def weaken(self, conjs = None, button=None):
if conjs == None:
udc = self.conjectures
udc_text = [str(il.drop_universals(conj.to_formula())) for conj in udc]
msg = "Select conjecture to remove:"
cmd = lambda sel: self.weaken([udc[idx] for idx in sel])
self.ui_parent.listbox_dialog(msg,udc_text,command=cmd,multiple=True)
else:
for conj in conjs:
self.have_cti = False
self.conjectures.remove(conj)
self.ui_parent.text_dialog('Removed the following conjectures:',
'\n'.join(str(conj) for conj in conjs))
def weaken(self, conjs=None, button=None):
if conjs == None:
udc = self.conjectures
udc_text = [
str(il.drop_universals(conj.to_formula())) for conj in udc
]
msg = "Select conjecture to remove:"
cmd = lambda sel: self.weaken([udc[idx] for idx in sel])
self.ui_parent.listbox_dialog(msg,
udc_text,
command=cmd,
multiple=True)
else:
for conj in conjs:
self.have_cti = False
self.conjectures.remove(conj)
self.ui_parent.text_dialog('Removed the following conjectures:',
'\n'.join(str(conj) for conj in conjs))
def add_err_flag(action,erf,errconds):
if isinstance(action,ia.AssertAction):
errcond = ilu.dual_formula(il.drop_universals(action.args[0]))
res = ia.AssignAction(erf,il.Or(erf,errcond))
errconds.append(errcond)
res.lineno = action.lineno
return res
if isinstance(action,ia.AssumeAction):
res = ia.AssumeAction(il.Or(erf,action.args[0]))
res.lineno = action.lineno
return res
if isinstance(action,(ia.Sequence,ia.ChoiceAction,ia.EnvAction,ia.BindOldsAction)):
return action.clone([add_err_flag(a,erf,errconds) for a in action.args])
if isinstance(action,ia.IfAction):
return action.clone([action.args[0]] + [add_err_flag(a,erf,errconds) for a in action.args[1:]])
if isinstance(action,ia.LocalAction):
return action.clone(action.args[:-1] + [add_err_flag(action.args[-1],erf,errconds)])
return action
def property_tactic(self, decls, proof):
cut = proof.args[0]
goal = decls[0]
subgoal = goal_subst(goal, cut, cut.lineno)
lhs = proof.args[1]
if not isinstance(lhs, ia.NoneAST):
fmla = il.drop_universals(cut.formula)
if not il.is_exists(fmla) or len(fmla.variables) != 1:
raise IvyError(proof, 'property is not existential')
evar = list(fmla.variables)[0]
rng = evar.sort
vmap = dict((x.name, x) for x in lu.variables_ast(fmla))
used = set()
args = lhs.args
targs = []
for a in args:
if a.name in used:
raise IvyError(lhs, 'repeat parameter: {}'.format(a.name))
used.add(a.name)
if a.name in vmap:
v = vmap[a.name]
targs.append(v)
if not (il.is_topsort(a.sort) or a.sort != v.sort):
raise IvyError(lhs, 'bad sort for {}'.format(a.name))
else:
if il.is_topsort(a.sort):
raise IvyError(
lhs, 'cannot infer sort for {}'.format(a.name))
targs.append(a)
for x in vmap:
if x not in used:
raise IvyError(
lhs, '{} must be a parameter of {}'.format(x, lhs.rep))
dom = [x.sort for x in targs]
sym = il.Symbol(lhs.rep, il.FuncConstSort(*(dom + [rng])))
if sym in self.stale or sym in goal_defns(goal):
raise iu.IvyError(lhs, '{} is not fresh'.format(sym))
term = sym(*targs) if targs else sym
fmla = lu.substitute_ast(fmla.body, {evar.name: term})
cut = clone_goal(cut, [], fmla)
goal = goal_add_prem(goal, ia.ConstantDecl(sym), goal.lineno)
return [goal_add_prem(goal, cut, cut.lineno)] + decls[1:] + [subgoal]
def strengthen(self, button=None):
conj = self.get_selected_conjecture()
f = il.drop_universals(conj.to_formula())
self.ui_parent.text_dialog('Add the following conjecture:',
str(f),
command=lambda: self.add_conjecture(conj))
def _write_conj(f, lab, fmla):
fmla = il.drop_universals(fmla)
if lab:
f.write("invariant [{}] {}\n".format(lab, str(fmla)))
else:
f.write("invariant {}\n".format(str(fmla)))
def check_inductiveness(self, button=None):
import ivy_transrel
from ivy_solver import get_small_model
from proof import ProofGoal
from ivy_logic_utils import Clauses, and_clauses, dual_clauses
from random import randrange
from ivy_art import AnalysisGraph
with self.ui_parent.run_context():
ag, succeed, fail = ivy_trace.make_check_art(
precond=self.conjectures)
to_test = [None] + list(self.conjectures) # None = check safety
while len(to_test) > 0:
# choose randomly, so the user can get another result by
# clicking again
# conj = to_test.pop(randrange(len(to_test)))
conj = to_test.pop(0)
assert conj == None or conj.is_universal_first_order()
used_names = frozenset(x.name for x in il.sig.symbols.values())
def witness(v):
c = lg.Const('@' + v.name, v.sort)
assert c.name not in used_names
return c
# TODO: this is still a bit hacky, and without nice error reporting
if self.relations_to_minimize.value == 'relations to minimize':
self.relations_to_minimize.value = ' '.join(
sorted(k for k, v in il.sig.symbols.iteritems() if (
type(v.sort) is lg.FunctionSort
and v.sort.range == lg.Boolean
and v.name not in self.transitive_relations
# and '.' not in v.name
)))
if conj == None: # check safety
clauses = ilu.true_clauses()
post = fail
else:
clauses = dual_clauses(conj, witness)
post = succeed
history = ag.get_history(post)
rels_to_min = []
for x in self.relations_to_minimize.value.split():
relation = il.sig.symbols[x]
relation = history.maps[0].get(relation, relation)
rels_to_min.append(relation)
clauses.annot = ia.EmptyAnnotation()
res = ivy_trace.check_final_cond(ag, post, clauses,
rels_to_min, True)
# res = ag.bmc(post, clauses, None, None, _get_model_clauses)
if res is not None:
self.current_conjecture = conj
assert len(res.states) == 2
self.g = res
self.rebuild()
self.view_state(self.g.states[0], reset=True)
self.show_used_relations(clauses)
#self.post_graph.selected = self.get_relevant_elements(self.post_state[2], clauses)
if conj == None:
self.ui_parent.ok_dialog(
'An assertion failed. A failing state is displayed. You can step into\nthe failing action to observe the failing execution. '
)
else:
self.ui_parent.text_dialog(
'The following conjecture is not relatively inductive:',
str(il.drop_universals(conj.to_formula())),
on_cancel=None)
self.have_cti = True
return False
# self.set_states(False, False)
self.ui_parent.text_dialog(
'Inductive invariant found:',
'\n'.join(str(conj) for conj in self.conjectures))
self.have_cti = False
return True
def _write_conj(f,lab,fmla):
fmla = il.drop_universals(fmla)
if lab:
f.write("conjecture [{}] {}\n".format(lab,str(fmla)))
else:
f.write("conjecture {}\n".format(str(fmla)))
def _write_conj(f, lab, fmla):
fmla = il.drop_universals(fmla)
if lab:
f.write("conjecture [{}] {}\n".format(lab, str(fmla)))
else:
f.write("conjecture {}\n".format(str(fmla)))
def to_aiger(mod,ext_act):
erf = il.Symbol('err_flag',il.find_sort('bool'))
errconds = []
add_err_flag_mod(mod,erf,errconds)
# we use a special state variable __init to indicate the initial state
ext_acts = [mod.actions[x] for x in sorted(mod.public_actions)]
ext_act = ia.EnvAction(*ext_acts)
init_var = il.Symbol('__init',il.find_sort('bool'))
init = add_err_flag(ia.Sequence(*([a for n,a in mod.initializers]+[ia.AssignAction(init_var,il.And())])),erf,errconds)
action = ia.Sequence(ia.AssignAction(erf,il.Or()),ia.IfAction(init_var,ext_act,init))
# get the invariant to be proved, replacing free variables with
# skolems. First, we apply any proof tactics.
pc = ivy_proof.ProofChecker(mod.axioms,mod.definitions,mod.schemata)
pmap = dict((lf.id,p) for lf,p in mod.proofs)
conjs = []
for lf in mod.labeled_conjs:
if lf.id in pmap:
proof = pmap[lf.id]
subgoals = pc.admit_proposition(lf,proof)
conjs.extend(subgoals)
else:
conjs.append(lf)
invariant = il.And(*[il.drop_universals(lf.formula) for lf in conjs])
# iu.dbg('invariant')
skolemizer = lambda v: ilu.var_to_skolem('__',il.Variable(v.rep,v.sort))
vs = ilu.used_variables_in_order_ast(invariant)
sksubs = dict((v.rep,skolemizer(v)) for v in vs)
invariant = ilu.substitute_ast(invariant,sksubs)
invar_syms = ilu.used_symbols_ast(invariant)
# compute the transition relation
stvars,trans,error = action.update(mod,None)
# print 'action : {}'.format(action)
# print 'annotation: {}'.format(trans.annot)
annot = trans.annot
# match_annotation(action,annot,MatchHandler())
indhyps = [il.close_formula(il.Implies(init_var,lf.formula)) for lf in mod.labeled_conjs]
# trans = ilu.and_clauses(trans,indhyps)
# save the original symbols for trace
orig_syms = ilu.used_symbols_clauses(trans)
orig_syms.update(ilu.used_symbols_ast(invariant))
# TODO: get the axioms (or maybe only the ground ones?)
# axioms = mod.background_theory()
# rn = dict((sym,tr.new(sym)) for sym in stvars)
# next_axioms = ilu.rename_clauses(axioms,rn)
# return ilu.and_clauses(axioms,next_axioms)
funs = set()
for df in trans.defs:
funs.update(ilu.used_symbols_ast(df.args[1]))
for fmla in trans.fmlas:
funs.update(ilu.used_symbols_ast(fmla))
# funs = ilu.used_symbols_clauses(trans)
funs.update(ilu.used_symbols_ast(invariant))
funs = set(sym for sym in funs if il.is_function_sort(sym.sort))
iu.dbg('[str(fun) for fun in funs]')
# Propositionally abstract
# step 1: get rid of definitions of non-finite symbols by turning
# them into constraints
new_defs = []
new_fmlas = []
for df in trans.defs:
if len(df.args[0].args) == 0 and is_finite_sort(df.args[0].sort):
new_defs.append(df)
else:
fmla = df.to_constraint()
new_fmlas.append(fmla)
trans = ilu.Clauses(new_fmlas+trans.fmlas,new_defs)
# step 2: get rid of ite's over non-finite sorts, by introducing constraints
cnsts = []
new_defs = [elim_ite(df,cnsts) for df in trans.defs]
new_fmlas = [elim_ite(fmla,cnsts) for fmla in trans.fmlas]
trans = ilu.Clauses(new_fmlas+cnsts,new_defs)
# step 3: eliminate quantfiers using finite instantiations
from_asserts = il.And(*[il.Equals(x,x) for x in ilu.used_symbols_ast(il.And(*errconds)) if
tr.is_skolem(x) and not il.is_function_sort(x.sort)])
iu.dbg('from_asserts')
invar_syms.update(ilu.used_symbols_ast(from_asserts))
sort_constants = mine_constants(mod,trans,il.And(invariant,from_asserts))
sort_constants2 = mine_constants2(mod,trans,invariant)
print '\ninstantiations:'
trans,invariant = Qelim(sort_constants,sort_constants2)(trans,invariant,indhyps)
# print 'after qe:'
# print 'trans: {}'.format(trans)
# print 'invariant: {}'.format(invariant)
# step 4: instantiate the axioms using patterns
# We have to condition both the transition relation and the
# invariant on the axioms, so we define a boolean symbol '__axioms'
# to represent the axioms.
axs = instantiate_axioms(mod,stvars,trans,invariant,sort_constants,funs)
ax_conj = il.And(*axs)
ax_var = il.Symbol('__axioms',ax_conj.sort)
ax_def = il.Definition(ax_var,ax_conj)
invariant = il.Implies(ax_var,invariant)
trans = ilu.Clauses(trans.fmlas+[ax_var],trans.defs+[ax_def])
# step 5: eliminate all non-propositional atoms by replacing with fresh booleans
# An atom with next-state symbols is converted to a next-state symbol if possible
stvarset = set(stvars)
prop_abs = dict() # map from atoms to proposition variables
global prop_abs_ctr # sigh -- python lameness
prop_abs_ctr = 0 # counter for fresh symbols
new_stvars = [] # list of fresh symbols
# get the propositional abstraction of an atom
def new_prop(expr):
res = prop_abs.get(expr,None)
if res is None:
prev = prev_expr(stvarset,expr,sort_constants)
if prev is not None:
# print 'stvar: old: {} new: {}'.format(prev,expr)
pva = new_prop(prev)
res = tr.new(pva)
new_stvars.append(pva)
prop_abs[expr] = res # prevent adding this again to new_stvars
else:
global prop_abs_ctr
res = il.Symbol('__abs[{}]'.format(prop_abs_ctr),expr.sort)
# print '{} = {}'.format(res,expr)
prop_abs[expr] = res
prop_abs_ctr += 1
return res
# propositionally abstract an expression
global mk_prop_fmlas
mk_prop_fmlas = []
def mk_prop_abs(expr):
if il.is_quantifier(expr) or len(expr.args) > 0 and any(not is_finite_sort(a.sort) for a in expr.args):
return new_prop(expr)
return expr.clone(map(mk_prop_abs,expr.args))
# apply propositional abstraction to the transition relation
new_defs = map(mk_prop_abs,trans.defs)
new_fmlas = [mk_prop_abs(il.close_formula(fmla)) for fmla in trans.fmlas]
# find any immutable abstract variables, and give them a next definition
def my_is_skolem(x):
res = tr.is_skolem(x) and x not in invar_syms
return res
def is_immutable_expr(expr):
res = not any(my_is_skolem(sym) or tr.is_new(sym) or sym in stvarset for sym in ilu.used_symbols_ast(expr))
return res
for expr,v in prop_abs.iteritems():
if is_immutable_expr(expr):
new_stvars.append(v)
print 'new state: {}'.format(expr)
new_defs.append(il.Definition(tr.new(v),v))
trans = ilu.Clauses(new_fmlas+mk_prop_fmlas,new_defs)
# apply propositional abstraction to the invariant
invariant = mk_prop_abs(invariant)
# create next-state symbols for atoms in the invariant (is this needed?)
rn = dict((sym,tr.new(sym)) for sym in stvars)
mk_prop_abs(ilu.rename_ast(invariant,rn)) # this is to pick up state variables from invariant
# update the state variables by removing the non-finite ones and adding the fresh state booleans
stvars = [sym for sym in stvars if is_finite_sort(sym.sort)] + new_stvars
# iu.dbg('trans')
# iu.dbg('stvars')
# iu.dbg('invariant')
# exit(0)
# For each state var, create a variable that corresponds to the input of its latch
# Also, havoc all the state bits except the init flag at the initial time. This
# is needed because in aiger, all latches start at 0!
def fix(v):
return v.prefix('nondet')
def curval(v):
return v.prefix('curval')
def initchoice(v):
return v.prefix('initchoice')
stvars_fix_map = dict((tr.new(v),fix(v)) for v in stvars)
stvars_fix_map.update((v,curval(v)) for v in stvars if v != init_var)
trans = ilu.rename_clauses(trans,stvars_fix_map)
# iu.dbg('trans')
new_defs = trans.defs + [il.Definition(ilu.sym_inst(tr.new(v)),ilu.sym_inst(fix(v))) for v in stvars]
new_defs.extend(il.Definition(curval(v),il.Ite(init_var,v,initchoice(v))) for v in stvars if v != init_var)
trans = ilu.Clauses(trans.fmlas,new_defs)
# Turn the transition constraint into a definition
cnst_var = il.Symbol('__cnst',il.find_sort('bool'))
new_defs = list(trans.defs)
new_defs.append(il.Definition(tr.new(cnst_var),fix(cnst_var)))
new_defs.append(il.Definition(fix(cnst_var),il.Or(cnst_var,il.Not(il.And(*trans.fmlas)))))
stvars.append(cnst_var)
trans = ilu.Clauses([],new_defs)
# Input are all the non-defined symbols. Output indicates invariant is false.
# iu.dbg('trans')
def_set = set(df.defines() for df in trans.defs)
def_set.update(stvars)
# iu.dbg('def_set')
used = ilu.used_symbols_clauses(trans)
used.update(ilu.symbols_ast(invariant))
inputs = [sym for sym in used if
sym not in def_set and not il.is_interpreted_symbol(sym)]
fail = il.Symbol('__fail',il.find_sort('bool'))
outputs = [fail]
# iu.dbg('trans')
# make an aiger
aiger = Encoder(inputs,stvars,outputs)
comb_defs = [df for df in trans.defs if not tr.is_new(df.defines())]
invar_fail = il.Symbol('invar__fail',il.find_sort('bool')) # make a name for invariant fail cond
comb_defs.append(il.Definition(invar_fail,il.Not(invariant)))
aiger.deflist(comb_defs)
for df in trans.defs:
if tr.is_new(df.defines()):
aiger.set(tr.new_of(df.defines()),aiger.eval(df.args[1]))
miter = il.And(init_var,il.Not(cnst_var),il.Or(invar_fail,il.And(fix(erf),il.Not(fix(cnst_var)))))
aiger.set(fail,aiger.eval(miter))
# aiger.sub.debug()
# make a decoder for the abstract propositions
decoder = dict((y,x) for x,y in prop_abs.iteritems())
for sym in aiger.inputs + aiger.latches:
if sym not in decoder and sym in orig_syms:
decoder[sym] = sym
cnsts = set(sym for syms in sort_constants.values() for sym in syms)
return aiger,decoder,annot,cnsts,action,stvarset
def strengthen(self, button=None):
conj = self.get_selected_conjecture()
f = il.drop_universals(conj.to_formula())
self.ui_parent.text_dialog('Add the following conjecture:',str(f),
command = lambda : self.add_conjecture(conj))
def check_inductiveness(self, button=None):
import ivy_transrel
from ivy_solver import get_small_model
from proof import ProofGoal
from ivy_logic_utils import Clauses, and_clauses, dual_clauses
from random import randrange
from ivy_art import AnalysisGraph
with self.ui_parent.run_context():
ag = self.new_ag()
pre = State()
pre.clauses = and_clauses(*self.conjectures)
action = im.module.actions['ext']
with EvalContext(check=False): # don't check safety
post = ag.execute(action, pre, None, 'ext')
post.clauses = ilu.true_clauses()
to_test = [None] + list(self.conjectures) # None = check safety
while len(to_test) > 0:
# choose randomly, so the user can get another result by
# clicking again
# conj = to_test.pop(randrange(len(to_test)))
conj = to_test.pop(0)
assert conj == None or conj.is_universal_first_order()
used_names = frozenset(x.name for x in il.sig.symbols.values())
def witness(v):
c = lg.Const('@' + v.name, v.sort)
assert c.name not in used_names
return c
# TODO: this is still a bit hacky, and without nice error reporting
if self.relations_to_minimize.value == 'relations to minimize':
self.relations_to_minimize.value = ' '.join(sorted(
k for k, v in il.sig.symbols.iteritems()
if (type(v.sort) is lg.FunctionSort and
v.sort.range == lg.Boolean and
v.name not in self.transitive_relations
# and '.' not in v.name
)
))
if conj == None: # check safety
clauses = ilu.true_clauses()
rels_to_min = [il.sig.symbols[x] for x in self.relations_to_minimize.value.split()]
else:
clauses = dual_clauses(conj, witness)
history = ag.get_history(post)
rels_to_min = []
for x in self.relations_to_minimize.value.split():
relation = il.sig.symbols[x]
relation = history.maps[0].get(relation, relation)
rels_to_min.append(relation)
_get_model_clauses = lambda clauses, final_cond=False: get_small_model(
clauses,
sorted(il.sig.sorts.values()),
rels_to_min,
final_cond = final_cond
)
if conj == None:
res = ag.check_bounded_safety(post, _get_model_clauses)
else:
res = ag.bmc(post, clauses, None, None, _get_model_clauses)
if res is not None:
self.current_conjecture = conj
assert len(res.states) == 2
# self.set_states(res.states[0], res.states[1])
# self.cti = self.ui_parent.add(res)
self.g = res
self.rebuild()
self.view_state(self.g.states[0], reset=True)
self.show_used_relations(clauses)
#self.post_graph.selected = self.get_relevant_elements(self.post_state[2], clauses)
if conj == None:
self.ui_parent.ok_dialog('An assertion failed. A failing state is displayed. You can decompose\nthe failing action to observe the failing execution. ')
else:
self.ui_parent.text_dialog('The following conjecture is not relatively inductive:',
str(il.drop_universals(conj.to_formula())),on_cancel=None)
self.have_cti = True
return False
# self.set_states(False, False)
self.ui_parent.text_dialog('Inductive invariant found:',
'\n'.join(str(conj) for conj in self.conjectures))
self.have_cti = False
return True