def setup_orthotope_vars():
fol = _fol.Context()
fol.declare(
x=(0, 5),
y=(2, 14),
px=(0, 5),
qx=(0, 5),
py=(2, 14),
qy=(2, 14),
ax=(0, 5),
bx=(0, 5),
ay=(2, 14),
by=(2, 14),
)
xvars = ['x', 'y']
px = dict(x=dict(a='px', b='qx'), y=dict(a='py', b='qy'))
qx = dict(x=dict(a='ax', b='bx'), y=dict(a='ay', b='by'))
prm = lat.Parameters()
prm.x_vars = xvars
prm._px = px
prm._qx = qx
prm.p_to_q = dict(px='ax', py='ay', qx='bx', qy='by')
prm.p_vars = set(prm.p_to_q)
prm.q_vars = set(prm.p_to_q.values())
varmap = lat.parameter_varmap(px, qx)
prm.p_leq_q = lat.subseteq(varmap, fol)
prm.p_eq_q = lat.eq(varmap, fol)
return fol, prm
def test_orthotope_eq():
fol, prm = setup_aut()
varmap = prm._varmap
r = lat.eq(varmap, fol)
r_ = fol.add_expr('a_x = u_x /\ b_x = v_x /\ ' 'a_y = u_y /\ b_y = v_y')
assert r == r_, (r, r_)
d = dict(a_x=1, b_x=2, a_y=0, b_y=3)
r = fol.let(d, r)
d = dict(u_x=4, v_x=6, u_y=7, v_y=10)
r = fol.let(d, r)
assert r == fol.false
r = lat.eq(varmap, fol)
d = dict(a_x=1, b_x=2, a_y=0, b_y=3)
r = fol.let(d, r)
d = dict(u_x=1, v_x=2, u_y=0, v_y=3)
r = fol.let(d, r)
assert r == fol.true
def test_orthotope_eq():
fol, prm = setup_aut()
varmap = prm._varmap
r = lat.eq(varmap, fol)
r_ = fol.add_expr(
'a_x = u_x /\ b_x = v_x /\ '
'a_y = u_y /\ b_y = v_y')
assert r == r_, (r, r_)
d = dict(a_x=1, b_x=2, a_y=0, b_y=3)
r = fol.let(d, r)
d = dict(u_x=4, v_x=6, u_y=7, v_y=10)
r = fol.let(d, r)
assert r == fol.false
r = lat.eq(varmap, fol)
d = dict(a_x=1, b_x=2, a_y=0, b_y=3)
r = fol.let(d, r)
d = dict(u_x=1, v_x=2, u_y=0, v_y=3)
r = fol.let(d, r)
assert r == fol.true
def test_cost():
r = cov._cost(None, '?', '?')
assert r == float('inf'), r
fol, prm = setup_aut()
# assign here to avoid calling `eq` from `setup_aut`
# to ensure unit testing
prm.p_eq_q = lat.eq(prm._varmap, fol)
s = ('1 <= a_x /\ a_x <= 3 /\ b_x = 6 /\ '
'2 <= a_y /\ a_y <= 5 /\ '
'0 <= b_y /\ b_y <= 7')
u = fol.add_expr(s)
r = cov._cost(u, prm, fol)
assert r == 96, r
def test_cost():
r = cov._cost(None, '?', '?')
assert r == float('inf'), r
fol, prm = setup_aut()
# assign here to avoid calling `eq` from `setup_aut`
# to ensure unit testing
prm.p_eq_q = lat.eq(prm._varmap, fol)
s = (
'1 <= a_x /\ a_x <= 3 /\ b_x = 6 /\ '
'2 <= a_y /\ a_y <= 5 /\ '
'0 <= b_y /\ b_y <= 7')
u = fol.add_expr(s)
r = cov._cost(u, prm, fol)
assert r == 96, r
def test_orthotopes_using_robots_example():
aut, prm = setup_aut(15, 15)
p_vars = prm.p_vars
# this predicate is constructed by `contract_maker`
# for the robots example in ACC 2016
f = robots_example(aut)
prm.p_leq_q = lat.subseteq(prm._varmap, aut)
prm.p_eq_q = lat.eq(prm._varmap, aut)
u = lat.prime_implicants(f, prm, aut)
support = aut.support(u)
assert support == set(p_vars), (support, p_vars)
n_primes = aut.count(u)
k = aut.count(u)
assert n_primes == k, (n_primes, k)
log.info('{n} prime implicants'.format(n=n_primes))
u = lat.essential_orthotopes(f, prm, aut)
support = aut.support(u)
assert support == set(p_vars), (support, p_vars)
n_essential = aut.count(u)
k = aut.count(u)
assert n_essential == k, (n_essential, k)
log.info('{n} essential prime implicants'.format(n=n_essential))
assert n_essential == 7, n_essential
# result: all primes are essential in this example
#
care = aut.true
s = cov.dumps_cover(u, f, care, aut)
log.info(s)
log.info('BDD has {n} nodes'.format(n=len(aut.bdd)))
# confirm that essential orthotopes cover exactly `f`
c = lat.list_expr(u, prm, aut, simple=True)
s = stx.disj(c)
log.info(s)
z = aut.add_expr(s)
z = aut.exist(['a_x', 'b_x', 'a_y', 'b_y'], z)
assert aut.support(z) == aut.support(f)
assert z == f
if plt is not None:
_plot_orthotopes_for_robots_example(u, f, prm._px, xvars, aut)
# pprint.pprint(aut.bdd.statistics())
# pprint.pprint(aut.bdd.vars)
log.info('{n} nodes in manager'.format(n=len(aut.bdd)))
def setup_orthotope_vars():
fol = _fol.Context()
fol.declare(
x=(0, 5), y=(2, 14),
px=(0, 5), qx=(0, 5),
py=(2, 14), qy=(2, 14),
ax=(0, 5), bx=(0, 5),
ay=(2, 14), by=(2, 14),)
xvars = ['x', 'y']
px = dict(x=dict(a='px', b='qx'),
y=dict(a='py', b='qy'))
qx = dict(x=dict(a='ax', b='bx'),
y=dict(a='ay', b='by'))
prm = lat.Parameters()
prm.x_vars = xvars
prm._px = px
prm._qx = qx
prm.p_to_q = dict(px='ax', py='ay', qx='bx', qy='by')
prm.p_vars = set(prm.p_to_q)
prm.q_vars = set(prm.p_to_q.values())
varmap = lat.parameter_varmap(px, qx)
prm.p_leq_q = lat.subseteq(varmap, fol)
prm.p_eq_q = lat.eq(varmap, fol)
return fol, prm