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Public Member Functions | Data Fields
Fixedpoint Class Reference

Fixedpoint. More...

+ Inheritance diagram for Fixedpoint:

Public Member Functions

 __init__ (self, fixedpoint=None, ctx=None)
 
 __deepcopy__ (self, memo={})
 
 __del__ (self)
 
 set (self, *args, **keys)
 
 help (self)
 
 param_descrs (self)
 
 assert_exprs (self, *args)
 
 add (self, *args)
 
 __iadd__ (self, fml)
 
 append (self, *args)
 
 insert (self, *args)
 
 add_rule (self, head, body=None, name=None)
 
 rule (self, head, body=None, name=None)
 
 fact (self, head, name=None)
 
 query (self, *query)
 
 query_from_lvl (self, lvl, *query)
 
 update_rule (self, head, body, name)
 
 get_answer (self)
 
 get_ground_sat_answer (self)
 
 get_rules_along_trace (self)
 
 get_rule_names_along_trace (self)
 
 get_num_levels (self, predicate)
 
 get_cover_delta (self, level, predicate)
 
 add_cover (self, level, predicate, property)
 
 register_relation (self, *relations)
 
 set_predicate_representation (self, f, *representations)
 
 parse_string (self, s)
 
 parse_file (self, f)
 
 get_rules (self)
 
 get_assertions (self)
 
 __repr__ (self)
 
 sexpr (self)
 
 to_string (self, queries)
 
 statistics (self)
 
 reason_unknown (self)
 
 declare_var (self, *vars)
 
 abstract (self, fml, is_forall=True)
 
- Public Member Functions inherited from Z3PPObject
 use_pp (self)
 

Data Fields

 ctx
 
 fixedpoint
 
 vars
 

Additional Inherited Members

- Protected Member Functions inherited from Z3PPObject
 _repr_html_ (self)
 

Detailed Description

Fixedpoint.

Fixedpoint API provides methods for solving with recursive predicates

Definition at line 7430 of file z3py.py.

Constructor & Destructor Documentation

◆ __init__()

__init__ (   self,
  fixedpoint = None,
  ctx = None 
)

Definition at line 7433 of file z3py.py.

7433 def __init__(self, fixedpoint=None, ctx=None):
7434 assert fixedpoint is None or ctx is not None
7435 self.ctx = _get_ctx(ctx)
7436 self.fixedpoint = None
7437 if fixedpoint is None:
7438 self.fixedpoint = Z3_mk_fixedpoint(self.ctx.ref())
7439 else:
7440 self.fixedpoint = fixedpoint
7441 Z3_fixedpoint_inc_ref(self.ctx.ref(), self.fixedpoint)
7442 self.vars = []
7443
void Z3_API Z3_fixedpoint_inc_ref(Z3_context c, Z3_fixedpoint d)
Increment the reference counter of the given fixedpoint context.
Z3_fixedpoint Z3_API Z3_mk_fixedpoint(Z3_context c)
Create a new fixedpoint context.

◆ __del__()

__del__ (   self)

Definition at line 7447 of file z3py.py.

7447 def __del__(self):
7448 if self.fixedpoint is not None and self.ctx.ref() is not None and Z3_fixedpoint_dec_ref is not None:
7449 Z3_fixedpoint_dec_ref(self.ctx.ref(), self.fixedpoint)
7450
void Z3_API Z3_fixedpoint_dec_ref(Z3_context c, Z3_fixedpoint d)
Decrement the reference counter of the given fixedpoint context.

Member Function Documentation

◆ __deepcopy__()

__deepcopy__ (   self,
  memo = {} 
)

Definition at line 7444 of file z3py.py.

7444 def __deepcopy__(self, memo={}):
7445 return FixedPoint(self.fixedpoint, self.ctx)
7446

◆ __iadd__()

__iadd__ (   self,
  fml 
)

Definition at line 7483 of file z3py.py.

7483 def __iadd__(self, fml):
7484 self.add(fml)
7485 return self
7486

◆ __repr__()

__repr__ (   self)
Return a formatted string with all added rules and constraints.

Definition at line 7644 of file z3py.py.

7644 def __repr__(self):
7645 """Return a formatted string with all added rules and constraints."""
7646 return self.sexpr()
7647

◆ abstract()

abstract (   self,
  fml,
  is_forall = True 
)

Definition at line 7681 of file z3py.py.

7681 def abstract(self, fml, is_forall=True):
7682 if self.vars == []:
7683 return fml
7684 if is_forall:
7685 return ForAll(self.vars, fml)
7686 else:
7687 return Exists(self.vars, fml)
7688
7689

Referenced by Fixedpoint.add_rule(), Fixedpoint.assert_exprs(), Fixedpoint.query(), Fixedpoint.query_from_lvl(), and Fixedpoint.update_rule().

◆ add()

add (   self,
args 
)
Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr.

Definition at line 7479 of file z3py.py.

7479 def add(self, *args):
7480 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7481 self.assert_exprs(*args)
7482

Referenced by Solver.__iadd__(), Fixedpoint.__iadd__(), and Optimize.__iadd__().

◆ add_cover()

add_cover (   self,
  level,
  predicate,
  property 
)
Add property to predicate for the level'th unfolding.
-1 is treated as infinity (infinity)

Definition at line 7606 of file z3py.py.

7606 def add_cover(self, level, predicate, property):
7607 """Add property to predicate for the level'th unfolding.
7608 -1 is treated as infinity (infinity)
7609 """
7610 Z3_fixedpoint_add_cover(self.ctx.ref(), self.fixedpoint, level, predicate.ast, property.ast)
7611
void Z3_API Z3_fixedpoint_add_cover(Z3_context c, Z3_fixedpoint d, int level, Z3_func_decl pred, Z3_ast property)
Add property about the predicate pred. Add a property of predicate pred at level. It gets pushed forw...

◆ add_rule()

add_rule (   self,
  head,
  body = None,
  name = None 
)
Assert rules defining recursive predicates to the fixedpoint solver.
>>> a = Bool('a')
>>> b = Bool('b')
>>> s = Fixedpoint()
>>> s.register_relation(a.decl())
>>> s.register_relation(b.decl())
>>> s.fact(a)
>>> s.rule(b, a)
>>> s.query(b)
sat

Definition at line 7495 of file z3py.py.

7495 def add_rule(self, head, body=None, name=None):
7496 """Assert rules defining recursive predicates to the fixedpoint solver.
7497 >>> a = Bool('a')
7498 >>> b = Bool('b')
7499 >>> s = Fixedpoint()
7500 >>> s.register_relation(a.decl())
7501 >>> s.register_relation(b.decl())
7502 >>> s.fact(a)
7503 >>> s.rule(b, a)
7504 >>> s.query(b)
7505 sat
7506 """
7507 if name is None:
7508 name = ""
7509 name = to_symbol(name, self.ctx)
7510 if body is None:
7511 head = self.abstract(head)
7512 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, head.as_ast(), name)
7513 else:
7514 body = _get_args(body)
7515 f = self.abstract(Implies(And(body, self.ctx), head))
7516 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7517
void Z3_API Z3_fixedpoint_add_rule(Z3_context c, Z3_fixedpoint d, Z3_ast rule, Z3_symbol name)
Add a universal Horn clause as a named rule. The horn_rule should be of the form:

Referenced by Fixedpoint.fact(), and Fixedpoint.rule().

◆ append()

append (   self,
args 
)
Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr.

Definition at line 7487 of file z3py.py.

7487 def append(self, *args):
7488 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7489 self.assert_exprs(*args)
7490

◆ assert_exprs()

assert_exprs (   self,
args 
)
Assert constraints as background axioms for the fixedpoint solver.

Definition at line 7465 of file z3py.py.

7465 def assert_exprs(self, *args):
7466 """Assert constraints as background axioms for the fixedpoint solver."""
7467 args = _get_args(args)
7468 s = BoolSort(self.ctx)
7469 for arg in args:
7470 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7471 for f in arg:
7472 f = self.abstract(f)
7473 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, f.as_ast())
7474 else:
7475 arg = s.cast(arg)
7476 arg = self.abstract(arg)
7477 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, arg.as_ast())
7478
void Z3_API Z3_fixedpoint_assert(Z3_context c, Z3_fixedpoint d, Z3_ast axiom)
Assert a constraint to the fixedpoint context.

Referenced by Goal.add(), Solver.add(), Fixedpoint.add(), Optimize.add(), Goal.append(), Solver.append(), Fixedpoint.append(), Goal.insert(), Solver.insert(), and Fixedpoint.insert().

◆ declare_var()

declare_var (   self,
vars 
)
Add variable or several variables.
The added variable or variables will be bound in the rules
and queries

Definition at line 7672 of file z3py.py.

7672 def declare_var(self, *vars):
7673 """Add variable or several variables.
7674 The added variable or variables will be bound in the rules
7675 and queries
7676 """
7677 vars = _get_args(vars)
7678 for v in vars:
7679 self.vars += [v]
7680

◆ fact()

fact (   self,
  head,
  name = None 
)
Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule.

Definition at line 7522 of file z3py.py.

7522 def fact(self, head, name=None):
7523 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7524 self.add_rule(head, None, name)
7525

◆ get_answer()

get_answer (   self)
Retrieve answer from last query call.

Definition at line 7573 of file z3py.py.

7573 def get_answer(self):
7574 """Retrieve answer from last query call."""
7575 r = Z3_fixedpoint_get_answer(self.ctx.ref(), self.fixedpoint)
7576 return _to_expr_ref(r, self.ctx)
7577
Z3_ast Z3_API Z3_fixedpoint_get_answer(Z3_context c, Z3_fixedpoint d)
Retrieve a formula that encodes satisfying answers to the query.

◆ get_assertions()

get_assertions (   self)
retrieve assertions that have been added to fixedpoint context

Definition at line 7640 of file z3py.py.

7640 def get_assertions(self):
7641 """retrieve assertions that have been added to fixedpoint context"""
7642 return AstVector(Z3_fixedpoint_get_assertions(self.ctx.ref(), self.fixedpoint), self.ctx)
7643
Z3_ast_vector Z3_API Z3_fixedpoint_get_assertions(Z3_context c, Z3_fixedpoint f)
Retrieve set of background assertions from fixedpoint context.

◆ get_cover_delta()

get_cover_delta (   self,
  level,
  predicate 
)
Retrieve properties known about predicate for the level'th unfolding.
-1 is treated as the limit (infinity)

Definition at line 7599 of file z3py.py.

7599 def get_cover_delta(self, level, predicate):
7600 """Retrieve properties known about predicate for the level'th unfolding.
7601 -1 is treated as the limit (infinity)
7602 """
7603 r = Z3_fixedpoint_get_cover_delta(self.ctx.ref(), self.fixedpoint, level, predicate.ast)
7604 return _to_expr_ref(r, self.ctx)
7605
Z3_ast Z3_API Z3_fixedpoint_get_cover_delta(Z3_context c, Z3_fixedpoint d, int level, Z3_func_decl pred)

◆ get_ground_sat_answer()

get_ground_sat_answer (   self)
Retrieve a ground cex from last query call.

Definition at line 7578 of file z3py.py.

7578 def get_ground_sat_answer(self):
7579 """Retrieve a ground cex from last query call."""
7580 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.fixedpoint)
7581 return _to_expr_ref(r, self.ctx)
7582

◆ get_num_levels()

get_num_levels (   self,
  predicate 
)
Retrieve number of levels used for predicate in PDR engine

Definition at line 7595 of file z3py.py.

7595 def get_num_levels(self, predicate):
7596 """Retrieve number of levels used for predicate in PDR engine"""
7597 return Z3_fixedpoint_get_num_levels(self.ctx.ref(), self.fixedpoint, predicate.ast)
7598
unsigned Z3_API Z3_fixedpoint_get_num_levels(Z3_context c, Z3_fixedpoint d, Z3_func_decl pred)
Query the PDR engine for the maximal levels properties are known about predicate.

◆ get_rule_names_along_trace()

get_rule_names_along_trace (   self)
retrieve rule names along the counterexample trace

Definition at line 7587 of file z3py.py.

7587 def get_rule_names_along_trace(self):
7588 """retrieve rule names along the counterexample trace"""
7589 # this is a hack as I don't know how to return a list of symbols from C++;
7590 # obtain names as a single string separated by semicolons
7591 names = _symbol2py(self.ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.fixedpoint))
7592 # split into individual names
7593 return names.split(";")
7594

◆ get_rules()

get_rules (   self)
retrieve rules that have been added to fixedpoint context

Definition at line 7636 of file z3py.py.

7636 def get_rules(self):
7637 """retrieve rules that have been added to fixedpoint context"""
7638 return AstVector(Z3_fixedpoint_get_rules(self.ctx.ref(), self.fixedpoint), self.ctx)
7639
Z3_ast_vector Z3_API Z3_fixedpoint_get_rules(Z3_context c, Z3_fixedpoint f)
Retrieve set of rules from fixedpoint context.

◆ get_rules_along_trace()

get_rules_along_trace (   self)
retrieve rules along the counterexample trace

Definition at line 7583 of file z3py.py.

7583 def get_rules_along_trace(self):
7584 """retrieve rules along the counterexample trace"""
7585 return AstVector(Z3_fixedpoint_get_rules_along_trace(self.ctx.ref(), self.fixedpoint), self.ctx)
7586

◆ help()

help (   self)
Display a string describing all available options.

Definition at line 7457 of file z3py.py.

7457 def help(self):
7458 """Display a string describing all available options."""
7459 print(Z3_fixedpoint_get_help(self.ctx.ref(), self.fixedpoint))
7460
Z3_string Z3_API Z3_fixedpoint_get_help(Z3_context c, Z3_fixedpoint f)
Return a string describing all fixedpoint available parameters.

◆ insert()

insert (   self,
args 
)
Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr.

Definition at line 7491 of file z3py.py.

7491 def insert(self, *args):
7492 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7493 self.assert_exprs(*args)
7494

◆ param_descrs()

param_descrs (   self)
Return the parameter description set.

Definition at line 7461 of file z3py.py.

7461 def param_descrs(self):
7462 """Return the parameter description set."""
7463 return ParamDescrsRef(Z3_fixedpoint_get_param_descrs(self.ctx.ref(), self.fixedpoint), self.ctx)
7464
Z3_param_descrs Z3_API Z3_fixedpoint_get_param_descrs(Z3_context c, Z3_fixedpoint f)
Return the parameter description set for the given fixedpoint object.

◆ parse_file()

parse_file (   self,
  f 
)
Parse rules and queries from a file

Definition at line 7632 of file z3py.py.

7632 def parse_file(self, f):
7633 """Parse rules and queries from a file"""
7634 return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)
7635
Z3_ast_vector Z3_API Z3_fixedpoint_from_file(Z3_context c, Z3_fixedpoint f, Z3_string s)
Parse an SMT-LIB2 file with fixedpoint rules. Add the rules to the current fixedpoint context....

◆ parse_string()

parse_string (   self,
  s 
)
Parse rules and queries from a string

Definition at line 7628 of file z3py.py.

7628 def parse_string(self, s):
7629 """Parse rules and queries from a string"""
7630 return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)
7631
Z3_ast_vector Z3_API Z3_fixedpoint_from_string(Z3_context c, Z3_fixedpoint f, Z3_string s)
Parse an SMT-LIB2 string with fixedpoint rules. Add the rules to the current fixedpoint context....

◆ query()

query (   self,
query 
)
Query the fixedpoint engine whether formula is derivable.
   You can also pass an tuple or list of recursive predicates.

Definition at line 7526 of file z3py.py.

7526 def query(self, *query):
7527 """Query the fixedpoint engine whether formula is derivable.
7528 You can also pass an tuple or list of recursive predicates.
7529 """
7530 query = _get_args(query)
7531 sz = len(query)
7532 if sz >= 1 and isinstance(query[0], FuncDeclRef):
7533 _decls = (FuncDecl * sz)()
7534 i = 0
7535 for q in query:
7536 _decls[i] = q.ast
7537 i = i + 1
7538 r = Z3_fixedpoint_query_relations(self.ctx.ref(), self.fixedpoint, sz, _decls)
7539 else:
7540 if sz == 1:
7541 query = query[0]
7542 else:
7543 query = And(query, self.ctx)
7544 query = self.abstract(query, False)
7545 r = Z3_fixedpoint_query(self.ctx.ref(), self.fixedpoint, query.as_ast())
7546 return CheckSatResult(r)
7547
Z3_lbool Z3_API Z3_fixedpoint_query(Z3_context c, Z3_fixedpoint d, Z3_ast query)
Pose a query against the asserted rules.
Z3_lbool Z3_API Z3_fixedpoint_query_relations(Z3_context c, Z3_fixedpoint d, unsigned num_relations, Z3_func_decl const relations[])
Pose multiple queries against the asserted rules.

◆ query_from_lvl()

query_from_lvl (   self,
  lvl,
query 
)
Query the fixedpoint engine whether formula is derivable starting at the given query level.

Definition at line 7548 of file z3py.py.

7548 def query_from_lvl(self, lvl, *query):
7549 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7550 """
7551 query = _get_args(query)
7552 sz = len(query)
7553 if sz >= 1 and isinstance(query[0], FuncDecl):
7554 _z3_assert(False, "unsupported")
7555 else:
7556 if sz == 1:
7557 query = query[0]
7558 else:
7559 query = And(query)
7560 query = self.abstract(query, False)
7561 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.fixedpoint, query.as_ast(), lvl)
7562 return CheckSatResult(r)
7563

◆ reason_unknown()

reason_unknown (   self)
Return a string describing why the last `query()` returned `unknown`.

Definition at line 7667 of file z3py.py.

7667 def reason_unknown(self):
7668 """Return a string describing why the last `query()` returned `unknown`.
7669 """
7670 return Z3_fixedpoint_get_reason_unknown(self.ctx.ref(), self.fixedpoint)
7671
Z3_string Z3_API Z3_fixedpoint_get_reason_unknown(Z3_context c, Z3_fixedpoint d)
Retrieve a string that describes the last status returned by Z3_fixedpoint_query.

◆ register_relation()

register_relation (   self,
relations 
)
Register relation as recursive

Definition at line 7612 of file z3py.py.

7612 def register_relation(self, *relations):
7613 """Register relation as recursive"""
7614 relations = _get_args(relations)
7615 for f in relations:
7616 Z3_fixedpoint_register_relation(self.ctx.ref(), self.fixedpoint, f.ast)
7617
void Z3_API Z3_fixedpoint_register_relation(Z3_context c, Z3_fixedpoint d, Z3_func_decl f)
Register relation as Fixedpoint defined. Fixedpoint defined relations have least-fixedpoint semantics...

◆ rule()

rule (   self,
  head,
  body = None,
  name = None 
)
Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule.

Definition at line 7518 of file z3py.py.

7518 def rule(self, head, body=None, name=None):
7519 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7520 self.add_rule(head, body, name)
7521

◆ set()

set (   self,
args,
**  keys 
)
Set a configuration option. The method `help()` return a string containing all available options.

Definition at line 7451 of file z3py.py.

7451 def set(self, *args, **keys):
7452 """Set a configuration option. The method `help()` return a string containing all available options.
7453 """
7454 p = args2params(args, keys, self.ctx)
7455 Z3_fixedpoint_set_params(self.ctx.ref(), self.fixedpoint, p.params)
7456
void Z3_API Z3_fixedpoint_set_params(Z3_context c, Z3_fixedpoint f, Z3_params p)
Set parameters on fixedpoint context.

◆ set_predicate_representation()

set_predicate_representation (   self,
  f,
representations 
)
Control how relation is represented

Definition at line 7618 of file z3py.py.

7618 def set_predicate_representation(self, f, *representations):
7619 """Control how relation is represented"""
7620 representations = _get_args(representations)
7621 representations = [to_symbol(s) for s in representations]
7622 sz = len(representations)
7623 args = (Symbol * sz)()
7624 for i in range(sz):
7625 args[i] = representations[i]
7626 Z3_fixedpoint_set_predicate_representation(self.ctx.ref(), self.fixedpoint, f.ast, sz, args)
7627
void Z3_API Z3_fixedpoint_set_predicate_representation(Z3_context c, Z3_fixedpoint d, Z3_func_decl f, unsigned num_relations, Z3_symbol const relation_kinds[])
Configure the predicate representation.

◆ sexpr()

sexpr (   self)
Return a formatted string (in Lisp-like format) with all added constraints.
We say the string is in s-expression format.

Definition at line 7648 of file z3py.py.

7648 def sexpr(self):
7649 """Return a formatted string (in Lisp-like format) with all added constraints.
7650 We say the string is in s-expression format.
7651 """
7652 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, 0, (Ast * 0)())
7653
Z3_string Z3_API Z3_fixedpoint_to_string(Z3_context c, Z3_fixedpoint f, unsigned num_queries, Z3_ast queries[])
Print the current rules and background axioms as a string.

Referenced by Fixedpoint.__repr__(), and Optimize.__repr__().

◆ statistics()

statistics (   self)
Return statistics for the last `query()`.

Definition at line 7662 of file z3py.py.

7662 def statistics(self):
7663 """Return statistics for the last `query()`.
7664 """
7665 return Statistics(Z3_fixedpoint_get_statistics(self.ctx.ref(), self.fixedpoint), self.ctx)
7666
Z3_stats Z3_API Z3_fixedpoint_get_statistics(Z3_context c, Z3_fixedpoint d)
Retrieve statistics information from the last call to Z3_fixedpoint_query.

◆ to_string()

to_string (   self,
  queries 
)
Return a formatted string (in Lisp-like format) with all added constraints.
   We say the string is in s-expression format.
   Include also queries.

Definition at line 7654 of file z3py.py.

7654 def to_string(self, queries):
7655 """Return a formatted string (in Lisp-like format) with all added constraints.
7656 We say the string is in s-expression format.
7657 Include also queries.
7658 """
7659 args, len = _to_ast_array(queries)
7660 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, len, args)
7661

◆ update_rule()

update_rule (   self,
  head,
  body,
  name 
)
update rule

Definition at line 7564 of file z3py.py.

7564 def update_rule(self, head, body, name):
7565 """update rule"""
7566 if name is None:
7567 name = ""
7568 name = to_symbol(name, self.ctx)
7569 body = _get_args(body)
7570 f = self.abstract(Implies(And(body, self.ctx), head))
7571 Z3_fixedpoint_update_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7572
void Z3_API Z3_fixedpoint_update_rule(Z3_context c, Z3_fixedpoint d, Z3_ast a, Z3_symbol name)
Update a named rule. A rule with the same name must have been previously created.

Field Documentation

◆ ctx

ctx

Definition at line 7435 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(), 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(), QuantifierRef.body(), Solver.check(), Optimize.check(), UserPropagateBase.conflict(), Solver.consequences(), Goal.convert_model(), AstRef.ctx_ref(), UserPropagateBase.ctx_ref(), ExprRef.decl(), ModelRef.decls(), ArrayRef.default(), RatNumRef.denominator(), Goal.depth(), Goal.dimacs(), Solver.dimacs(), 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(), CharRef.is_digit(), FPNumRef.isInf(), FPNumRef.isNaN(), FPNumRef.isNegative(), FPNumRef.isNormal(), FPNumRef.isPositive(), FPNumRef.isSubnormal(), FPNumRef.isZero(), AstMap.keys(), Statistics.keys(), Optimize.maximize(), Optimize.minimize(), Solver.model(), Optimize.model(), SortRef.name(), Solver.next(), QuantifierRef.no_pattern(), Solver.non_units(), FuncEntry.num_args(), FuncInterp.num_entries(), Solver.num_scopes(), ModelRef.num_sorts(), 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(), 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(), 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.significand(), FPNumRef.significand_as_bv(), FPNumRef.significand_as_long(), ParamDescrsRef.size(), Goal.size(), Tactic.solver(), 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(), 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().

◆ fixedpoint

fixedpoint

◆ vars

vars

Definition at line 7442 of file z3py.py.

Referenced by Fixedpoint.abstract(), and Fixedpoint.declare_var().