def slice_defs(prop, defs, assumes_state, assumes_trans):
"""
Return a new (potentially empty) def dictionary from the old one
consisting of only necessary variable definitions to prove property
"""
if __debug__:
assert is_dict(defs), defs
assert is_list(assumes_state), assumes_state
assert is_list(assumes_trans), assumes_trans
fs = [prop] + assumes_state + assumes_trans
fs = [f for f in fs if is_expr(f)]
vs = [get_vars(f) for f in fs]
vs = [cur(v_) if is_pre(v_) else v_ for v_ in vflatten(vs)]
vs = vset(vs, fhash)
vs_ = [Prog.get_influence_vs(v, defs, []) for v in vs]
vs = vset(vflatten(vs + vs_), fhash)
a_defs = OrderedDict()
for v in vs:
k = fhash(v)
if k in defs:
a_defs[k] = defs[k]
return a_defs
def expr_set(fs):
"""
Return a set of formulas (i.e. all items are distinct) using hashing
"""
assert all(f is None or is_expr(f) for f in fs), fs
return vset(fs, lambda f: None if f is None else fhash(f))
def build_vts_poly(ts, tcs, mpp_opt):
vts = [[t.subs(tc) for t in ts] for tc in tcs]
vts = vset(vts, idfun=repr)
#add 0 to the end of each vertex and identity elem to terms
vts = [vt + [SR(0)] for vt in vts]
ts = ts + [SR(0)] #the identity element is 0 in MPP
if mpp_opt == IeqMPP.opt_max_then_min:
def worker_(Q, ts, is_max_plus):
Q.put(IeqMPPGen.build_poly(vts, ts, is_max_plus))
Q = mp.Queue()
workers = [
mp.Process(target=worker_, args=(Q, ts, is_max_plus))
for is_max_plus in [True, False]
]
for w in workers:
w.start()
rs = []
for _ in workers:
rs.extend(Q.get())
else:
is_max_plus = mpp_opt == IeqMPP.opt_max_plus
rs = IeqMPPGen.build_poly(vts, ts, is_max_plus=is_max_plus)
return rs
def build_vts_poly(ts,tcs,mpp_opt):
vts = [[t.subs(tc) for t in ts] for tc in tcs]
vts = vset(vts,idfun=repr)
#add 0 to the end of each vertex and identity elem to terms
vts = [vt + [SR(0)] for vt in vts]
ts = ts + [SR(0)] #the identity element is 0 in MPP
if mpp_opt == IeqMPP.opt_max_then_min:
def worker_(Q,ts,is_max_plus):
Q.put(IeqMPPGen.build_poly(vts,ts,is_max_plus))
Q = mp.Queue()
workers = [mp.Process(target=worker_,args=(Q,ts,is_max_plus))
for is_max_plus in [True,False]]
for w in workers: w.start()
rs = []
for _ in workers: rs.extend(Q.get())
else:
is_max_plus = mpp_opt == IeqMPP.opt_max_plus
rs = IeqMPPGen.build_poly(vts,ts,is_max_plus=is_max_plus)
return rs
def getTermsFixedCoefs(ss, subsetSiz):
"""
sage: var('x y z t s u')
(x, y, z, t, s, u)
sage: getTermsFixedCoefs([x,y^2], 2)
[-y^2 - x, -x, y^2 - x, -y^2, y^2, -y^2 + x, x, y^2 + x]
"""
if len(ss) < subsetSiz: subsetSiz = len(ss)
rs = []
for ssSubset in itertools.combinations(ss, subsetSiz):
css = itertools.product(*([[0, -1, 1]] * len(ssSubset)))
r = (sum(c * t for c, t in zip(ssSubset, cs)) for cs in css
if not all(c == 0 for c in cs))
rs.extend(r)
return CM.vset(rs)
def f_eq(d):
if isinstance(d, list):
f_ = template
for d_ in d:
f_ = f_.subs(d_)
rhsVals = CM.vset([d_.rhs() for d_ in d])
uk_vars = sageutil.get_vars(rhsVals)
else:
f_ = template(d)
uk_vars = sageutil.get_vars(d.values()) #e.g., r15,r16 ...
if not uk_vars: return f_
iM = sage.all.identity_matrix(len(uk_vars)) #standard basis
rs = [dict(zip(uk_vars, l)) for l in iM.rows()]
rs = [f_(r) for r in rs]
return rs
def __init__(self, ps):
if __debug__:
assert is_list(ps) and all(isinstance(p,Inv) for p in ps), ps
self.ps = vset(ps)
Refine.print_diff('vset', len(ps), len(self.ps))
def get_influence_vs(v, defs, rs):
"""
Return a list of variables that influences v
(i.e. the definition of v depends on these variables)
>>> from z3 import Bools, BoolVal
>>> from scr_miscs import mk_OIA
>>> s,t = Bools('s t')
>>> x,y,z = Bools('x y z')
>>> vs = [x,y,z]
>>> o = mk_OIA(vs)
>>> vv = [o,o,And(o,s)]
>>> vs2 = [t]
>>> vv2 = [BoolVal(True)]
>>> vs_k = map(fhash,vs + vs2)
>>> vs_v =vv + vv2
>>> defs = OrderedDict(zip(vs_k,vs_v))
>>> print Prog.get_influence_vs(x,defs,rs=[])
[s, y, z]
#>>> print Prog.get_influence_vs(x,defs,assumes=[x==s],rs=[])
#[s, y, z]
#>>> print Prog.get_influence_vs(x,defs,assumes=[y==t],rs=[])
#[s, y, z, t]
"""
if __debug__:
assert is_expr_var(v), v
assert is_dict(defs), defs
assert is_list(rs), rs
if is_pre(v):
v = cur(v)
#return if already in the result set
if expr_member(v, rs):
return rs
try:
vs = get_vars(defs[fhash(v)])
#print vs
except KeyError:
return rs
rs = rs + [v]
#convert v_pre to v
vs = [cur(v_) if is_pre(v_) else v_ for v_ in vs]
vs = vset(vs, fhash)
for v_ in vs:
rs_ = Prog.get_influence_vs(v_, defs, rs)
rs = rs + rs_
rs = rs + vs
rs = vset(rs, fhash)
#remove myself
v_idx = map(fhash, rs).index(fhash(v))
rs = rs[:v_idx] + rs[v_idx + 1:]
return sorted(rs, key=str)
def benchmark_file(filename,runs,use_specific_deg,read_only,do_parallel):
def get_deg_auto(nss, nts=200, max_deg=7):
if __debug__:
assert nss >= 1, nss
assert nts >= nss, (nts, nss)
assert max_deg >= 1, max_deg
for d in range(1,max_deg+1):
deg = d
if binomial(nss+deg, deg) - 1 > nts:
deg = d - 1
break
return deg
def get_deg_specific(filename):
deg3=['dijkstra',
'cohencu','prod4br','knuth',
'geo3','ps3']
deg4=['ps4']
deg5=['ps5']
deg6=['ps6']
deg7=['ps7']
if any(x in filename for x in deg7):
return 7
elif any(x in filename for x in deg6):
return 6
elif any(x in filename for x in deg5):
return 5
elif any(x in filename for x in deg4):
return 4
elif any(x in filename for x in deg3):
return 3
else:
return 2
def get_invs(ig, seed, deg):
start_time = time.time()
ig.set_seed(seed)
#For MPP
#rs = ig.get_ieqs_max_min_fixed()
# if len(ig.ss_num) <= 3:
# print 'also getting general form, {} vars'.format(len(ig.ss_num))
# rs_ = ig.get_ieqs_max_min_gen()
# rs = rs_ + rs
# rs = vset(rs)
# print len(rs)
#DO NOT USE fixed_3, will generate
#lots of formulas that screw up Z3
#stick with fixed_2
#For NLA
#rs = ig.get_eqts_ieqs_max_min_fixed_2(deg=deg)
#eqts
rs = ig.get_invs(deg=deg)
return rs, (time.time() - start_time)
sols_filename = []
start_time = time.time()
ig = DIG(filename)
print "Read time {}".format(time.time() - start_time)
if read_only:
return '', [], []
if len(ig.ss_num) <= 1:
deg = 1
else:
if any(x in filename for x in ['AesKeySetupEnc_w_LRA',
'AesKeySetupDec_w_LRA']):
deg = 1
elif use_specific_deg:
deg = get_deg_specific(filename)
print 'Use *specific* max degree {}'.format(deg)
else:
if 'l_init' in filename:
deg = 2
print 'Use default max deg {} for l_init'.format(deg)
else:
deg = get_deg_auto(len(ig.ss_num))
print 'Use *auto* max deg {}'.format(deg)
sols_run = []
for nr in range(runs):
print '\n--- Run {}/{} ({}) ---\n'.format(nr+1,runs,filename)
rs,etime = get_invs(ig, seed=nr, deg=deg)
print etime
sols_filename = sols_filename + [(nr,rs,deg,etime)]
sols_run = sols_run + rs
sols_run = vset(sols_run)
expect = ig.xinfo['Expect']
print_summary(filename,expect,sols_filename,sols_run)
return expect, sols_filename, sols_run
def benchmark_file(filename, runs, use_specific_deg, read_only, do_parallel):
def get_deg_auto(nss, nts=200, max_deg=7):
if __debug__:
assert nss >= 1, nss
assert nts >= nss, (nts, nss)
assert max_deg >= 1, max_deg
for d in range(1, max_deg + 1):
deg = d
if binomial(nss + deg, deg) - 1 > nts:
deg = d - 1
break
return deg
def get_deg_specific(filename):
deg3 = ['dijkstra', 'cohencu', 'prod4br', 'knuth', 'geo3', 'ps3']
deg4 = ['ps4']
deg5 = ['ps5']
deg6 = ['ps6']
deg7 = ['ps7']
if any(x in filename for x in deg7):
return 7
elif any(x in filename for x in deg6):
return 6
elif any(x in filename for x in deg5):
return 5
elif any(x in filename for x in deg4):
return 4
elif any(x in filename for x in deg3):
return 3
else:
return 2
def get_invs(ig, seed, deg):
start_time = time.time()
ig.set_seed(seed)
#For MPP
#rs = ig.get_ieqs_max_min_fixed()
# if len(ig.ss_num) <= 3:
# print 'also getting general form, {} vars'.format(len(ig.ss_num))
# rs_ = ig.get_ieqs_max_min_gen()
# rs = rs_ + rs
# rs = vset(rs)
# print len(rs)
#DO NOT USE fixed_3, will generate
#lots of formulas that screw up Z3
#stick with fixed_2
#For NLA
#rs = ig.get_eqts_ieqs_max_min_fixed_2(deg=deg)
#eqts
rs = ig.get_invs(deg=deg)
return rs, (time.time() - start_time)
sols_filename = []
start_time = time.time()
ig = DIG(filename)
print "Read time {}".format(time.time() - start_time)
if read_only:
return '', [], []
if len(ig.ss_num) <= 1:
deg = 1
else:
if any(x in filename
for x in ['AesKeySetupEnc_w_LRA', 'AesKeySetupDec_w_LRA']):
deg = 1
elif use_specific_deg:
deg = get_deg_specific(filename)
print 'Use *specific* max degree {}'.format(deg)
else:
if 'l_init' in filename:
deg = 2
print 'Use default max deg {} for l_init'.format(deg)
else:
deg = get_deg_auto(len(ig.ss_num))
print 'Use *auto* max deg {}'.format(deg)
sols_run = []
for nr in range(runs):
print '\n--- Run {}/{} ({}) ---\n'.format(nr + 1, runs, filename)
rs, etime = get_invs(ig, seed=nr, deg=deg)
print etime
sols_filename = sols_filename + [(nr, rs, deg, etime)]
sols_run = sols_run + rs
sols_run = vset(sols_run)
expect = ig.xinfo['Expect']
print_summary(filename, expect, sols_filename, sols_run)
return expect, sols_filename, sols_run
def gen_nodes_parts(nodes, k, is_commute=False):
"""
Divides n nodes into k parts
sage: gen_nodes_parts([],5)
[([], [], [], [], [])]
sage: gen_nodes_parts([1,2,3],0)
[]
sage: gen_nodes_parts([1,2],1)
[([1, 2],)]
sage: gen_nodes_parts([1,2],2)
[([], [1, 2]), ([1], [2]), ([2], [1]), ([1, 2], [])]
sage: gen_nodes_parts([1,2],3)
[([], [], [1, 2]),
([], [1], [2]),
([], [2], [1]),
([], [1, 2], []),
([1], [], [2]),
([1], [2], []),
([2], [], [1]),
([2], [1], []),
([1, 2], [], [])]
sage: gen_nodes_parts([1,2,4],3)
[([], [], [1, 2, 4]),
([], [1], [2, 4]),
([], [2], [1, 4]),
([], [4], [1, 2]),
([], [1, 2], [4]),
([], [1, 4], [2]),
([], [2, 4], [1]),
([], [1, 2, 4], []),
([1], [], [2, 4]),
([1], [2], [4]),
([1], [4], [2]),
([1], [2, 4], []),
([2], [], [1, 4]),
([2], [1], [4]),
([2], [4], [1]),
([2], [1, 4], []),
([4], [], [1, 2]),
([4], [1], [2]),
([4], [2], [1]),
([4], [1, 2], []),
([1, 2], [], [4]),
([1, 2], [4], []),
([1, 4], [], [2]),
([1, 4], [2], []),
([2, 4], [], [1]),
([2, 4], [1], []),
([1, 2, 4], [], [])]
sage: [len(gen_nodes_parts(range(i),2)) for i in range(6)]
[1, 2, 4, 8, 16, 32]
sage: [len(gen_nodes_parts(range(i),3)) for i in range(6)]
[1, 3, 9, 27, 81, 243]
sage: [len(gen_nodes_parts(range(i),3,is_commute=True)) for i in range(6)]
[1, 1, 2, 5, 14, 41]
"""
assert k >= 0
if len(nodes) == 0: return [((), ) * k]
if k == 0: return []
rs = []
l = len(nodes) + 1
for i in range(l):
gs = itertools.combinations(nodes, i)
for g in gs:
rest = [node for node in nodes if node not in g]
p_rest = gen_nodes_parts(rest, k - 1, is_commute)
rs_ = [tuple([g] + list(p)) for p in p_rest]
rs.extend(rs_)
if is_commute:
rs = CM.vset(rs, idfun=frozenset)
return rs
def __init__(self, ps):
if __debug__:
assert is_list(ps) and all(isinstance(p,Inv) for p in ps), ps
self.ps = vset(ps)
Refine.print_diff('vset', len(ps), len(self.ps))
