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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 = _get_ctx(ctx)
 fixedpoint = None
list 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 7600 of file z3py.py.

Constructor & Destructor Documentation

◆ __init__()

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

Definition at line 7603 of file z3py.py.

7603 def __init__(self, fixedpoint=None, ctx=None):
7604 assert fixedpoint is None or ctx is not None
7605 self.ctx = _get_ctx(ctx)
7606 self.fixedpoint = None
7607 if fixedpoint is None:
7608 self.fixedpoint = Z3_mk_fixedpoint(self.ctx.ref())
7609 else:
7610 self.fixedpoint = fixedpoint
7611 Z3_fixedpoint_inc_ref(self.ctx.ref(), self.fixedpoint)
7612 self.vars = []
7613
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 7617 of file z3py.py.

7617 def __del__(self):
7618 if self.fixedpoint is not None and self.ctx.ref() is not None and Z3_fixedpoint_dec_ref is not None:
7619 Z3_fixedpoint_dec_ref(self.ctx.ref(), self.fixedpoint)
7620
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 7614 of file z3py.py.

7614 def __deepcopy__(self, memo={}):
7615 return FixedPoint(self.fixedpoint, self.ctx)
7616

◆ __iadd__()

__iadd__ ( self,
fml )

Definition at line 7653 of file z3py.py.

7653 def __iadd__(self, fml):
7654 self.add(fml)
7655 return self
7656

◆ __repr__()

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

Definition at line 7814 of file z3py.py.

7814 def __repr__(self):
7815 """Return a formatted string with all added rules and constraints."""
7816 return self.sexpr()
7817

◆ abstract()

abstract ( self,
fml,
is_forall = True )

Definition at line 7851 of file z3py.py.

7851 def abstract(self, fml, is_forall=True):
7852 if self.vars == []:
7853 return fml
7854 if is_forall:
7855 return ForAll(self.vars, fml)
7856 else:
7857 return Exists(self.vars, fml)
7858
7859

◆ add()

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

Definition at line 7649 of file z3py.py.

7649 def add(self, *args):
7650 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7651 self.assert_exprs(*args)
7652

◆ 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 7776 of file z3py.py.

7776 def add_cover(self, level, predicate, property):
7777 """Add property to predicate for the level'th unfolding.
7778 -1 is treated as infinity (infinity)
7779 """
7780 Z3_fixedpoint_add_cover(self.ctx.ref(), self.fixedpoint, level, predicate.ast, property.ast)
7781
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 7665 of file z3py.py.

7665 def add_rule(self, head, body=None, name=None):
7666 """Assert rules defining recursive predicates to the fixedpoint solver.
7667 >>> a = Bool('a')
7668 >>> b = Bool('b')
7669 >>> s = Fixedpoint()
7670 >>> s.register_relation(a.decl())
7671 >>> s.register_relation(b.decl())
7672 >>> s.fact(a)
7673 >>> s.rule(b, a)
7674 >>> s.query(b)
7675 sat
7676 """
7677 if name is None:
7678 name = ""
7679 name = to_symbol(name, self.ctx)
7680 if body is None:
7681 head = self.abstract(head)
7682 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, head.as_ast(), name)
7683 else:
7684 body = _get_args(body)
7685 f = self.abstract(Implies(And(body, self.ctx), head))
7686 Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7687
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:

◆ append()

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

Definition at line 7657 of file z3py.py.

7657 def append(self, *args):
7658 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7659 self.assert_exprs(*args)
7660

◆ assert_exprs()

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

Definition at line 7635 of file z3py.py.

7635 def assert_exprs(self, *args):
7636 """Assert constraints as background axioms for the fixedpoint solver."""
7637 args = _get_args(args)
7638 s = BoolSort(self.ctx)
7639 for arg in args:
7640 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7641 for f in arg:
7642 f = self.abstract(f)
7643 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, f.as_ast())
7644 else:
7645 arg = s.cast(arg)
7646 arg = self.abstract(arg)
7647 Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, arg.as_ast())
7648
void Z3_API Z3_fixedpoint_assert(Z3_context c, Z3_fixedpoint d, Z3_ast axiom)
Assert a constraint to the fixedpoint context.

◆ 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 7842 of file z3py.py.

7842 def declare_var(self, *vars):
7843 """Add variable or several variables.
7844 The added variable or variables will be bound in the rules
7845 and queries
7846 """
7847 vars = _get_args(vars)
7848 for v in vars:
7849 self.vars += [v]
7850

◆ fact()

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

Definition at line 7692 of file z3py.py.

7692 def fact(self, head, name=None):
7693 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7694 self.add_rule(head, None, name)
7695

◆ get_answer()

get_answer ( self)
Retrieve answer from last query call.

Definition at line 7743 of file z3py.py.

7743 def get_answer(self):
7744 """Retrieve answer from last query call."""
7745 r = Z3_fixedpoint_get_answer(self.ctx.ref(), self.fixedpoint)
7746 return _to_expr_ref(r, self.ctx)
7747
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 7810 of file z3py.py.

7810 def get_assertions(self):
7811 """retrieve assertions that have been added to fixedpoint context"""
7812 return AstVector(Z3_fixedpoint_get_assertions(self.ctx.ref(), self.fixedpoint), self.ctx)
7813
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 7769 of file z3py.py.

7769 def get_cover_delta(self, level, predicate):
7770 """Retrieve properties known about predicate for the level'th unfolding.
7771 -1 is treated as the limit (infinity)
7772 """
7773 r = Z3_fixedpoint_get_cover_delta(self.ctx.ref(), self.fixedpoint, level, predicate.ast)
7774 return _to_expr_ref(r, self.ctx)
7775
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 7748 of file z3py.py.

7748 def get_ground_sat_answer(self):
7749 """Retrieve a ground cex from last query call."""
7750 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.fixedpoint)
7751 return _to_expr_ref(r, self.ctx)
7752

◆ get_num_levels()

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

Definition at line 7765 of file z3py.py.

7765 def get_num_levels(self, predicate):
7766 """Retrieve number of levels used for predicate in PDR engine"""
7767 return Z3_fixedpoint_get_num_levels(self.ctx.ref(), self.fixedpoint, predicate.ast)
7768
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 7757 of file z3py.py.

7757 def get_rule_names_along_trace(self):
7758 """retrieve rule names along the counterexample trace"""
7759 # this is a hack as I don't know how to return a list of symbols from C++;
7760 # obtain names as a single string separated by semicolons
7761 names = _symbol2py(self.ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.fixedpoint))
7762 # split into individual names
7763 return names.split(";")
7764

◆ get_rules()

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

Definition at line 7806 of file z3py.py.

7806 def get_rules(self):
7807 """retrieve rules that have been added to fixedpoint context"""
7808 return AstVector(Z3_fixedpoint_get_rules(self.ctx.ref(), self.fixedpoint), self.ctx)
7809
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 7753 of file z3py.py.

7753 def get_rules_along_trace(self):
7754 """retrieve rules along the counterexample trace"""
7755 return AstVector(Z3_fixedpoint_get_rules_along_trace(self.ctx.ref(), self.fixedpoint), self.ctx)
7756

◆ help()

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

Definition at line 7627 of file z3py.py.

7627 def help(self):
7628 """Display a string describing all available options."""
7629 print(Z3_fixedpoint_get_help(self.ctx.ref(), self.fixedpoint))
7630
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 7661 of file z3py.py.

7661 def insert(self, *args):
7662 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7663 self.assert_exprs(*args)
7664

◆ param_descrs()

param_descrs ( self)
Return the parameter description set.

Definition at line 7631 of file z3py.py.

7631 def param_descrs(self):
7632 """Return the parameter description set."""
7633 return ParamDescrsRef(Z3_fixedpoint_get_param_descrs(self.ctx.ref(), self.fixedpoint), self.ctx)
7634
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 7802 of file z3py.py.

7802 def parse_file(self, f):
7803 """Parse rules and queries from a file"""
7804 return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)
7805
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 7798 of file z3py.py.

7798 def parse_string(self, s):
7799 """Parse rules and queries from a string"""
7800 return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)
7801
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 7696 of file z3py.py.

7696 def query(self, *query):
7697 """Query the fixedpoint engine whether formula is derivable.
7698 You can also pass an tuple or list of recursive predicates.
7699 """
7700 query = _get_args(query)
7701 sz = len(query)
7702 if sz >= 1 and isinstance(query[0], FuncDeclRef):
7703 _decls = (FuncDecl * sz)()
7704 i = 0
7705 for q in query:
7706 _decls[i] = q.ast
7707 i = i + 1
7708 r = Z3_fixedpoint_query_relations(self.ctx.ref(), self.fixedpoint, sz, _decls)
7709 else:
7710 if sz == 1:
7711 query = query[0]
7712 else:
7713 query = And(query, self.ctx)
7714 query = self.abstract(query, False)
7715 r = Z3_fixedpoint_query(self.ctx.ref(), self.fixedpoint, query.as_ast())
7716 return CheckSatResult(r)
7717
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 7718 of file z3py.py.

7718 def query_from_lvl(self, lvl, *query):
7719 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7720 """
7721 query = _get_args(query)
7722 sz = len(query)
7723 if sz >= 1 and isinstance(query[0], FuncDecl):
7724 _z3_assert(False, "unsupported")
7725 else:
7726 if sz == 1:
7727 query = query[0]
7728 else:
7729 query = And(query)
7730 query = self.abstract(query, False)
7731 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.fixedpoint, query.as_ast(), lvl)
7732 return CheckSatResult(r)
7733

◆ reason_unknown()

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

Definition at line 7837 of file z3py.py.

7837 def reason_unknown(self):
7838 """Return a string describing why the last `query()` returned `unknown`.
7839 """
7840 return Z3_fixedpoint_get_reason_unknown(self.ctx.ref(), self.fixedpoint)
7841
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 7782 of file z3py.py.

7782 def register_relation(self, *relations):
7783 """Register relation as recursive"""
7784 relations = _get_args(relations)
7785 for f in relations:
7786 Z3_fixedpoint_register_relation(self.ctx.ref(), self.fixedpoint, f.ast)
7787
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 7688 of file z3py.py.

7688 def rule(self, head, body=None, name=None):
7689 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7690 self.add_rule(head, body, name)
7691

◆ set()

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

Definition at line 7621 of file z3py.py.

7621 def set(self, *args, **keys):
7622 """Set a configuration option. The method `help()` return a string containing all available options.
7623 """
7624 p = args2params(args, keys, self.ctx)
7625 Z3_fixedpoint_set_params(self.ctx.ref(), self.fixedpoint, p.params)
7626
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 7788 of file z3py.py.

7788 def set_predicate_representation(self, f, *representations):
7789 """Control how relation is represented"""
7790 representations = _get_args(representations)
7791 representations = [to_symbol(s) for s in representations]
7792 sz = len(representations)
7793 args = (Symbol * sz)()
7794 for i in range(sz):
7795 args[i] = representations[i]
7796 Z3_fixedpoint_set_predicate_representation(self.ctx.ref(), self.fixedpoint, f.ast, sz, args)
7797
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 7818 of file z3py.py.

7818 def sexpr(self):
7819 """Return a formatted string (in Lisp-like format) with all added constraints.
7820 We say the string is in s-expression format.
7821 """
7822 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, 0, (Ast * 0)())
7823
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.

◆ statistics()

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

Definition at line 7832 of file z3py.py.

7832 def statistics(self):
7833 """Return statistics for the last `query()`.
7834 """
7835 return Statistics(Z3_fixedpoint_get_statistics(self.ctx.ref(), self.fixedpoint), self.ctx)
7836
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 7824 of file z3py.py.

7824 def to_string(self, queries):
7825 """Return a formatted string (in Lisp-like format) with all added constraints.
7826 We say the string is in s-expression format.
7827 Include also queries.
7828 """
7829 args, len = _to_ast_array(queries)
7830 return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, len, args)
7831

◆ update_rule()

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

Definition at line 7734 of file z3py.py.

7734 def update_rule(self, head, body, name):
7735 """update rule"""
7736 if name is None:
7737 name = ""
7738 name = to_symbol(name, self.ctx)
7739 body = _get_args(body)
7740 f = self.abstract(Implies(And(body, self.ctx), head))
7741 Z3_fixedpoint_update_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)
7742
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 = _get_ctx(ctx)

Definition at line 7605 of file z3py.py.

◆ fixedpoint

fixedpoint = None

Definition at line 7606 of file z3py.py.

◆ vars

vars = []

Definition at line 7612 of file z3py.py.