Fixedpoint Class Reference

Fixedpoint. More...

Inheritance diagram for Fixedpoint:

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

Data Fields
	ctx
	fixedpoint
	vars

Detailed Description

Fixedpoint.

Fixedpoint API provides methods for solving with recursive predicates

Definition at line 6481 of file z3py.py.

Constructor & Destructor Documentation

__init__()

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

Definition at line 6484 of file z3py.py.

    def __init__(self, fixedpoint=None, ctx=None):
        assert fixedpoint is None or ctx is not None
        self.ctx    = _get_ctx(ctx)
        self.fixedpoint = None
        if fixedpoint is None:
            self.fixedpoint = Z3_mk_fixedpoint(self.ctx.ref())
        else:
            self.fixedpoint = fixedpoint
        Z3_fixedpoint_inc_ref(self.ctx.ref(), self.fixedpoint)
        self.vars = []

__del__()

def __del__

(

self

)

Definition at line 6498 of file z3py.py.

    def __del__(self):
        if self.fixedpoint is not None and self.ctx.ref() is not None:
            Z3_fixedpoint_dec_ref(self.ctx.ref(), self.fixedpoint)

Member Function Documentation

__deepcopy__()

def __deepcopy__	(		self,
			memo = {}
	)

Definition at line 6495 of file z3py.py.

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

__iadd__()

def __iadd__	(		self,
			fml
	)

Definition at line 6534 of file z3py.py.

    def __iadd__(self, fml):
        self.add(fml)
        return self

__repr__()

def __repr__

(

self

)

Return a formatted string with all added rules and constraints.

Definition at line 6705 of file z3py.py.

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

abstract()

def abstract	(		self,
			fml,
			is_forall = True
	)

Definition at line 6741 of file z3py.py.

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

    def abstract(self, fml, is_forall=True):
        if self.vars == []:
            return fml
        if is_forall:
            return ForAll(self.vars, fml)
        else:
            return Exists(self.vars, fml)

add()

def add	(		self,
			args
	)

Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr.

Definition at line 6530 of file z3py.py.

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

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

add_cover()

def add_cover	(		self,
			level,
			predicate,
			property
	)

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

Definition at line 6663 of file z3py.py.

    def add_cover(self, level, predicate, property):
        """Add property to predicate for the level'th unfolding. -1 is treated as infinity (infinity)"""
        Z3_fixedpoint_add_cover(self.ctx.ref(), self.fixedpoint, level, predicate.ast, property.ast)

add_rule()

def 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 6546 of file z3py.py.

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

    def 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
        """
        if name is None:
            name = ""
        name = to_symbol(name, self.ctx)
        if body is None:
            head = self.abstract(head)
            Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, head.as_ast(), name)
        else:
            body = _get_args(body)
            f    = self.abstract(Implies(And(body, self.ctx),head))
            Z3_fixedpoint_add_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)

append()

def append	(		self,
			args
	)

Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr.

Definition at line 6538 of file z3py.py.

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

assert_exprs()

def assert_exprs	(		self,
			args
	)

Assert constraints as background axioms for the fixedpoint solver.

Definition at line 6516 of file z3py.py.

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

    def assert_exprs(self, *args):
        """Assert constraints as background axioms for the fixedpoint solver."""
        args = _get_args(args)
        s    = BoolSort(self.ctx)
        for arg in args:
            if isinstance(arg, Goal) or isinstance(arg, AstVector):
                for f in arg:
                    f = self.abstract(f)
                    Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, f.as_ast())
            else:
                arg = s.cast(arg)
                arg = self.abstract(arg)
                Z3_fixedpoint_assert(self.ctx.ref(), self.fixedpoint, arg.as_ast())

declare_var()

def 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 6732 of file z3py.py.

    def declare_var(self, *vars):
        """Add variable or several variables.
        The added variable or variables will be bound in the rules
        and queries
        """
        vars = _get_args(vars)
        for v in vars:
            self.vars += [v]

fact()

def fact	(		self,
			head,
			name = None
	)

Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule.

Definition at line 6573 of file z3py.py.

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

get_answer()

def get_answer

(

self

)

Retrieve answer from last query call.

Definition at line 6632 of file z3py.py.

    def get_answer(self):
        """Retrieve answer from last query call."""
        r = Z3_fixedpoint_get_answer(self.ctx.ref(), self.fixedpoint)
        return _to_expr_ref(r, self.ctx)

get_assertions()

def get_assertions

(

self

)

retrieve assertions that have been added to fixedpoint context

Definition at line 6701 of file z3py.py.

    def get_assertions(self):
        """retrieve assertions that have been added to fixedpoint context"""
        return AstVector(Z3_fixedpoint_get_assertions(self.ctx.ref(), self.fixedpoint), self.ctx)

get_cover_delta()

def 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 6658 of file z3py.py.

    def get_cover_delta(self, level, predicate):
        """Retrieve properties known about predicate for the level'th unfolding. -1 is treated as the limit (infinity)"""
        r = Z3_fixedpoint_get_cover_delta(self.ctx.ref(), self.fixedpoint, level, predicate.ast)
        return _to_expr_ref(r, self.ctx)

get_ground_sat_answer()

def get_ground_sat_answer

(

self

)

Retrieve a ground cex from last query call.

Definition at line 6637 of file z3py.py.

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

get_num_levels()

def get_num_levels	(		self,
			predicate
	)

Retrieve number of levels used for predicate in PDR engine

Definition at line 6654 of file z3py.py.

    def get_num_levels(self, predicate):
        """Retrieve number of levels used for predicate in PDR engine"""
        return Z3_fixedpoint_get_num_levels(self.ctx.ref(), self.fixedpoint, predicate.ast)

get_rule_names_along_trace()

def get_rule_names_along_trace

(

self

)

retrieve rule names along the counterexample trace

Definition at line 6646 of file z3py.py.

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

get_rules()

def get_rules

(

self

)

retrieve rules that have been added to fixedpoint context

Definition at line 6697 of file z3py.py.

    def get_rules(self):
        """retrieve rules that have been added to fixedpoint context"""
        return AstVector(Z3_fixedpoint_get_rules(self.ctx.ref(), self.fixedpoint), self.ctx)

get_rules_along_trace()

def get_rules_along_trace

(

self

)

retrieve rules along the counterexample trace

Definition at line 6642 of file z3py.py.

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

help()

def help

(

self

)

Display a string describing all available options.

Definition at line 6508 of file z3py.py.

    def help(self):
        """Display a string describing all available options."""
        print(Z3_fixedpoint_get_help(self.ctx.ref(), self.fixedpoint))

insert()

def insert	(		self,
			args
	)

Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr.

Definition at line 6542 of file z3py.py.

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

param_descrs()

def param_descrs

(

self

)

Return the parameter description set.

Definition at line 6512 of file z3py.py.

    def param_descrs(self):
        """Return the parameter description set."""
        return ParamDescrsRef(Z3_fixedpoint_get_param_descrs(self.ctx.ref(), self.fixedpoint), self.ctx)

parse_file()

def parse_file	(		self,
			f
	)

Parse rules and queries from a file

Definition at line 6690 of file z3py.py.

    def parse_file(self, f):
        """Parse rules and queries from a file"""
        try:
            return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)
        except Z3Exception as e:
            _handle_parse_error(e, self.ctx)

parse_string()

def parse_string	(		self,
			s
	)

Parse rules and queries from a string

Definition at line 6683 of file z3py.py.

    def parse_string(self, s):
        """Parse rules and queries from a string"""
        try:
            return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)
        except Z3Exception as e:
            _handle_parse_error(e, self.ctx)

pop()

def pop

(

self

)

restore to previously created backtracking point

Definition at line 6619 of file z3py.py.

    def pop(self):
        """restore to previously created backtracking point"""
        Z3_fixedpoint_pop(self.ctx.ref(), self.fixedpoint)

push()

def push

(

self

)

create a backtracking point for added rules, facts and assertions

Definition at line 6615 of file z3py.py.

    def push(self):
        """create a backtracking point for added rules, facts and assertions"""
        Z3_fixedpoint_push(self.ctx.ref(), self.fixedpoint)

query()

def 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 6577 of file z3py.py.

    def query(self, *query):
        """Query the fixedpoint engine whether formula is derivable.
           You can also pass an tuple or list of recursive predicates.
        """
        query = _get_args(query)
        sz = len(query)
        if sz >= 1 and isinstance(query[0], FuncDeclRef):
            _decls = (FuncDecl * sz)()
            i = 0
            for q in query:
                _decls[i] = q.ast
                i = i + 1
            r = Z3_fixedpoint_query_relations(self.ctx.ref(), self.fixedpoint, sz, _decls)
        else:
            if sz == 1:
                query = query[0]
            else:
                query = And(query, self.ctx)
            query = self.abstract(query, False)
            r = Z3_fixedpoint_query(self.ctx.ref(), self.fixedpoint, query.as_ast())
        return CheckSatResult(r)

query_from_lvl()

def query_from_lvl	(		self,
			lvl,
			query
	)

Query the fixedpoint engine whether formula is derivable starting at the given query level.

Definition at line 6599 of file z3py.py.

    def query_from_lvl (self, lvl, *query):
        """Query the fixedpoint engine whether formula is derivable starting at the given query level.
        """
        query = _get_args(query)
        sz = len(query)
        if sz >= 1 and isinstance(query[0], FuncDecl):
            _z3_assert (False, "unsupported")
        else:
            if sz == 1:
                query = query[0]
            else:
                query = And(query)
            query = self.abstract(query, False)
            r = Z3_fixedpoint_query_from_lvl (self.ctx.ref(), self.fixedpoint, query.as_ast(), lvl)
        return CheckSatResult(r)

reason_unknown()

def reason_unknown

(

self

)

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

Definition at line 6727 of file z3py.py.

    def reason_unknown(self):
        """Return a string describing why the last `query()` returned `unknown`.
        """
        return Z3_fixedpoint_get_reason_unknown(self.ctx.ref(), self.fixedpoint)

register_relation()

def register_relation	(		self,
			relations
	)

Register relation as recursive

Definition at line 6667 of file z3py.py.

    def register_relation(self, *relations):
        """Register relation as recursive"""
        relations = _get_args(relations)
        for f in relations:
            Z3_fixedpoint_register_relation(self.ctx.ref(), self.fixedpoint, f.ast)

rule()

def rule	(		self,
			head,
			body = None,
			name = None
	)

Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule.

Definition at line 6569 of file z3py.py.

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

set()

def set	(		self,
			args,
			keys
	)

Set a configuration option. The method `help()` return a string containing all available options.

Definition at line 6502 of file z3py.py.

    def set(self, *args, **keys):
        """Set a configuration option. The method `help()` return a string containing all available options.
        """
        p = args2params(args, keys, self.ctx)
        Z3_fixedpoint_set_params(self.ctx.ref(), self.fixedpoint, p.params)

set_predicate_representation()

def set_predicate_representation	(		self,
			f,
			representations
	)

Control how relation is represented

Definition at line 6673 of file z3py.py.

    def set_predicate_representation(self, f, *representations):
        """Control how relation is represented"""
        representations = _get_args(representations)
        representations = [to_symbol(s) for s in representations]
        sz = len(representations)
        args = (Symbol * sz)()
        for i in range(sz):
            args[i] = representations[i]
        Z3_fixedpoint_set_predicate_representation(self.ctx.ref(), self.fixedpoint, f.ast, sz, args)

sexpr()

def 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 6709 of file z3py.py.

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

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

statistics()

def statistics

(

self

)

Return statistics for the last `query()`.

Definition at line 6722 of file z3py.py.

    def statistics(self):
        """Return statistics for the last `query()`.
        """
        return Statistics(Z3_fixedpoint_get_statistics(self.ctx.ref(), self.fixedpoint), self.ctx)

to_string()

def 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 6714 of file z3py.py.

    def 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.
        """
        args, len = _to_ast_array(queries)
        return Z3_fixedpoint_to_string(self.ctx.ref(), self.fixedpoint, len, args)

update_rule()

def update_rule	(		self,
			head,
			body,
			name
	)

update rule

Definition at line 6623 of file z3py.py.

    def update_rule(self, head, body, name):
        """update rule"""
        if name is None:
            name = ""
        name = to_symbol(name, self.ctx)
        body = _get_args(body)
        f    = self.abstract(Implies(And(body, self.ctx),head))
        Z3_fixedpoint_update_rule(self.ctx.ref(), self.fixedpoint, f.as_ast(), name)

Field Documentation

ctx

ctx

Definition at line 6486 of file z3py.py.

Referenced by Probe.__call__(), Fixedpoint.__deepcopy__(), Optimize.__deepcopy__(), ApplyResult.__deepcopy__(), Tactic.__deepcopy__(), Probe.__deepcopy__(), Fixedpoint.__del__(), Optimize.__del__(), ApplyResult.__del__(), Tactic.__del__(), Probe.__del__(), Probe.__eq__(), Probe.__ge__(), ApplyResult.__getitem__(), Probe.__gt__(), Probe.__le__(), ApplyResult.__len__(), Probe.__lt__(), Probe.__ne__(), Fixedpoint.add_cover(), Fixedpoint.add_rule(), Optimize.add_soft(), Tactic.apply(), ApplyResult.as_expr(), Fixedpoint.assert_exprs(), Optimize.assert_exprs(), Optimize.assertions(), Optimize.check(), ApplyResult.convert_model(), Optimize.from_file(), Optimize.from_string(), Fixedpoint.get_answer(), Fixedpoint.get_assertions(), Fixedpoint.get_cover_delta(), Fixedpoint.get_ground_sat_answer(), Fixedpoint.get_num_levels(), Fixedpoint.get_rule_names_along_trace(), Fixedpoint.get_rules(), Fixedpoint.get_rules_along_trace(), Fixedpoint.help(), Optimize.help(), Tactic.help(), Optimize.maximize(), Optimize.minimize(), Optimize.model(), Optimize.objectives(), Fixedpoint.param_descrs(), Optimize.param_descrs(), Tactic.param_descrs(), Fixedpoint.parse_file(), Fixedpoint.parse_string(), Fixedpoint.pop(), Optimize.pop(), Fixedpoint.push(), Optimize.push(), Fixedpoint.query(), Fixedpoint.query_from_lvl(), Fixedpoint.reason_unknown(), Optimize.reason_unknown(), Fixedpoint.register_relation(), Fixedpoint.set(), Optimize.set(), Fixedpoint.set_predicate_representation(), Fixedpoint.sexpr(), Optimize.sexpr(), ApplyResult.sexpr(), Tactic.solver(), Fixedpoint.statistics(), Optimize.statistics(), Fixedpoint.to_string(), and Fixedpoint.update_rule().

fixedpoint

fixedpoint

Definition at line 6487 of file z3py.py.

Referenced by Fixedpoint.__deepcopy__(), Fixedpoint.__del__(), Fixedpoint.add_cover(), Fixedpoint.add_rule(), Fixedpoint.assert_exprs(), Fixedpoint.get_answer(), Fixedpoint.get_assertions(), Fixedpoint.get_cover_delta(), Fixedpoint.get_ground_sat_answer(), Fixedpoint.get_num_levels(), Fixedpoint.get_rule_names_along_trace(), Fixedpoint.get_rules(), Fixedpoint.get_rules_along_trace(), Fixedpoint.help(), Fixedpoint.param_descrs(), Fixedpoint.parse_file(), Fixedpoint.parse_string(), Fixedpoint.pop(), Fixedpoint.push(), Fixedpoint.query(), Fixedpoint.query_from_lvl(), Fixedpoint.reason_unknown(), Fixedpoint.register_relation(), Fixedpoint.set(), Fixedpoint.set_predicate_representation(), Fixedpoint.sexpr(), Fixedpoint.statistics(), Fixedpoint.to_string(), and Fixedpoint.update_rule().

vars

vars

Definition at line 6493 of file z3py.py.

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