def test_strengthen2(self):
"""
Forall(i) GFa_i and G(b_i) -> Forall(j) GF(c_j) and G(d_j)
replaced by
'liveness': Forall(i) GFa_i and G(b_i) -> Forall(j) GF(c_j)
and
'safety': Forall(i) G(b_i) -> Forall(j) G(d_j)
"""
a_i, b_i = QuantifiedSignal("a", "i"), QuantifiedSignal("b", "i")
c_j, d_j = QuantifiedSignal("c", "j"), QuantifiedSignal("d", "j")
ass = ForallExpr(["i"], BinOp("*", UnaryOp("G", UnaryOp("F", a_i)), UnaryOp("G", b_i)))
gua = ForallExpr(["j"], BinOp("*", UnaryOp("G", UnaryOp("F", c_j)), UnaryOp("G", d_j)))
property = SpecProperty([ass], [gua])
safety_properties, liveness_properties = strengthen(property, self._get_converter())
assert len(liveness_properties) == 1, str(liveness_properties)
assert len(safety_properties) == 1, str(safety_properties)
expected_liveness_gua = ForallExpr(["j"], UnaryOp("G", UnaryOp("F", c_j)))
#: :type: SpecProperty
liveness_prop = liveness_properties[0]
assert str(liveness_prop.assumptions) == str([ass]), str(liveness_prop)
assert str(liveness_prop.guarantees) == str([expected_liveness_gua])
safety_prop = safety_properties[0]
expected_safety_ass = ForallExpr(["i"], UnaryOp("G", b_i))
expected_safety_gua = ForallExpr(["j"], UnaryOp("G", d_j))
expected_safety_prop = SpecProperty([expected_safety_ass], [expected_safety_gua])
assert str(expected_safety_prop) == str(safety_prop), str(safety_prop)
def test_strengthen3(self):
"""
Forall(i,j) GFa_i * GFb_i_j * Gc_i_j -> Forall(k,m) GF(d_k_m) * G(e_k)
replaced by
'safety': Forall(i) Gc_i_j -> Forall(k) G(e_k)
'liveness': Forall(i,j) GFa_i * GFb_i_j * Gc_i -> Forall(k,m) GF(d_k_m)
"""
a_i, b_i_j, c_i_j = _get_is_true("a", "i"), _get_is_true("b", "i", "j"), _get_is_true("c", "i", "j")
ass = ForallExpr(
["i", "j"],
BinOp(
"*", UnaryOp("G", UnaryOp("F", a_i)), BinOp("*", UnaryOp("G", UnaryOp("F", b_i_j)), UnaryOp("G", c_i_j))
),
)
d_k_m = _get_is_true("d", "k", "m")
e_k = _get_is_true("e", "k")
gua = ForallExpr(["k", "m"], BinOp("*", UnaryOp("G", UnaryOp("F", d_k_m)), UnaryOp("G", e_k)))
property = SpecProperty([ass], [gua])
safety_properties, liveness_properties = strengthen(property, self._get_converter())
# lazy..
print("safety_properties", safety_properties)
assert len(safety_properties) == 1, str(safety_properties)
assert len(list(chain(*[sp.assumptions for sp in safety_properties]))) == 1
assert len(list(chain(*[sp.guarantees for sp in safety_properties]))) == 1
print("liveness_properties", liveness_properties)
def test_strengthen3(self):
"""
Forall(i,j) GFa_i * GFb_i_j * Gc_i_j -> Forall(k,m) GF(d_k_m) * G(e_k)
replaced by
'safety': Forall(i) Gc_i_j -> Forall(k) G(e_k)
'liveness': Forall(i,j) GFa_i * GFb_i_j * Gc_i -> Forall(k,m) GF(d_k_m)
"""
a_i, b_i_j, c_i_j = _get_is_true('a', 'i'), _get_is_true(
'b', 'i', 'j'), _get_is_true('c', 'i', 'j')
ass = ForallExpr(['i', 'j'],
BinOp(
'*', UnaryOp('G', UnaryOp('F', a_i)),
BinOp('*', UnaryOp('G', UnaryOp('F', b_i_j)),
UnaryOp('G', c_i_j))))
d_k_m = _get_is_true('d', 'k', 'm')
e_k = _get_is_true('e', 'k')
gua = ForallExpr(['k', 'm'],
BinOp('*', UnaryOp('G', UnaryOp('F', d_k_m)),
UnaryOp('G', e_k)))
property = SpecProperty([ass], [gua])
safety_properties, liveness_properties = strengthen(
property, self._get_converter())
#lazy..
print('safety_properties', safety_properties)
assert len(safety_properties) == 1, str(safety_properties)
assert len(list(chain(*[sp.assumptions
for sp in safety_properties]))) == 1
assert len(list(chain(*[sp.guarantees
for sp in safety_properties]))) == 1
print('liveness_properties', liveness_properties)
def test_strengthen2(self):
"""
Forall(i) GFa_i -> Forall(j) GF(b_j)
is left as it is
"""
a_i, b_j = QuantifiedSignal("a", "i"), QuantifiedSignal("b", "j")
liveness_ass = ForallExpr(["i"], UnaryOp("G", UnaryOp("F", a_i)))
liveness_gua = ForallExpr(["j"], UnaryOp("G", UnaryOp("F", b_j)))
property = SpecProperty([liveness_ass], [liveness_gua])
safety_properties, liveness_properties = strengthen(property, self._get_converter())
assert len(liveness_properties) == 1, str(liveness_properties)
assert len(safety_properties) == 0, str(safety_properties)
actual = liveness_properties[0]
expected = property
assert str(actual) == str(expected), str(actual) + " vs " + str(expected)
def test_strengthen2(self):
"""
Forall(i) GFa_i and G(b_i) -> Forall(j) GF(c_j) and G(d_j)
replaced by
'liveness': Forall(i) GFa_i and G(b_i) -> Forall(j) GF(c_j)
and
'safety': Forall(i) G(b_i) -> Forall(j) G(d_j)
"""
a_i, b_i = QuantifiedSignal('a', 'i'), QuantifiedSignal('b', 'i')
c_j, d_j = QuantifiedSignal('c', 'j'), QuantifiedSignal('d', 'j')
ass = ForallExpr(['i'],
BinOp('*', UnaryOp('G', UnaryOp('F', a_i)),
UnaryOp('G', b_i)))
gua = ForallExpr(['j'],
BinOp('*', UnaryOp('G', UnaryOp('F', c_j)),
UnaryOp('G', d_j)))
property = SpecProperty([ass], [gua])
safety_properties, liveness_properties = strengthen(
property, self._get_converter())
assert len(liveness_properties) == 1, str(liveness_properties)
assert len(safety_properties) == 1, str(safety_properties)
expected_liveness_gua = ForallExpr(['j'],
UnaryOp('G', UnaryOp('F', c_j)))
#: :type: SpecProperty
liveness_prop = liveness_properties[0]
assert str(liveness_prop.assumptions) == str([ass]), str(liveness_prop)
assert str(liveness_prop.guarantees) == str([expected_liveness_gua])
safety_prop = safety_properties[0]
expected_safety_ass = ForallExpr(['i'], UnaryOp('G', b_i))
expected_safety_gua = ForallExpr(['j'], UnaryOp('G', d_j))
expected_safety_prop = SpecProperty([expected_safety_ass],
[expected_safety_gua])
assert str(expected_safety_prop) == str(safety_prop), str(safety_prop)
def test_strengthen1(self):
"""
Forall(i) GFa_i -> Forall(j) G(b_j)
replaced by
'safety': Forall(j) G(b_j)
'liveness': []
"""
a_i, b_j = QuantifiedSignal("a", "i"), QuantifiedSignal("b", "j")
liveness_ass = ForallExpr(["i"], UnaryOp("G", UnaryOp("F", a_i)))
safety_gua = ForallExpr(["j"], UnaryOp("G", b_j))
property = SpecProperty([liveness_ass], [safety_gua])
safety_properties, liveness_properties = strengthen(property, self._get_converter())
assert len(liveness_properties) == 0, str(liveness_properties)
assert len(safety_properties) == 1, str(safety_properties)
actual_guarantees = safety_properties[0].guarantees
assert str(actual_guarantees) == str([safety_gua]), "\n" + str(actual_guarantees) + "\nvs\n" + str([safety_gua])
def test_strengthen2(self):
"""
Forall(i) GFa_i -> Forall(j) GF(b_j)
is left as it is
"""
a_i, b_j = QuantifiedSignal('a', 'i'), QuantifiedSignal('b', 'j')
liveness_ass = ForallExpr(['i'], UnaryOp('G', UnaryOp('F', a_i)))
liveness_gua = ForallExpr(['j'], UnaryOp('G', UnaryOp('F', b_j)))
property = SpecProperty([liveness_ass], [liveness_gua])
safety_properties, liveness_properties = strengthen(
property, self._get_converter())
assert len(liveness_properties) == 1, str(liveness_properties)
assert len(safety_properties) == 0, str(safety_properties)
actual = liveness_properties[0]
expected = property
assert str(actual) == str(
expected), str(actual) + ' vs ' + str(expected)
def test_strengthen1(self):
"""
Forall(i) GFa_i -> Forall(j) G(b_j)
replaced by
'safety': Forall(j) G(b_j)
'liveness': []
"""
a_i, b_j = QuantifiedSignal('a', 'i'), QuantifiedSignal('b', 'j')
liveness_ass = ForallExpr(['i'], UnaryOp('G', UnaryOp('F', a_i)))
safety_gua = ForallExpr(['j'], UnaryOp('G', b_j))
property = SpecProperty([liveness_ass], [safety_gua])
safety_properties, liveness_properties = strengthen(
property, self._get_converter())
assert len(liveness_properties) == 0, str(liveness_properties)
assert len(safety_properties) == 1, str(safety_properties)
actual_guarantees = safety_properties[0].guarantees
assert str(actual_guarantees) == str([safety_gua]), \
'\n' + str(actual_guarantees) + '\nvs\n' + str([safety_gua])