def reach_state(state, clauses=None):
""" Try to reach a state in one step from it's predecessor's
underapproximation. If reachable, update the state's
underapproximation with some known reachable state. Return the
reachable state. Else return None.
"""
if not (state.pred != None and state.update != None):
return None
pre = join_unders(state.pred)
if clauses == None:
clauses = state.clauses
print "reach_state: clauses = {}".format(clauses)
axioms = state.domain.background_theory(state.in_scope)
img = and_clauses(forward_image(pre, axioms, state.update), axioms,
clauses)
m = get_model_clauses(img)
ignore = lambda s, d=state.domain: s not in d.relations and s not in d.functions
if m:
# print "reach_state model = {}".format(m.model)
idx = find_true_disjunct(pre, m.eval)
post = clauses_model_to_clauses(img, ignore, model=m)
return add_under(
state, post, state.unders[idx],
dict((s, [c.skolem() for c in m.sort_universe(s)])
for s in m.sorts()))
return None
def forward_image(pre_fact, action):
"""
"""
axioms = _ivy_interp.background_theory()
return ivy_transrel.forward_image(
pre_fact,
axioms,
action.update(_ivy_interp, None),
)
def forward_image(pre_fact, action):
"""
"""
axioms = _ivy_interp.background_theory()
return ivy_transrel.forward_image(
pre_fact,
axioms,
action.update(_ivy_interp, None),
)
def reach_state(state,clauses=None):
""" Try to reach a state in one step from it's predecessor's
underapproximation. If reachable, update the state's
underapproximation with some known reachable state. Return the
reachable state. Else return None.
"""
if not(state.pred != None and state.update != None):
return None
pre = join_unders(state.pred)
if clauses == None:
clauses = state.clauses
print "reach_state: clauses = {}".format(clauses)
axioms = state.domain.background_theory(state.in_scope)
img = and_clauses(forward_image(pre,state.update),axioms,clauses)
m = get_model_clauses(img)
ignore = lambda s,d=state.domain: s not in d.relations and s not in d.functions
if m:
# print "reach_state model = {}".format(m.model)
idx = find_true_disjunct(pre,m.eval)
post = clauses_model_to_clauses(img,ignore,model=m)
return add_under(state,post,state.unders[idx],dict((s,[c.skolem() for c in m.sort_universe(s)]) for s in m.sorts()))
return None
def interactive_updr():
frames = ta._ivy_ag.states
if len(frames) != 1:
raise InteractionError(
"Interactive UPDR can only be started when the ARG " +
"contains nothing but the initial state.")
bad_states = negate_clauses(ta.get_safety_property())
action = ta.get_big_action()
ta._ivy_ag.actions[repr(action)] = action
init_frame = last_frame = frames[0]
# TODO: test conjecture in initial
while True:
# the property is true in all frames and all "clauses" are pushed
# the goal stack is empty
# check if we found an infuctive invariant
for i in range(len(frames) - 1):
if t.check_cover(frames[i + 1], frames[i]):
ta.step(msg="Inductive invariant found at frame {}".format(i),
i=i)
# return True
# add new frame
last_frame = ta.arg_add_action_node(last_frame, action, None)
ta.push_goal(ta.goal_at_arg_node(bad_states, last_frame))
ta.step(msg="Added new frame")
# push facts to last frame
t.recalculate_facts(last_frame,
ta.arg_get_conjuncts(ta.arg_get_pred(last_frame)))
while True:
current_goal = ta.top_goal()
if current_goal is None:
# goal stack is empty
break
if t.remove_if_refuted(current_goal):
continue
if current_goal.node == init_frame:
# no invariant
print "No Invariant!"
# return False
dg = ta.get_diagram(current_goal, False)
options = OrderedDict()
for c in simplify_clauses(dg.formula).conjuncts():
options[str(c)] = c
user_selection = (yield UserSelectMultiple(
options=options,
title="Generalize Diagram",
prompt="Choose which literals to take as the refutation goal",
default=options.values()))
assert user_selection is not None
ug = ta.goal_at_arg_node(Clauses(list(user_selection)),
current_goal.node)
ta.push_goal(ug)
ta.step(msg='Pushed user selected goal', ug=ug)
goal = ta.top_goal()
preds, action = ta.arg_get_preds_action(goal.node)
assert action != 'join'
assert len(preds) == 1
pred = preds[0]
axioms = ta._ivy_interp.background_theory()
theory = and_clauses(
ivy_transrel.forward_image(pred.clauses, axioms,
action.update(ta._ivy_interp,
None)), axioms)
goal_clauses = simplify_clauses(goal.formula)
assert len(goal_clauses.defs) == 0
s = z3.Solver()
s.add(clauses_to_z3(theory))
s.add(clauses_to_z3(goal_clauses))
is_sat = s.check()
if is_sat == z3.sat:
bi = ta.backward_image(goal.formula, action)
x, y = False, ta.goal_at_arg_node(bi, pred)
elif is_sat == z3.unsat:
user_selection, user_is_sat = yield UserSelectCore(
theory=theory,
constrains=goal_clauses.fmlas,
title="Refinement",
prompt="Choose the literals to use",
)
assert user_is_sat is False
core = Clauses(user_selection)
x, y = True, ivy_transrel.interp_from_unsat_core(
goal_clauses, theory, core, None)
else:
assert False, is_sat
t.custom_refine_or_reverse(goal, x, y, False)
# propagate phase
for i in range(1, len(frames)):
facts_to_check = (set(ta.arg_get_conjuncts(frames[i - 1])) -
set(ta.arg_get_conjuncts(frames[i])))
t.recalculate_facts(frames[i], list(facts_to_check))
def interactive_updr():
frames = ta._ivy_ag.states
if len(frames) != 1:
raise InteractionError(
"Interactive UPDR can only be started when the ARG " + "contains nothing but the initial state."
)
bad_states = negate_clauses(ta.get_safety_property())
action = ta.get_big_action()
ta._ivy_ag.actions[repr(action)] = action
init_frame = last_frame = frames[0]
# TODO: test conjecture in initial
while True:
# the property is true in all frames and all "clauses" are pushed
# the goal stack is empty
# check if we found an infuctive invariant
for i in range(len(frames) - 1):
if t.check_cover(frames[i + 1], frames[i]):
ta.step(msg="Inductive invariant found at frame {}".format(i), i=i)
# return True
# add new frame
last_frame = ta.arg_add_action_node(last_frame, action, None)
ta.push_goal(ta.goal_at_arg_node(bad_states, last_frame))
ta.step(msg="Added new frame")
# push facts to last frame
t.recalculate_facts(last_frame, ta.arg_get_conjuncts(ta.arg_get_pred(last_frame)))
while True:
current_goal = ta.top_goal()
if current_goal is None:
# goal stack is empty
break
if t.remove_if_refuted(current_goal):
continue
if current_goal.node == init_frame:
# no invariant
print "No Invariant!"
# return False
dg = ta.get_diagram(current_goal, False)
options = OrderedDict()
for c in simplify_clauses(dg.formula).conjuncts():
options[str(c)] = c
user_selection = (
yield UserSelectMultiple(
options=options,
title="Generalize Diagram",
prompt="Choose which literals to take as the refutation goal",
default=options.values(),
)
)
assert user_selection is not None
ug = ta.goal_at_arg_node(Clauses(list(user_selection)), current_goal.node)
ta.push_goal(ug)
ta.step(msg="Pushed user selected goal", ug=ug)
goal = ta.top_goal()
preds, action = ta.arg_get_preds_action(goal.node)
assert action != "join"
assert len(preds) == 1
pred = preds[0]
axioms = ta._ivy_interp.background_theory()
theory = and_clauses(
ivy_transrel.forward_image(pred.clauses, axioms, action.update(ta._ivy_interp, None)), axioms
)
goal_clauses = simplify_clauses(goal.formula)
assert len(goal_clauses.defs) == 0
s = z3.Solver()
s.add(clauses_to_z3(theory))
s.add(clauses_to_z3(goal_clauses))
is_sat = s.check()
if is_sat == z3.sat:
bi = ta.backward_image(goal.formula, action)
x, y = False, ta.goal_at_arg_node(bi, pred)
elif is_sat == z3.unsat:
user_selection, user_is_sat = yield UserSelectCore(
theory=theory,
constrains=goal_clauses.fmlas,
title="Refinement",
prompt="Choose the literals to use",
)
assert user_is_sat is False
core = Clauses(user_selection)
x, y = True, ivy_transrel.interp_from_unsat_core(goal_clauses, theory, core, None)
else:
assert False, is_sat
t.custom_refine_or_reverse(goal, x, y, False)
# propagate phase
for i in range(1, len(frames)):
facts_to_check = set(ta.arg_get_conjuncts(frames[i - 1])) - set(ta.arg_get_conjuncts(frames[i]))
t.recalculate_facts(frames[i], list(facts_to_check))
