def update_blackboard(self, B):
"""
Saturates a Blackboard B with additive inferences.
"""
timer.start(timer.PADD)
messages.announce_module('polyhedron additive module')
# learn_additive_sign_info(blackboard)
comparisons = get_additive_information(B)
h_matrix = lrs_util.create_h_format_matrix(comparisons, B.num_terms)
messages.announce('Halfplane matrix:', messages.DEBUG)
messages.announce(h_matrix, messages.DEBUG)
v_matrix, v_lin_set = lrs_util.get_vertices(h_matrix)
messages.announce('Vertex matrix:', messages.DEBUG)
#messages.announce(str(v_matrix), messages.DEBUG)
for l in v_matrix:
messages.announce(str(l), messages.DEBUG)
messages.announce('Linear set:', messages.DEBUG)
messages.announce(str(v_lin_set), messages.DEBUG)
new_comparisons = get_2d_comparisons(v_matrix, v_lin_set)
for c in new_comparisons:
B.assert_comparison(c)
timer.stop(timer.PADD)
def update_blackboard(self, B):
"""
Instantiates all stored axioms with respect to B and asserts new clauses.
"""
timer.start(timer.FUN)
messages.announce_module('axiom module')
n = B.num_terms + len(B.equalities.keys()) + len(B.zero_equalities)
#if n == self.num_eqs:
# messages.announce("No new information for the axiom module to use.", messages.DEBUG)
# timer.stop(timer.FUN)
# return
self.num_eqs = n
for a in self.axioms:
messages.announce("Instantiating axiom: {}".format(a),
messages.DEBUG)
if a.unifiable:
clauses = instantiate(a, self.used_envs, B)
for c in clauses:
B.assert_clause(*c)
else:
clauses = instantiate_triggerless(a, self.used_envs, B)
for c in clauses:
B.assert_clause(*c)
timer.stop(timer.FUN)
def update_blackboard(self, B):
"""
Learns equalities and inequalities from additive information in B, and asserts them
to B.
"""
timer.start(timer.FMADD)
messages.announce_module('Fourier-Motzkin additive module')
eqs, comps = get_additive_information(B)
for i in range(B.num_terms):
# at this point, eqs and comps have all comparisons with indices >= i
i_eqs, i_comps = eqs, comps
# determine all comparisons with IVar(i) and IVar(j) with j >= i
for j in range(i + 1, B.num_terms):
# at this point, i_eqs and i_comps have all comparisons with i and indices >= j
ij_eqs, ij_comps = i_eqs, i_comps
# determine all comparisons between IVar(i) and IVar(j)
for k in range(j + 1, B.num_terms):
ij_eqs, ij_comps = elim(ij_eqs, ij_comps, k)
assert_comparisons_to_blackboard(ij_eqs, ij_comps, B)
# done with IVar(j)
i_eqs, i_comps = elim(i_eqs, i_comps, j)
# add this point, i_eqs and i_comps contain only comparisons with IVar(i) alone
assert_comparisons_to_blackboard(i_eqs, i_comps, B)
# done with IVar(i)
eqs, comps = elim(eqs, comps, i)
timer.stop(timer.FMADD)
def update_blackboard(self, B):
"""
Learns sign information and equalities and inequalities from multiplicative information in
B, and asserts them to B.
"""
timer.start(timer.FMMUL)
messages.announce_module('Fourier-Motzkin multiplicative module')
mul_util.derive_info_from_definitions(B)
mul_util.preprocess_cancellations(B)
eqs, comps = get_multiplicative_information(B)
# t0 = 1; ignore
for i in range(1, B.num_terms):
# at this point, eqs and comps have all comparisons with indices >= i
i_eqs, i_comps = eqs, comps
# determine all comparisons with IVar(i) and IVar(j) with j >= i
for j in range(i + 1, B.num_terms):
# at this point, i_eqs and i_comps have all comparisons with i and indices >= j
ij_eqs, ij_comps = i_eqs, i_comps
# determine all comparisons between IVar(i) and IVar(j)
for k in range(j + 1, B.num_terms):
ij_eqs, ij_comps = elim(ij_eqs, ij_comps, k)
#print 'comps:', ij_comps
assert_comparisons_to_blackboard(ij_eqs, ij_comps, B)
# done with IVar(j)
i_eqs, i_comps = elim(i_eqs, i_comps, j)
# add this point, i_eqs and i_comps contain only comparisons with IVar(i) alone
assert_comparisons_to_blackboard(i_eqs, i_comps, B)
# done with IVar(i)
eqs, comps = elim(eqs, comps, i)
timer.stop(timer.FMMUL)
def update_blackboard(self, B):
"""
Saturates a Blackboard B with additive inferences.
"""
timer.start(timer.PADD)
messages.announce_module('polyhedron additive module')
# learn_additive_sign_info(blackboard)
comparisons = get_additive_information(B)
h_matrix = lrs_util.create_h_format_matrix(comparisons, B.num_terms)
messages.announce('Halfplane matrix:', messages.DEBUG)
messages.announce(h_matrix, messages.DEBUG)
v_matrix, v_lin_set = lrs_util.get_vertices(h_matrix)
messages.announce('Vertex matrix:', messages.DEBUG)
#messages.announce(str(v_matrix), messages.DEBUG)
for l in v_matrix:
messages.announce(str(l), messages.DEBUG)
messages.announce('Linear set:', messages.DEBUG)
messages.announce(str(v_lin_set), messages.DEBUG)
new_comparisons = get_2d_comparisons(v_matrix, v_lin_set)
for c in new_comparisons:
B.assert_comparison(c)
timer.stop(timer.PADD)
def update_blackboard(self, B):
"""
Adds axioms corresponding to each nth root function present.
"""
messages.announce_module('nth root value module')
timer.start(timer.ROOT)
#nth_roots = []
def is_nth_root_term(i):
"""
Returns True if t_i is of the form abs(t_j).
"""
return (isinstance(B.term_defs[i], terms.FuncTerm)
and isinstance(B.term_defs[i].func, terms.NthRoot))
def root_degree(i):
"""
If t_i is of the form NthRoot(n, t_j), returns n.
"""
return B.term_defs[i].func.n
nth_roots = set([root_degree(i) for i in range(B.num_terms) if is_nth_root_term(i)])
x = terms.Var('x')
for n in nth_roots:
if n % 2 == 0:
self.am.add_axiom(formulas.Forall([x], formulas.Implies(x >= 0,
terms.root(n, x) ** n == x)))
self.am.add_axiom(formulas.Forall([x], formulas.Implies(x >= 0,
terms.root(n, x) >= 0)))
else:
self.am.add_axiom(formulas.Forall([x], terms.root(n, x) ** n == x))
timer.stop(timer.ROOT)
def update_blackboard(self, B):
"""
Learns sign information and equalities and inequalities from multiplicative information in
B, and asserts them to B.
"""
timer.start(timer.FMMUL)
messages.announce_module('Fourier-Motzkin multiplicative module')
mul_util.derive_info_from_definitions(B)
mul_util.preprocess_cancellations(B)
eqs, comps = get_multiplicative_information(B)
# t0 = 1; ignore
for i in range(1, B.num_terms):
# at this point, eqs and comps have all comparisons with indices >= i
i_eqs, i_comps = eqs, comps
# determine all comparisons with IVar(i) and IVar(j) with j >= i
for j in range(i + 1, B.num_terms):
# at this point, i_eqs and i_comps have all comparisons with i and indices >= j
ij_eqs, ij_comps = i_eqs, i_comps
# determine all comparisons between IVar(i) and IVar(j)
for k in range(j + 1, B.num_terms):
ij_eqs, ij_comps = elim(ij_eqs, ij_comps, k)
#print 'comps:', ij_comps
assert_comparisons_to_blackboard(ij_eqs, ij_comps, B)
# done with IVar(j)
i_eqs, i_comps = elim(i_eqs, i_comps, j)
# add this point, i_eqs and i_comps contain only comparisons with IVar(i) alone
assert_comparisons_to_blackboard(i_eqs, i_comps, B)
# done with IVar(i)
eqs, comps = elim(eqs, comps, i)
timer.stop(timer.FMMUL)
def update_blackboard(self, B):
"""
Saturates a Blackboard B with multiplicative inferences.
"""
timer.start(timer.PMUL)
messages.announce_module('polyhedron multiplicative module')
mul_util.derive_info_from_definitions(B)
mul_util.preprocess_cancellations(B)
m_comparisons = mul_util.get_multiplicative_information(B)
# Each ti in m_comparisons really represents |t_i|.
p = add_of_mul_comps(m_comparisons, B.num_terms)
a_comparisons, prime_of_index, num_terms = p
a_comparisons = [terms.comp_eval[c[1]](c[0], 0) for c in a_comparisons]
h_matrix = lrs_util.create_h_format_matrix(a_comparisons, num_terms)
messages.announce('Halfplane matrix:', messages.DEBUG)
messages.announce(h_matrix, messages.DEBUG)
v_matrix, v_lin_set = lrs_util.get_vertices(h_matrix)
messages.announce('Vertex matrix:', messages.DEBUG)
for l in v_matrix:
messages.announce(str(l), messages.DEBUG)
messages.announce('Linear set:', messages.DEBUG)
messages.announce(str(v_lin_set), messages.DEBUG)
new_comparisons = get_mul_comparisons(v_matrix, v_lin_set, B.num_terms,
prime_of_index)
for m1, m2, coeff, comp in new_comparisons:
c = mul_util.process_mul_comp(m1, m2, coeff, comp, B)
if c is not None:
B.assert_comparison(c)
timer.stop(timer.PMUL)
def update_blackboard(self, B):
"""
Asserts identities about minm terms
"""
messages.announce_module('minimum module')
timer.start(timer.MINM)
for i in range(B.num_terms):
if isinstance(
B.term_defs[i],
terms.FuncTerm) and B.term_defs[i].func_name == 'minm':
# t_i is of the form minm(...)
args = B.term_defs[i].args
# assert that t_i is le all of its arguments
for a in args:
B.assert_comparison(terms.IVar(i) <= a)
# see if we can infer the sign
# TODO: optimize
if all(B.implies_comparison(a > 0) for a in args):
B.assert_comparison(terms.IVar(i) > 0)
elif all(B.implies_comparison(a >= 0) for a in args):
B.assert_comparison(terms.IVar(i) >= 0)
if any(B.implies_comparison(a < 0) for a in args):
B.assert_comparison(terms.IVar(i) < 0)
elif any(B.implies_comparison(a <= 0) for a in args):
B.assert_comparison(terms.IVar(i) <= 0)
# see if any multiple of another problem term is known to be less than all the
# arguments.
for j in range(B.num_terms):
if j != i:
comp_range = geometry.ComparisonRange(
geometry.neg_infty, geometry.infty, True, True,
True)
for a in args:
new_comp_range = B.le_coeff_range(
j, a.term.index, a.coeff)
comp_range = comp_range & new_comp_range
if comp_range.is_empty():
break
if not comp_range.is_empty():
if comp_range.lower.type == geometry.VAL:
c = comp_range.lower.val
if comp_range.lower_strict:
B.assert_comparison(
c * terms.IVar(j) < terms.IVar(i))
else:
B.assert_comparison(
c * terms.IVar(j) <= terms.IVar(i))
if comp_range.upper.type == geometry.VAL:
c = comp_range.upper.val
if comp_range.upper_strict:
B.assert_comparison(
c * terms.IVar(j) < terms.IVar(i))
else:
B.assert_comparison(
c * terms.IVar(j) <= terms.IVar(i))
timer.stop(timer.MINM)
def update_blackboard(self, B):
"""
Asserts identities about exp and log terms found in B.
"""
timer.start(timer.EXP)
messages.announce_module('exponential module')
if any(isinstance(t, terms.FuncTerm) and t.func == terms.exp for t in B.term_defs.values()):
B.assert_comparison(terms.exp(0) == 1)
if any(isinstance(t, terms.FuncTerm) and t.func == terms.log for t in B.term_defs.values()):
B.assert_comparison(terms.log(1) == 0)
exp_factor_constant(B)
exp_factor_sum(B)
log_factor_exponent(B)
log_factor_product(B)
timer.stop(timer.EXP)
def update_blackboard(self, B):
"""
Asserts identities about minm terms
"""
messages.announce_module('minimum module')
timer.start(timer.MINM)
for i in range(B.num_terms):
if isinstance(B.term_defs[i], terms.FuncTerm) and B.term_defs[i].func_name == 'minm':
# t_i is of the form minm(...)
args = B.term_defs[i].args
# assert that t_i is le all of its arguments
for a in args:
B.assert_comparison(terms.IVar(i) <= a)
# see if we can infer the sign
# TODO: optimize
if all(B.implies_comparison(a > 0) for a in args):
B.assert_comparison(terms.IVar(i) > 0)
elif all(B.implies_comparison(a >= 0) for a in args):
B.assert_comparison(terms.IVar(i) >= 0)
if any(B.implies_comparison(a < 0) for a in args):
B.assert_comparison(terms.IVar(i) < 0)
elif any(B.implies_comparison(a <= 0) for a in args):
B.assert_comparison(terms.IVar(i) <= 0)
# see if any multiple of another problem term is known to be less than all the
# arguments.
for j in range(B.num_terms):
if j != i:
comp_range = geometry.ComparisonRange(geometry.neg_infty, geometry.infty,
True, True, True)
for a in args:
new_comp_range = B.le_coeff_range(j, a.term.index, a.coeff)
comp_range = comp_range & new_comp_range
if comp_range.is_empty():
break
if not comp_range.is_empty():
if comp_range.lower.type == geometry.VAL:
c = comp_range.lower.val
if comp_range.lower_strict:
B.assert_comparison(c * terms.IVar(j) < terms.IVar(i))
else:
B.assert_comparison(c * terms.IVar(j) <= terms.IVar(i))
if comp_range.upper.type == geometry.VAL:
c = comp_range.upper.val
if comp_range.upper_strict:
B.assert_comparison(c * terms.IVar(j) < terms.IVar(i))
else:
B.assert_comparison(c * terms.IVar(j) <= terms.IVar(i))
timer.stop(timer.MINM)
def update_blackboard(self, B):
"""
Asserts identities about exp and log terms found in B.
"""
timer.start(timer.EXP)
messages.announce_module('exponential module')
if any(isinstance(t, terms.FuncTerm) and t.func == terms.exp for t in B.term_defs.values()):
B.assert_comparison(terms.exp(0) == 1)
if any(isinstance(t, terms.FuncTerm) and t.func == terms.log for t in B.term_defs.values()):
B.assert_comparison(terms.log(1) == 0)
exp_factor_constant(B)
exp_factor_sum(B)
#exp_factor_both(B)
log_factor_exponent(B)
log_factor_product(B)
timer.stop(timer.EXP)
def update_blackboard(self, B):
"""
Adds axioms corresponding to each nth root function present.
"""
messages.announce_module('nth root value module')
timer.start(timer.ROOT)
#nth_roots = []
def is_nth_root_term(i):
"""
Returns True if t_i is of the form abs(t_j).
"""
return (isinstance(B.term_defs[i], terms.FuncTerm)
and isinstance(B.term_defs[i].func, terms.NthRoot))
def root_degree(i):
"""
If t_i is of the form NthRoot(n, t_j), returns n.
"""
return B.term_defs[i].func.n
nth_roots = set([
root_degree(i) for i in range(B.num_terms) if is_nth_root_term(i)
])
x = terms.Var('x')
for n in nth_roots:
if n % 2 == 0:
self.am.add_axiom(
formulas.Forall([x],
formulas.Implies(x >= 0,
terms.root(n,
x)**n == x)))
self.am.add_axiom(
formulas.Forall([x],
formulas.Implies(x >= 0,
terms.root(n, x) >= 0)))
else:
self.am.add_axiom(
formulas.Forall([x],
terms.root(n, x)**n == x))
timer.stop(timer.ROOT)
def update_blackboard(self, B):
"""
Checks the blackboard B for function terms with equal arguments, and asserts that the
function terms are equal.
"""
def eq_func_terms(f1, f2):
"""
Returns true if f1 and f2 have the same name and arity, and all args are equal.
"""
if f1.func_name != f2.func_name or len(f1.args) != len(f2.args):
return False
for i in range(len(f1.args)):
arg1, arg2 = f1.args[i], f2.args[i]
if arg1.coeff == 0:
eq = B.implies(arg2.term.index, terms.EQ, 0,
0) or arg2.coeff == 0
else:
eq = B.implies(arg1.term.index, terms.EQ,
fractions.Fraction(arg2.coeff, arg1.coeff),
arg2.term.index)
if not eq:
return False
return True
timer.start(timer.CCM)
messages.announce_module('congruence closure module')
func_classes = {}
for i in (d for d in range(B.num_terms)
if isinstance(B.term_defs[d], terms.FuncTerm)):
name = B.term_defs[i].func_name
func_classes[name] = func_classes.get(name, []) + [i]
for name in func_classes:
tinds = func_classes[name]
for (i, j) in itertools.combinations(tinds, 2):
# ti and tj are function terms with the same symbols. check if they're equal.
f1, f2 = B.term_defs[i], B.term_defs[j]
if eq_func_terms(f1, f2):
B.assert_comparison(terms.IVar(i) == terms.IVar(j))
timer.stop(timer.CCM)
def update_blackboard(self, B):
"""
Saturates a Blackboard B with multiplicative inferences.
"""
timer.start(timer.PMUL)
messages.announce_module('polyhedron multiplicative module')
mul_util.derive_info_from_definitions(B)
mul_util.preprocess_cancellations(B)
m_comparisons = mul_util.get_multiplicative_information(B)
# Each ti in m_comparisons really represents |t_i|.
p = add_of_mul_comps(m_comparisons, B.num_terms)
a_comparisons, prime_of_index, num_terms = p
a_comparisons = [terms.comp_eval[c[1]](c[0], 0) for c in a_comparisons]
h_matrix = lrs_util.create_h_format_matrix(a_comparisons, num_terms)
messages.announce('Halfplane matrix:', messages.DEBUG)
messages.announce(h_matrix, messages.DEBUG)
v_matrix, v_lin_set = lrs_util.get_vertices(h_matrix)
messages.announce('Vertex matrix:', messages.DEBUG)
for l in v_matrix:
messages.announce(str(l), messages.DEBUG)
messages.announce('Linear set:', messages.DEBUG)
messages.announce(str(v_lin_set), messages.DEBUG)
new_comparisons = get_mul_comparisons(v_matrix, v_lin_set,
B.num_terms, prime_of_index)
for m1, m2, coeff, comp in new_comparisons:
c = mul_util.process_mul_comp(m1, m2, coeff, comp, B)
if c is not None:
B.assert_comparison(c)
timer.stop(timer.PMUL)
def update_blackboard(self, B):
"""
Instantiates all stored axioms with respect to B and asserts new clauses.
"""
timer.start(timer.FUN)
messages.announce_module('axiom module')
n = B.num_terms + len(B.equalities.keys()) + len(B.zero_equalities)
#if n == self.num_eqs:
# messages.announce("No new information for the axiom module to use.", messages.DEBUG)
# timer.stop(timer.FUN)
# return
self.num_eqs = n
for a in self.axioms:
messages.announce("Instantiating axiom: {}".format(a), messages.DEBUG)
if a.unifiable:
clauses = instantiate(a, self.used_envs, B)
for c in clauses:
B.assert_clause(*c)
else:
clauses = instantiate_triggerless(a, self.used_envs, B)
for c in clauses:
B.assert_clause(*c)
timer.stop(timer.FUN)
def update_blackboard(self, B):
"""
Adds variations on the triangle inequality.
Looks for expressions abs(c1 * t1 + ... + ck * tk) for which each ti either
occurs in an abs term, or has a known sign. In that case, adds inequalities corresponding
to
abs(c1 * t1 + ... + ck * tk) <= abs(c1 * t1) + ... + abs(ck * tk)
abs(c1 * t1 + ... + ck * tk) >= abs(cj * tj) - (abs(c1 * t1) + ... + abs(ck * tk))
"""
messages.announce_module('absolute value module')
timer.start(timer.ABS)
def is_abs_term(i):
"""
Returns True if t_i is of the form abs(t_j).
"""
return (isinstance(B.term_defs[i], terms.FuncTerm)
and B.term_defs[i].func_name == 'abs')
def abs_arg_index(i):
"""
If t_i is of the form abs(t_j), returns j.
"""
return B.term_defs[i].args[0].term.index
def is_sum_term(i):
"""
Return True if t_i is a sum.
"""
return isinstance(B.term_defs[i], terms.AddTerm)
def sum_args(i):
"""
Assuming t_i is a sum, returns the arguments.
"""
return B.term_defs[i].args
# indices i of terms t_i of the form abs(t_j)
abs_indices = [i for i in range(B.num_terms) if is_abs_term(i)]
# indices j of terms occurring in the context abs(t_j)
abs_wrapped_indices = [abs_arg_index(i) for i in abs_indices]
# indices of terms of the form abs(c1 * t1 + ... + ck * tk)
abs_sum_indices = [i for i in abs_indices if is_sum_term(abs_arg_index(i))]
def abs_present(i):
"""
Returns True if t_i occurs in the context abs(t_i) or has known sign, which is to say,
something equivalent to abs(t_i) is already a problem term.
"""
return i in abs_wrapped_indices or B.weak_sign(i) == 1 or B.weak_sign(i) == -1
def abs_of(i):
"""
Assuming abs_present(i), returns an expression equal to abs(t_i).
"""
if B.weak_sign(i) == 1:
return terms.IVar(i)
elif B.weak_sign(i) == -1:
return terms.IVar(i) * -1
else:
return terms.IVar(next(j for j in abs_indices if abs_arg_index(j) == i))
for i in abs_sum_indices:
args = sum_args(abs_arg_index(i))
if all(abs_present(a.term.index) for a in args):
abs_of_args = [a.coeff * abs_of(a.term.index) for a in args]
sum_of_abs_of_args = reduce(lambda x, y: x + y, abs_of_args, 0)
B.assert_comparison(terms.IVar(i) <= sum_of_abs_of_args)
for a in abs_of_args:
B.assert_comparison(terms.IVar(i) >= a * 2 - sum_of_abs_of_args)
timer.stop(timer.ABS)
def update_blackboard(self, B):
"""
Adds variations on the triangle inequality.
Looks for expressions abs(c1 * t1 + ... + ck * tk) for which each ti either
occurs in an abs term, or has a known sign. In that case, adds inequalities corresponding
to
abs(c1 * t1 + ... + ck * tk) <= abs(c1 * t1) + ... + abs(ck * tk)
abs(c1 * t1 + ... + ck * tk) >= abs(cj * tj) - (abs(c1 * t1) + ... + abs(ck * tk))
"""
messages.announce_module('absolute value module')
timer.start(timer.ABS)
def is_abs_term(i):
"""
Returns True if t_i is of the form abs(t_j).
"""
return (isinstance(B.term_defs[i], terms.FuncTerm)
and B.term_defs[i].func_name == 'abs')
def abs_arg_index(i):
"""
If t_i is of the form abs(t_j), returns j.
"""
return B.term_defs[i].args[0].term.index
def is_sum_term(i):
"""
Return True if t_i is a sum.
"""
return isinstance(B.term_defs[i], terms.AddTerm)
def sum_args(i):
"""
Assuming t_i is a sum, returns the arguments.
"""
return B.term_defs[i].args
# indices i of terms t_i of the form abs(t_j)
abs_indices = [i for i in range(B.num_terms) if is_abs_term(i)]
# indices j of terms occurring in the context abs(t_j)
abs_wrapped_indices = [abs_arg_index(i) for i in abs_indices]
# indices of terms of the form abs(c1 * t1 + ... + ck * tk)
abs_sum_indices = [
i for i in abs_indices if is_sum_term(abs_arg_index(i))
]
def abs_present(i):
"""
Returns True if t_i occurs in the context abs(t_i) or has known sign, which is to say,
something equivalent to abs(t_i) is already a problem term.
"""
return i in abs_wrapped_indices or B.weak_sign(
i) == 1 or B.weak_sign(i) == -1
def abs_of(i):
"""
Assuming abs_present(i), returns an expression equal to abs(t_i).
"""
if B.weak_sign(i) == 1:
return terms.IVar(i)
elif B.weak_sign(i) == -1:
return terms.IVar(i) * -1
else:
return terms.IVar(
next(j for j in abs_indices if abs_arg_index(j) == i))
for i in abs_sum_indices:
args = sum_args(abs_arg_index(i))
if all(abs_present(a.term.index) for a in args):
abs_of_args = [a.coeff * abs_of(a.term.index) for a in args]
sum_of_abs_of_args = reduce(lambda x, y: x + y, abs_of_args, 0)
B.assert_comparison(terms.IVar(i) <= sum_of_abs_of_args)
for a in abs_of_args:
B.assert_comparison(
terms.IVar(i) >= a * 2 - sum_of_abs_of_args)
timer.stop(timer.ABS)