def simulates_forwards(topo, a, b, field="vlan", edge_policy={}):
"""Determine if b simulates a up to field on one hop."""
p, pp = Consts("p pp", Packet)
v, vv = Ints("v vv")
# Z3 emits a warning about not finding a pattern for our quantification.
# This is fine, so ignore it.
set_option("WARNING", False)
solv = Solver()
solv.add(on_valid_port(topo, p))
# b doesn't need to forward packets on external links that don't satisfy the
# ingress predicate
edge_option = And(external_link(edge_policy, p), Not(edges_ingress(edge_policy, p)))
solv.add(
And(
forwards(a, p, pp),
ForAll([v, vv], Not(Or(forwards_with(b, p, {field: v}, pp, {field: vv}), edge_option)), patterns=[]),
)
)
if solv.check() == unsat:
set_option("WARNING", True)
return None
else:
set_option("WARNING", True)
return solv.model(), (p, pp), HEADER_INDEX
def simulates_forwards2(topo, a, b, field="vlan", edge_policy={}):
"""Determine if b simulates a up to field on two hop on topo."""
p, pp, q, qq = Consts("p pp q qq", Packet)
v, vv, vvv = Ints("v vv, vvv")
# Z3 emits a warning about not finding a pattern for our quantification.
# This is fine, so ignore it.
set_option("WARNING", False)
solv = Solver()
solv.add(on_valid_port(topo, p))
# b doesn't need to forward packets on external links that don't satisfy the
# ingress predicate, but we only care about the first hop
edge_option = And(external_link(edge_policy, p), Not(edges_ingress(edge_policy, p)))
# This case breaks the And inside the ForAll because they're both False and
# z3 can't handle that.
# However, it does mean that they simulate each other, because neither
# forwards packets, so just short-circuit.
if forwards(b, p, pp) is False and forwards(b, q, qq) is False:
return None
c = And(
forwards(a, p, pp),
transfer(topo, pp, q),
forwards(a, q, qq),
ForAll(
[v, vv, vvv],
Not(
Or(
And(
forwards_with(b, p, {field: v}, pp, {field: vv}),
forwards_with(b, q, {field: vv}, qq, {field: vvv}),
),
edge_option,
)
),
),
)
solv.add(c)
if solv.check() == unsat:
set_option("WARNING", True)
return None
else:
set_option("WARNING", True)
return solv.model(), (p, pp), HEADER_INDEX
def simulates_observes(topo, a, b, field="vlan", edge_policy={}):
p = Const("p", Packet)
o, v = Ints("o v")
# Z3 emits a warning about not finding a pattern for our quantification.
# This is fine, so ignore it.
set_option("WARNING", False)
solv = Solver()
solv.add(on_valid_port(topo, p))
# b doesn't need to observe packets on external links that don't satisfy the
# ingress predicate
edge_option = And(external_link(edge_policy, p), Not(edges_ingress(edge_policy, p)))
solv.add(And(observes(a, p, o), ForAll([v], Not(Or(observes_with(b, p, {field: v}, o), edge_option)), patterns=[])))
if solv.check() == unsat:
set_option("WARNING", True)
return None
else:
set_option("WARNING", True)
return solv.model(), (p), HEADER_INDEX
