def test_normalise_fixed_point():
root_expr = sigma(v('x'), product([prob([v('z'), v('y')], [v('b'), v('x'), do(v('a'))]),
prob([v('z'), v('y'), v('x')], [do(v('a'))])]))
bindings = {'x' : 'xxx', 'z' : 'zzz', 'y' : 'yyy', 'a' : 'aaa'}
state = ProofState(0, 0, bindings, root_expr)
normalised_state = state.normalise()
expected_result = sigma(v(0), product((prob((v(0), v(1), v(2)),(do(v(3)), )),
prob((v(1), v(2)), (do(v(3)), v(0), v(4))))))
assert normalised_state.root_expr == expected_result
def test_gen_matches_deep():
# sigma_y { p(x|y,do(z)) * p(y|do(z)) }
root_expr = sigma(v("y"), product([prob([v("x")], [v("y"), do(v("z"))]), prob([v("y")], [do(v("z"))])]))
matches = list(gen_matches(is_v, root_expr))
assert len(matches) == 6
expr, inject = matches[3]
assert expr == v("z")
root_expr_prime = inject("walrus")
assert root_expr_prime == sigma(
v("y"), product([prob([v("x")], [v("y"), do("walrus")]), prob([v("y")], [do(v("z"))])])
)
def gen_expansions(value, proof_state):
for (prob_expr, inject) in E.gen_matches(E.is_prob, proof_state.root_expr):
prob_vars = get_variable_order(prob_expr)
prob_values = [proof_state.bindings[v] for v in prob_vars]
if value in prob_values:
continue
# prob([x],[w]) -> sigma(y, product([prob([x], [y, w]), p([y], [w])]))
i = new_variable_name(proof_state.bindings)
v_i = E.v(i)
alpha_left = tuple(prob_expr[1])
alpha_right = (v_i, ) + tuple(prob_expr[2])
alpha = E.prob(alpha_left, alpha_right)
beta_left = (v_i, )
beta_right = tuple(prob_expr[2])
beta = E.prob(beta_left, beta_right)
expr_prime = E.sigma(v_i, E.product([alpha, beta]))
succ_length = proof_state.length + 1
succ_heuristic = 0
succ_bindings = dict(proof_state.bindings)
succ_bindings[i] = value
succ_root_expr = inject(expr_prime)
succ_comment = 'conditioned %s on %s' % (
pleasantly_fmt(proof_state.bindings, prob_expr),
make_canonical_variable_name(value))
succ_proof_state = ProofState(succ_length, succ_heuristic, succ_bindings, succ_root_expr,
parent=proof_state, comment=succ_comment)
yield succ_proof_state
def test_gen_matches_deep():
# sigma_y { p(x|y,do(z)) * p(y|do(z)) }
root_expr = sigma(
v('y'),
product([
prob([v('x')], [v('y'), do(v('z'))]),
prob([v('y')], [do(v('z'))])
]))
matches = list(gen_matches(is_v, root_expr))
assert len(matches) == 6
expr, inject = matches[3]
assert expr == v('z')
root_expr_prime = inject('walrus')
assert root_expr_prime == sigma(
v('y'),
product([
prob([v('x')], [v('y'), do('walrus')]),
prob([v('y')], [do(v('z'))])
]))
def test_normalise_single_iter():
root_expr = sigma(v('x'), product([prob([v('z'), v('y')], [v('b'), v('x'), do(v('a'))]),
prob([v('z'), v('y'), v('x')], [do(v('a'))])]))
bindings = {'x' : 'xxx', 'z' : 'zzz', 'y' : 'yyy', 'a' : 'aaa'}
state = ProofState(0, 0, bindings, root_expr)
normalised_state = state.normalise(max_iters=1)
# first up: expression ordering (nb do(v()) comes before v() in sorted lists)
# sigma(x, product([prob([x y z],[do(a)]), prob([y z], [(do a) b x])]))
# so, variable order should be:
# x y z a b
# so, new variable names should be
# 0 1 2 3 4
# so, normalised state should be
# sigma(0, product([prob([0 1 2],[do(3)]), prob([1 2], [(do 3) 4 0])]))
expected_result = sigma(v(0), product((prob((v(0), v(1), v(2)),(do(v(3)), )),
prob((v(1), v(2)), (do(v(3)), v(4), v(0))))))
assert normalised_state.root_expr == expected_result