Fixedpoint Class Reference

Fixedpoint. More...

Inheritance diagram for Fixedpoint:

Public Member Functions
def	__init__
def	__deepcopy__
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
def	rule
def	fact
def	query (self, query)
def	query_from_lvl (self, lvl, query)
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
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 7595 of file z3py.py.

Constructor & Destructor Documentation

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

Definition at line 7598 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 = []

def __del__

(

self

)

Definition at line 7612 of file z3py.py.

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

Member Function Documentation

def __deepcopy__	(		self,
			memo = {}
	)

Definition at line 7609 of file z3py.py.

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

def __iadd__	(		self,
			fml
	)

Definition at line 7648 of file z3py.py.

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

def __repr__

(

self

)

Return a formatted string with all added rules and constraints.

Definition at line 7809 of file z3py.py.

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

def abstract	(		self,
			fml,
			is_forall = True
	)

Definition at line 7846 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)

def add	(		self,
			args
	)

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

Definition at line 7644 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)

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 7771 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)

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 7660 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)

def append	(		self,
			args
	)

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

Definition at line 7652 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)

def assert_exprs	(		self,
			args
	)

Assert constraints as background axioms for the fixedpoint solver.

Definition at line 7630 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())

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 7837 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]

def fact	(		self,
			head,
			name = None
	)

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

Definition at line 7687 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)

def get_answer

(

self

)

Retrieve answer from last query call.

Definition at line 7738 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)

def get_assertions

(

self

)

retrieve assertions that have been added to fixedpoint context

Definition at line 7805 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)

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 7764 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)

def get_ground_sat_answer

(

self

)

Retrieve a ground cex from last query call.

Definition at line 7743 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)

def get_num_levels	(		self,
			predicate
	)

Retrieve number of levels used for predicate in PDR engine

Definition at line 7760 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)

def get_rule_names_along_trace

(

self

)

retrieve rule names along the counterexample trace

Definition at line 7752 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(";")

def get_rules

(

self

)

retrieve rules that have been added to fixedpoint context

Definition at line 7801 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)

def get_rules_along_trace

(

self

)

retrieve rules along the counterexample trace

Definition at line 7748 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)

def help

(

self

)

Display a string describing all available options.

Definition at line 7622 of file z3py.py.

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

def insert	(		self,
			args
	)

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

Definition at line 7656 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)

def param_descrs

(

self

)

Return the parameter description set.

Definition at line 7626 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)

def parse_file	(		self,
			f
	)

Parse rules and queries from a file

Definition at line 7797 of file z3py.py.

    def parse_file(self, f):
        """Parse rules and queries from a file"""
        return AstVector(Z3_fixedpoint_from_file(self.ctx.ref(), self.fixedpoint, f), self.ctx)

def parse_string	(		self,
			s
	)

Parse rules and queries from a string

Definition at line 7793 of file z3py.py.

    def parse_string(self, s):
        """Parse rules and queries from a string"""
        return AstVector(Z3_fixedpoint_from_string(self.ctx.ref(), self.fixedpoint, s), self.ctx)

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 7691 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)

def query_from_lvl	(		self,
			lvl,
			query
	)

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

Definition at line 7713 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)

def reason_unknown

(

self

)

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

Definition at line 7832 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)

def register_relation	(		self,
			relations
	)

Register relation as recursive

Definition at line 7777 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)

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

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

Definition at line 7683 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)

def set	(		self,
			args,
			keys
	)

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

Definition at line 7616 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)

def set_predicate_representation	(		self,
			f,
			representations
	)

Control how relation is represented

Definition at line 7783 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)

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 7813 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)())

def statistics

(

self

)

Return statistics for the last `query()`.

Definition at line 7827 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)

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 7819 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)

def update_rule	(		self,
			head,
			body,
			name
	)

update rule

Definition at line 7729 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

Definition at line 7600 of file z3py.py.

Referenced by Fixedpoint.__deepcopy__(), Optimize.__deepcopy__(), ApplyResult.__deepcopy__(), Simplifier.__deepcopy__(), Tactic.__deepcopy__(), Probe.__deepcopy__(), Probe.__eq__(), Probe.__ge__(), ApplyResult.__getitem__(), Probe.__gt__(), Probe.__le__(), Probe.__lt__(), Probe.__ne__(), Simplifier.add(), Fixedpoint.add_rule(), Optimize.add_soft(), Tactic.apply(), ApplyResult.as_expr(), Optimize.assert_and_track(), Fixedpoint.assert_exprs(), Optimize.assert_exprs(), Optimize.assertions(), ParserContext.from_string(), Fixedpoint.get_answer(), Fixedpoint.get_assertions(), Fixedpoint.get_cover_delta(), Fixedpoint.get_ground_sat_answer(), Fixedpoint.get_rule_names_along_trace(), Fixedpoint.get_rules(), Fixedpoint.get_rules_along_trace(), Optimize.model(), Optimize.objectives(), Fixedpoint.param_descrs(), Optimize.param_descrs(), Simplifier.param_descrs(), Tactic.param_descrs(), Fixedpoint.parse_file(), Fixedpoint.parse_string(), Fixedpoint.query(), Fixedpoint.set(), Optimize.set(), Optimize.set_on_model(), Tactic.solver(), Fixedpoint.statistics(), Optimize.statistics(), Optimize.unsat_core(), Fixedpoint.update_rule(), and Simplifier.using_params().

fixedpoint

Definition at line 7601 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.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

Definition at line 7607 of file z3py.py.

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