def recur(action,annot,env,pos=None):
if isinstance(annot,ia.RenameAnnotation):
save = dict()
for x,y in annot.map.iteritems():
if x in env:
save[x] = env[x]
env[x] = env.get(y,y)
recur(action,annot.arg,env,pos)
env.update(save)
return
if isinstance(action,ia.Sequence):
if pos is None:
pos = len(action.args)
if pos == 0:
assert isinstance(annot,ia.EmptyAnnotation),annot
return
if not isinstance(annot,ia.ComposeAnnotation):
iu.dbg('len(action.args)')
iu.dbg('pos')
iu.dbg('annot')
assert isinstance(annot,ia.ComposeAnnotation)
recur(action,annot.args[0],env,pos-1)
recur(action.args[pos-1],annot.args[1],env)
return
if isinstance(action,ia.IfAction):
assert isinstance(annot,ia.IteAnnotation),annot
rncond = env.get(annot.cond,annot.cond)
try:
cond = handler.eval(rncond)
except KeyError:
print '{}skipping conditional'.format(action.lineno)
iu.dbg('str_map(env)')
iu.dbg('env.get(annot.cond,annot.cond)')
return
if cond:
recur(action.args[1],annot.thenb,env)
else:
if len(action.args) > 2:
recur(action.args[2],annot.elseb,env)
return
if isinstance(action,ia.ChoiceAction):
assert isinstance(annot,ia.IteAnnotation)
annots = unite_annot(annot)
assert len(annots) == len(action.args)
for act,(cond,ann) in reversed(zip(action.args,annots)):
if handler.eval(cond):
recur(act,ann,env)
return
assert False,'problem in match_annotation'
if isinstance(action,ia.CallAction):
callee = im.module.actions[action.args[0].rep]
seq = ia.Sequence(*([ia.Sequence() for x in callee.formal_params]
+ [callee]
+ [ia.Sequence() for x in callee.formal_returns]))
recur(seq,annot,env)
return
if isinstance(action,ia.LocalAction):
recur(action.args[-1],annot,env)
return
handler.handle(action,env)
def check_fcs_in_state(mod,ag,post,fcs):
# iu.dbg('"foo"')
history = ag.get_history(post)
# iu.dbg('history.actions')
gmc = lambda cls, final_cond: itr.small_model_clauses(cls,final_cond,shrink=diagnose.get())
axioms = im.module.background_theory()
if opt_trace.get():
clauses = history.post
clauses = lut.and_clauses(clauses,axioms)
ffcs = filter_fcs(fcs)
model = itr.small_model_clauses(clauses,ffcs,shrink=True)
if model is not None:
# iu.dbg('history.actions')
mclauses = lut.and_clauses(*([clauses] + [c.cond() for c in ffcs if c.failed]))
vocab = lut.used_symbols_clauses(mclauses)
handler = MatchHandler(mclauses,model,vocab)
assert all(x is not None for x in history.actions)
# work around a bug in ivy_interp
actions = [im.module.actions[a] if isinstance(a,str) else a for a in history.actions]
# iu.dbg('actions')
action = act.Sequence(*actions)
act.match_annotation(action,clauses.annot,handler)
handler.end()
exit(0)
else:
res = history.satisfy(axioms,gmc,filter_fcs(fcs))
if res is not None and diagnose.get():
show_counterexample(ag,post,res)
return not any(fc.failed for fc in fcs)
def check_final_cond(ag,
post,
final_cond,
rels_to_min=[],
shrink=False,
handler_class=None):
history = ag.get_history(post)
axioms = im.module.background_theory()
clauses = history.post
clauses = lut.and_clauses(clauses, axioms)
model = slv.get_small_model(clauses,
lg.uninterpreted_sorts(),
rels_to_min,
final_cond=final_cond,
shrink=shrink)
if model is not None:
failed = ([final_cond] if not isinstance(final_cond, list) else
[c.cond() for c in ffcs if c.failed])
mclauses = lut.and_clauses(*([clauses] + failed))
vocab = lut.used_symbols_clauses(mclauses)
handler = (handler_class(mclauses, model, vocab) if handler_class
is not None else Trace(mclauses, model, vocab))
assert all(x is not None for x in history.actions)
# work around a bug in ivy_interp
actions = [
im.module.actions[a] if isinstance(a, str) else a
for a in history.actions
]
action = act.Sequence(*actions)
act.match_annotation(action, clauses.annot, handler)
handler.end()
return handler
return None
def normal_program_from_module(mod):
bindings = [ActionTermBinding(name,old_action_to_new(act)) for name,act in mod.actions.iteritems()]
init = iact.Sequence(*[action for actname,action in mod.initializers])
invars = mod.labeled_conjs
asms = mod.assumed_invariants
calls = sorted(mod.public_actions)
return NormalProgram(bindings,init,invars,asms,calls)
def init_method():
asserts = [ia.AssertAction(im.module.init_cond.to_formula())]
for a in im.module.axioms:
asserts.append(ia.AssertAction(a))
res = ia.Sequence(*asserts)
res.formal_params = []
res.formal_returns = []
return res
def env_action(bindings):
racts = []
for b in bindings:
name = b.name
act = b.action
ract = iact.Sequence(act.stmt,iact.ReturnAction())
ract.formal_params = act.inputs
ract.formal_returns = act.outputs
ract.label = name[4:] if name.startswith('ext:') else name
racts.append(ract)
action = iact.EnvAction(*racts)
return action
def check_fcs_in_state(mod, ag, post, fcs):
# iu.dbg('"foo"')
history = ag.get_history(post)
# iu.dbg('history.actions')
gmc = lambda cls, final_cond: itr.small_model_clauses(
cls, final_cond, shrink=diagnose.get())
axioms = im.module.background_theory()
if opt_trace.get() or diagnose.get():
clauses = history.post
clauses = lut.and_clauses(clauses, axioms)
ffcs = filter_fcs(fcs)
model = itr.small_model_clauses(clauses, ffcs, shrink=True)
if model is not None:
# iu.dbg('history.actions')
failed = [c for c in ffcs if c.failed]
mclauses = lut.and_clauses(*([clauses] +
[c.cond() for c in failed]))
vocab = lut.used_symbols_clauses(mclauses)
# handler = MatchHandler(mclauses,model,vocab) if opt_trace.get() else ivy_trace.Trace(mclauses,model,vocab)
handler = ivy_trace.Trace(mclauses, model, vocab)
thing = failed[-1].get_annot()
if thing is None:
assert all(x is not None for x in history.actions)
# work around a bug in ivy_interp
actions = [
im.module.actions[a] if isinstance(a, str) else a
for a in history.actions
]
action = act.Sequence(*actions)
annot = clauses.annot
else:
action, annot = thing
act.match_annotation(action, annot, handler)
handler.end()
ff = failed[0]
handler.is_cti = (lut.formula_to_clauses(ff.lf.formula)
if isinstance(ff, ConjChecker) else None)
if not opt_trace.get():
gui_art(handler)
else:
print str(handler)
exit(0)
else:
res = history.satisfy(axioms, gmc, filter_fcs(fcs))
if res is not None and diagnose.get():
show_counterexample(ag, post, res)
return not any(fc.failed for fc in fcs)
def add_initial_state(self, ic=None, abstractor=None):
if ic == None:
ic = im.init_cond
s = self.domain.new_state(ic)
if self.domain.initializers:
action = ivy_actions.Sequence(
*[a for n, a in self.domain.initializers])
s = action_app(action, s)
with AC(self, no_add=True):
with EvalContext(check=False):
s2 = eval_state(s)
s2.expr = s
self.add(s2)
else:
s2 = self.domain.new_state(ic)
self.add(s2, s)
if abstractor:
abstractor(s2)
def check_final_cond(ag,
post,
final_cond,
rels_to_min=[],
shrink=False,
handler_class=None):
history = ag.get_history(post)
axioms = im.module.background_theory()
clauses = history.post
clauses = lut.and_clauses(clauses, axioms)
assert all(x is not None for x in history.actions)
# work around a bug in ivy_interp
actions = [
im.module.actions[a] if isinstance(a, str) else a
for a in history.actions
]
action = act.Sequence(*actions)
return check_vc(clauses, action, final_cond, rels_to_min, shrink,
handler_class)
def summarize_action(action):
res = ia.Sequence()
res.lineno = action.lineno
res.formal_params = action.formal_params
res.formal_returns = action.formal_returns
return res
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
