def __init__(self, clauses, model, vocab):
# iu.dbg('clauses')
self.clauses = clauses
self.model = model
self.vocab = vocab
self.current = dict()
mod_clauses = islv.clauses_model_to_clauses(clauses,
model=model,
numerals=True)
# iu.dbg('mod_clauses')
self.eqs = defaultdict(list)
for fmla in mod_clauses.fmlas:
if lg.is_eq(fmla):
lhs, rhs = fmla.args
if lg.is_app(lhs):
self.eqs[lhs.rep].append(fmla)
elif isinstance(fmla, lg.Not):
app = fmla.args[0]
if lg.is_app(app):
self.eqs[app.rep].append(lg.Equals(app, lg.Or()))
else:
if lg.is_app(fmla):
self.eqs[fmla.rep].append(lg.Equals(fmla, lg.And()))
# for sym in vocab:
# if not itr.is_new(sym) and not itr.is_skolem(sym):
# self.show_sym(sym,sym)
self.started = False
self.renaming = dict()
print
print 'Trace follows...'
print 80 * '*'
def __init__(self, clauses, model, vocab, top_level=True):
TraceBase.__init__(self)
self.clauses = clauses
self.model = model
self.vocab = vocab
self.top_level = top_level
if clauses is not None:
ignore = lambda s: islv.solver_name(s) == None
mod_clauses = islv.clauses_model_to_clauses(clauses,
model=model,
numerals=True,
ignore=ignore)
self.eqs = defaultdict(list)
for fmla in mod_clauses.fmlas:
if lg.is_eq(fmla):
lhs, rhs = fmla.args
if lg.is_app(lhs):
self.eqs[lhs.rep].append(fmla)
elif isinstance(fmla, lg.Not):
app = fmla.args[0]
if lg.is_app(app):
self.eqs[app.rep].append(lg.Equals(app, lg.Or()))
else:
if lg.is_app(fmla):
self.eqs[fmla.rep].append(lg.Equals(fmla, lg.And()))
def __init__(self, clauses, model, vocab, top_level=True):
art.AnalysisGraph.__init__(self)
self.clauses = clauses
self.model = model
self.vocab = vocab
mod_clauses = islv.clauses_model_to_clauses(clauses,
model=model,
numerals=True)
self.eqs = defaultdict(list)
for fmla in mod_clauses.fmlas:
if lg.is_eq(fmla):
lhs, rhs = fmla.args
if lg.is_app(lhs):
self.eqs[lhs.rep].append(fmla)
elif isinstance(fmla, lg.Not):
app = fmla.args[0]
if lg.is_app(app):
self.eqs[app.rep].append(lg.Equals(app, lg.Or()))
else:
if lg.is_app(fmla):
self.eqs[fmla.rep].append(lg.Equals(fmla, lg.And()))
self.last_action = None
self.sub = None
self.returned = None
self.top_level = top_level
def sort_size_constraint(sort,size):
if isinstance(sort,ivy_logic.UninterpretedSort):
syms = [ivy_logic.Symbol('__'+sort.name+'$'+str(i),sort) for i in range(size)]
v = ivy_logic.Variable('X'+sort.name,sort)
res = ivy_logic.Or(*[ivy_logic.Equals(v,s) for s in syms])
# print "sort_size_constraint : {}".format(res)
return res
return ivy_logic.And()
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 get_truth(digits,idx,syms):
if (len(digits) != len(syms)):
badwit()
digit = digits[idx]
if digit == '0':
return il.Or()
elif digit == '1':
return il.And()
elif digit != 'x':
badwit()
return None
def constant_from_z3(sort, c):
if z3.is_true(c):
return ivy_logic.And()
if z3.is_false(c):
return ivy_logic.Or()
return ivy_logic.Constant(ivy_logic.Symbol(repr(c), sort))
def check_safety_in_state(mod, ag, post, report_pass=True):
return check_fcs_in_state(mod, ag, post,
[Checker(lg.Or(), report_pass=report_pass)])
def bdv(v):
""" Return a formula bounding a variable of ubninterpreted sort """
eqs = [
ivy_logic.Equals(v, reps[c.rep]) for c in h.sort_universe(v.sort)
]
return ivy_logic.Or(*eqs)
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 get_next_sym(self,v):
enc = self.encoding[v]
abits = self.sub.sym_next_vals(enc)
bits = [il.And() if b == '1' else il.Or() for b in abits]
return self.decode_val(bits,v)
def scenario(self, scen):
init_tokens = set(p.rep for p in scen.args[0].args)
transs_by_action = defaultdict(list)
for tr in scen.args[1:]:
transs_by_action[tr.args[2].args[1].args[0].rep].append(tr)
for (place_name, lineno) in scen.places():
sym = find_symbol(place_name)
iname = place_name + '[init]'
iact = AssignAction(
sym,
ivy_logic.And() if
(place_name in init_tokens) else ivy_logic.Or())
iact.formal_params = []
iact.formal_returns = []
iact.lineno = scen.lineno
self.mod.actions[iname] = iact
self.mixin(
ivy_ast.MixinAfterDef(ivy_ast.Atom(iname),
ivy_ast.Atom('init')))
for actname, trs in transs_by_action.iteritems():
choices = []
params = None
afters = []
for tr in trs:
scmix = tr.args[2]
is_after = isinstance(scmix, ivy_ast.ScenarioAfterMixin)
df = scmix.args[1]
body = compile_action_def(df, self.mod.sig)
seq = []
if not is_after:
for p in tr.args[0].args:
seq.append(AssumeAction(find_symbol(p.rep)))
for p in tr.args[0].args:
seq.append(
AssignAction(find_symbol(p.rep), ivy_logic.Or()))
for p in tr.args[1].args:
seq.append(
AssignAction(find_symbol(p.rep), ivy_logic.And()))
seq.append(body)
seq = Sequence(*seq)
else:
for p in tr.args[0].args:
seq.append(
AssignAction(find_symbol(p.rep), ivy_logic.Or()))
for p in tr.args[1].args:
seq.append(
AssignAction(find_symbol(p.rep), ivy_logic.And()))
seq.append(body)
seq = Sequence(*seq)
seq = IfAction(
And(*[find_symbol(p.rep) for p in tr.args[0].args]),
seq)
if params is None:
params = body.formal_params
returns = body.formal_returns
mixer = scmix.args[0]
mixee = scmix.args[1].args[0]
else:
aparams = df.formal_params + df.formal_returns
subst = dict(zip(aparams, params + returns))
seq = substitute_constants_ast(seq, subst)
seq.lineno = tr.lineno
if not is_after:
choices.append(seq)
else:
afters.append(seq)
if choices:
choice = BalancedChoice(choices)
choice.lineno = choices[0].lineno
choice.formal_params = params
choice.formal_returns = returns
self.mod.actions[mixer.rep] = choice
self.mixin(ivy_ast.MixinBeforeDef(mixer, mixee))
if afters:
choice = Sequence(*afters)
choice.lineno = afters[0].lineno
choice.formal_params = params
choice.formal_returns = returns
self.mod.actions[mixer.rep] = choice
self.mixin(ivy_ast.MixinAfterDef(mixer, mixee))
