.
◆ __init__() def __init__ ( self, m, ctx )Definition at line 6416 of file z3py.py.
6416 def__init__(self, m, ctx):
6417 assertctx
is not Nonevoid Z3_API Z3_model_inc_ref(Z3_context c, Z3_model m)
Increment the reference counter of the given model.
◆ __del__()Definition at line 6422 of file z3py.py.
6423 ifself.ctx.ref()
is not None andZ3_model_dec_ref
is not None:
void Z3_API Z3_model_dec_ref(Z3_context c, Z3_model m)
Decrement the reference counter of the given model.
◆ __copy__()Definition at line 6728 of file z3py.py.
6729 returnself.translate(self.ctx)
◆ __deepcopy__() def __deepcopy__ ( self, memo ={}
)
Definition at line 6731 of file z3py.py.
6731 def__deepcopy__(self, memo={}):
6732 returnself.translate(self.ctx)
◆ __getitem__() def __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 6634 of file z3py.py.
6634 def__getitem__(self, idx):
6635 """If `idx` is an integer, then the declaration at position `idx` in the model `self` is returned. 6636 If `idx` is a declaration, then the actual interpretation is returned. 6638 The elements can be retrieved using position or the actual declaration. 6640 >>> f = Function('f', IntSort(), IntSort()) 6643 >>> s.add(x > 0, x < 2, f(x) == 0) 6657 >>> for d in m: print("%s -> %s" % (d, m[d])) 6662 ifidx >= len(self):
6665 if(idx < num_consts):
6669 ifisinstance(idx, FuncDeclRef):
6670 returnself.get_interp(idx)
6672 returnself.get_interp(idx.decl())
6673 ifisinstance(idx, SortRef):
6674 returnself.get_universe(idx)
6676_z3_assert(
False,
"Integer, Z3 declaration, or Z3 constant expected")
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__()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 6490 of file z3py.py.
6491 """Return the number of constant and function declarations in the model `self`. 6493 >>> f = Function('f', IntSort(), IntSort()) 6496 >>> s.add(x > 0, f(x) != x) 6505 returnnum_consts + num_funcs
unsigned Z3_API Z3_model_get_num_funcs(Z3_context c, Z3_model m)
Return the number of function interpretations in the given model.
Referenced by AstVector.__getitem__(), and AstVector.__setitem__().
◆ __repr__()Definition at line 6426 of file z3py.py.
6427 returnobj_to_string(self)
◆ decls()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 6679 of file z3py.py.
6680 """Return a list with all symbols that have an interpretation in the model `self`. 6681 >>> f = Function('f', IntSort(), IntSort()) 6684 >>> s.add(x > 0, x < 2, f(x) == 0)expr range(expr const &lo, expr const &hi)
◆ eval() def 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 6433 of file z3py.py.
6433 defeval(self, t, model_completion=False):
6434 """Evaluate the expression `t` in the model `self`. 6435 If `model_completion` is enabled, then a default interpretation is automatically added 6436 for symbols that do not have an interpretation in the model `self`. 6440 >>> s.add(x > 0, x < 2) 6453 >>> m.eval(y, model_completion=True) 6455 >>> # Now, m contains an interpretation for y 6460 if Z3_model_eval(self.ctx.ref(), self.model, t.as_ast(), model_completion, r):
6461 return_to_expr_ref(r[0], self.ctx)
6462 raiseZ3Exception(
"failed to evaluate expression in the model")
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 ModelRef.evaluate().
◆ evaluate() def 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 6464 of file z3py.py.
6464 defevaluate(self, t, model_completion=False):
6465 """Alias for `eval`. 6469 >>> s.add(x > 0, x < 2) 6473 >>> m.evaluate(x + 1) 6475 >>> m.evaluate(x == 1) 6478 >>> m.evaluate(y + x) 6482 >>> m.evaluate(y, model_completion=True) 6484 >>> # Now, m contains an interpretation for y 6485 >>> m.evaluate(y + x) 6488 returnself.eval(t, model_completion)
◆ get_interp() def 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 6507 of file z3py.py.
6507 defget_interp(self, decl):
6508 """Return the interpretation for a given declaration or constant. 6510 >>> f = Function('f', IntSort(), IntSort()) 6513 >>> s.add(x > 0, x < 2, f(x) == 0) 6523_z3_assert(isinstance(decl, FuncDeclRef)
or is_const(decl),
"Z3 declaration expected")
6527 ifdecl.arity() == 0:
6529 if_r.value
is None:
6531r = _to_expr_ref(_r, self.ctx)
6545sz = fi.num_entries()
6549e =
Store(e, fe.arg_value(0), fe.value())
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 ModelRef.__getitem__(), and ModelRef.get_interp().
◆ get_sort() def 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 6574 of file z3py.py.
6574 defget_sort(self, idx):
6575 """Return the uninterpreted sort at position `idx` < self.num_sorts(). 6577 >>> A = DeclareSort('A') 6578 >>> B = DeclareSort('B') 6579 >>> a1, a2 = Consts('a1 a2', A) 6580 >>> b1, b2 = Consts('b1 b2', B) 6582 >>> s.add(a1 != a2, b1 != b2) 6593 ifidx >= self.num_sorts():
6595 return_to_sort_ref(
Z3_model_get_sort(self.ctx.ref(), self.model, idx), self.ctx)
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 ModelRef.sorts().
◆ get_universe() def 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 6614 of file z3py.py.
6614 defget_universe(self, s):
6615 """Return the interpretation for the uninterpreted sort `s` in the model `self`. 6617 >>> A = DeclareSort('A') 6618 >>> a, b = Consts('a b', A) 6624 >>> m.get_universe(A) 6628_z3_assert(isinstance(s, SortRef),
"Z3 sort expected")
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 ModelRef.__getitem__().
◆ num_sorts()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 6559 of file z3py.py.
6559 defnum_sorts(self):
6560 """Return the number of uninterpreted sorts that contain an interpretation in the model `self`. 6562 >>> A = DeclareSort('A') 6563 >>> a, b = Consts('a b', A)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 ModelRef.get_sort(), and ModelRef.sorts().
◆ sexpr()Return a textual representation of the s-expression representing the model.
Definition at line 6429 of file z3py.py.
6430 """Return a textual representation of the s-expression representing the model."""Z3_string Z3_API Z3_model_to_string(Z3_context c, Z3_model m)
Convert the given model into a string.
Referenced by Fixedpoint.__repr__(), and Optimize.__repr__().
◆ sorts()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 6597 of file z3py.py.
6598 """Return all uninterpreted sorts that have an interpretation in the model `self`. 6600 >>> A = DeclareSort('A') 6601 >>> B = DeclareSort('B') 6602 >>> a1, a2 = Consts('a1 a2', A) 6603 >>> b1, b2 = Consts('b1 b2', B) 6605 >>> s.add(a1 != a2, b1 != b2) 6612 return[self.get_sort(i)
fori
in range(self.num_sorts())]
◆ translate() def translate ( self, target )Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
Definition at line 6720 of file z3py.py.
6720 deftranslate(self, target):
6721 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`. 6724_z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
6726 returnModelRef(model, target)
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 AstRef.__copy__(), Goal.__copy__(), AstVector.__copy__(), FuncInterp.__copy__(), ModelRef.__copy__(), Solver.__copy__(), Goal.__deepcopy__(), AstVector.__deepcopy__(), FuncInterp.__deepcopy__(), ModelRef.__deepcopy__(), and Solver.__deepcopy__().
◆ update_value() def update_value ( self, x, value )Update the interpretation of a constant
Definition at line 6698 of file z3py.py.
6698 defupdate_value(self, x, value):
6699 """Update the interpretation of a constant""" 6702 if is_func_decl(x)
andx.arity() != 0
andisinstance(value, FuncInterp):
6705fi2 = FuncInterp(fi2, x.ctx)
6706 fori
in range(value.num_entries()):
6711v.push(e.arg_value(j))
6716 raiseZ3Exception(
"Expecting 0-ary function or constant expression")
6717value = _py2expr(value)
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.
◆ ctxDefinition at line 6419 of file z3py.py.
Referenced by ArithRef.__add__(), BitVecRef.__add__(), FPRef.__add__(), BitVecRef.__and__(), FuncDeclRef.__call__(), Probe.__call__(), AstMap.__contains__(), AstRef.__copy__(), Goal.__copy__(), AstVector.__copy__(), FuncInterp.__copy__(), ModelRef.__copy__(), Solver.__copy__(), AstRef.__deepcopy__(), Datatype.__deepcopy__(), ParamsRef.__deepcopy__(), ParamDescrsRef.__deepcopy__(), Goal.__deepcopy__(), AstVector.__deepcopy__(), AstMap.__deepcopy__(), FuncEntry.__deepcopy__(), FuncInterp.__deepcopy__(), ModelRef.__deepcopy__(), Statistics.__deepcopy__(), Solver.__deepcopy__(), Fixedpoint.__deepcopy__(), Optimize.__deepcopy__(), ApplyResult.__deepcopy__(), Simplifier.__deepcopy__(), Tactic.__deepcopy__(), Probe.__deepcopy__(), Context.__del__(), AstRef.__del__(), ScopedConstructor.__del__(), ScopedConstructorList.__del__(), ParamsRef.__del__(), ParamDescrsRef.__del__(), Goal.__del__(), AstVector.__del__(), AstMap.__del__(), FuncEntry.__del__(), FuncInterp.__del__(), ModelRef.__del__(), Statistics.__del__(), Solver.__del__(), Fixedpoint.__del__(), Optimize.__del__(), ApplyResult.__del__(), Simplifier.__del__(), Tactic.__del__(), Probe.__del__(), ParserContext.__del__(), ArithRef.__div__(), BitVecRef.__div__(), FPRef.__div__(), ExprRef.__eq__(), Probe.__eq__(), ArithRef.__ge__(), BitVecRef.__ge__(), Probe.__ge__(), FPRef.__ge__(), SeqRef.__ge__(), AstVector.__getitem__(), SeqRef.__getitem__(), ModelRef.__getitem__(), Statistics.__getitem__(), ApplyResult.__getitem__(), AstMap.__getitem__(), ArithRef.__gt__(), BitVecRef.__gt__(), Probe.__gt__(), FPRef.__gt__(), SeqRef.__gt__(), BitVecRef.__invert__(), ArithRef.__le__(), BitVecRef.__le__(), Probe.__le__(), FPRef.__le__(), SeqRef.__le__(), CharRef.__le__(), AstVector.__len__(), AstMap.__len__(), ModelRef.__len__(), Statistics.__len__(), ApplyResult.__len__(), BitVecRef.__lshift__(), ArithRef.__lt__(), BitVecRef.__lt__(), Probe.__lt__(), FPRef.__lt__(), SeqRef.__lt__(), ArithRef.__mod__(), BitVecRef.__mod__(), BoolRef.__mul__(), ArithRef.__mul__(), BitVecRef.__mul__(), FPRef.__mul__(), ExprRef.__ne__(), Probe.__ne__(), ArithRef.__neg__(), BitVecRef.__neg__(), BitVecRef.__or__(), ArithRef.__pow__(), ArithRef.__radd__(), BitVecRef.__radd__(), FPRef.__radd__(), BitVecRef.__rand__(), ArithRef.__rdiv__(), BitVecRef.__rdiv__(), FPRef.__rdiv__(), ParamsRef.__repr__(), ParamDescrsRef.__repr__(), AstMap.__repr__(), Statistics.__repr__(), BitVecRef.__rlshift__(), ArithRef.__rmod__(), BitVecRef.__rmod__(), ArithRef.__rmul__(), BitVecRef.__rmul__(), FPRef.__rmul__(), BitVecRef.__ror__(), ArithRef.__rpow__(), BitVecRef.__rrshift__(), BitVecRef.__rshift__(), ArithRef.__rsub__(), BitVecRef.__rsub__(), FPRef.__rsub__(), BitVecRef.__rxor__(), AstVector.__setitem__(), AstMap.__setitem__(), ArithRef.__sub__(), BitVecRef.__sub__(), FPRef.__sub__(), BitVecRef.__xor__(), DatatypeSortRef.accessor(), Simplifier.add(), Fixedpoint.add_cover(), ParserContext.add_decl(), Fixedpoint.add_rule(), Optimize.add_soft(), ParserContext.add_sort(), Tactic.apply(), AlgebraicNumRef.approx(), ExprRef.arg(), FuncEntry.arg_value(), FuncInterp.arity(), Goal.as_expr(), ApplyResult.as_expr(), FPNumRef.as_string(), Solver.assert_and_track(), Optimize.assert_and_track(), Goal.assert_exprs(), Solver.assert_exprs(), Fixedpoint.assert_exprs(), Optimize.assert_exprs(), Solver.assertions(), Optimize.assertions(), SeqRef.at(), SeqSortRef.basis(), ReSortRef.basis(), QuantifierRef.body(), BoolSortRef.cast(), Solver.check(), Optimize.check(), UserPropagateBase.conflict(), Solver.consequences(), DatatypeSortRef.constructor(), Goal.convert_model(), AstRef.ctx_ref(), UserPropagateBase.ctx_ref(), ExprRef.decl(), ModelRef.decls(), ArrayRef.default(), RatNumRef.denominator(), Goal.depth(), Goal.dimacs(), Solver.dimacs(), ArraySortRef.domain(), FuncDeclRef.domain(), ArraySortRef.domain_n(), FuncInterp.else_value(), FuncInterp.entry(), AstMap.erase(), ModelRef.eval(), FPNumRef.exponent(), FPNumRef.exponent_as_bv(), FPNumRef.exponent_as_long(), Solver.from_file(), Optimize.from_file(), Solver.from_string(), Optimize.from_string(), ParserContext.from_string(), Goal.get(), Fixedpoint.get_answer(), Fixedpoint.get_assertions(), Fixedpoint.get_cover_delta(), ParamDescrsRef.get_documentation(), Fixedpoint.get_ground_sat_answer(), ModelRef.get_interp(), Statistics.get_key_value(), ParamDescrsRef.get_kind(), ParamDescrsRef.get_name(), Fixedpoint.get_num_levels(), Fixedpoint.get_rule_names_along_trace(), Fixedpoint.get_rules(), Fixedpoint.get_rules_along_trace(), ModelRef.get_sort(), ModelRef.get_universe(), Solver.help(), Fixedpoint.help(), Optimize.help(), Simplifier.help(), Tactic.help(), Solver.import_model_converter(), Goal.inconsistent(), Solver.interrupt(), CharRef.is_digit(), FPNumRef.isInf(), FPNumRef.isNaN(), FPNumRef.isNegative(), FPNumRef.isNormal(), FPNumRef.isPositive(), FPNumRef.isSubnormal(), FPNumRef.isZero(), AstMap.keys(), Statistics.keys(), SortRef.kind(), Optimize.maximize(), Optimize.minimize(), Solver.model(), Optimize.model(), SortRef.name(), FuncDeclRef.name(), Solver.next(), QuantifierRef.no_pattern(), Solver.non_units(), FuncEntry.num_args(), FuncInterp.num_entries(), Solver.num_scopes(), ModelRef.num_sorts(), RatNumRef.numerator(), Optimize.objectives(), Solver.param_descrs(), Fixedpoint.param_descrs(), Optimize.param_descrs(), Simplifier.param_descrs(), Tactic.param_descrs(), FuncDeclRef.params(), Fixedpoint.parse_file(), Fixedpoint.parse_string(), QuantifierRef.pattern(), AlgebraicNumRef.poly(), Optimize.pop(), Solver.pop(), Goal.prec(), Solver.proof(), Solver.push(), Optimize.push(), AstVector.push(), QuantifierRef.qid(), Fixedpoint.query(), Fixedpoint.query_from_lvl(), FuncDeclRef.range(), ArraySortRef.range(), Solver.reason_unknown(), Fixedpoint.reason_unknown(), Optimize.reason_unknown(), DatatypeSortRef.recognizer(), Context.ref(), Fixedpoint.register_relation(), AstMap.reset(), Solver.reset(), AstVector.resize(), Solver.root(), Solver.set(), Fixedpoint.set(), Optimize.set(), ParamsRef.set(), Solver.set_initial_value(), Optimize.set_initial_value(), Optimize.set_on_model(), Fixedpoint.set_predicate_representation(), Goal.sexpr(), AstVector.sexpr(), ModelRef.sexpr(), Solver.sexpr(), Fixedpoint.sexpr(), Optimize.sexpr(), ApplyResult.sexpr(), FPNumRef.sign(), FPNumRef.sign_as_bv(), FPNumRef.significand(), FPNumRef.significand_as_bv(), FPNumRef.significand_as_long(), ParamDescrsRef.size(), Goal.size(), QuantifierRef.skolem_id(), Tactic.solver(), ExprRef.sort(), BoolRef.sort(), QuantifierRef.sort(), ArithRef.sort(), BitVecRef.sort(), ArrayRef.sort(), DatatypeRef.sort(), FiniteDomainRef.sort(), FPRef.sort(), SeqRef.sort(), Solver.statistics(), Fixedpoint.statistics(), Optimize.statistics(), CharRef.to_bv(), CharRef.to_int(), Solver.to_smt2(), Fixedpoint.to_string(), Solver.trail(), Solver.trail_levels(), AstVector.translate(), FuncInterp.translate(), AstRef.translate(), Goal.translate(), ModelRef.translate(), Solver.translate(), Solver.units(), Solver.unsat_core(), Optimize.unsat_core(), Fixedpoint.update_rule(), Simplifier.using_params(), ParamsRef.validate(), FuncEntry.value(), QuantifierRef.var_name(), and QuantifierRef.var_sort().
◆ modelDefinition at line 6418 of file z3py.py.
Referenced by ModelRef.__del__(), ModelRef.__getitem__(), ModelRef.__len__(), ModelRef.decls(), ModelRef.eval(), ModelRef.get_interp(), ModelRef.get_sort(), ModelRef.get_universe(), ModelRef.num_sorts(), ModelRef.sexpr(), FuncInterp.translate(), ModelRef.translate(), and ModelRef.update_value().
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