def get_induct_eq_hyp(p, split, restrs, n):
details = (split, (0, 1), [])
(tag, _) = p.node_tags[split]
visit = split_visit_one_visit(tag, details, restrs, vc_offs(0))
from syntax import mk_var, word32T, mk_word32
return eq_hyp((mk_var("%n", word32T), visit), (mk_word32(n), visit), (split, 0))
def linear_eq_induct_base_checks (p, restrs, hyps, tag, split, eqs):
tests = []
details = (split, (0, 1), eqs)
for i in [0, 1]:
reach = split_visit_one_visit (tag, details, restrs, vc_num (i))
nhyps = [pc_true_hyp (reach)]
tests.extend ([(hyps + nhyps, hyp,
'Base check (%s, %d) at induct step for %d' % (desc,
i, split)) for (hyp, desc) in
linear_eq_hyps_at_visit (tag, split, eqs,
restrs, vc_num (i))])
return tests
def linear_eq_induct_step_checks(p, restrs, hyps, tag, split, eqs_assume, eqs):
details = (split, (0, 1), eqs_assume + eqs)
cont = split_visit_one_visit(tag, details, restrs, vc_offs(1))
hyps = (
[pc_true_hyp(cont)]
+ hyps
+ [h for (h, _) in linear_eq_hyps_at_visit(tag, split, eqs_assume + eqs, restrs, vc_offs(0))]
)
return [
(hyps, hyp, "Induct check (%s) at inductive step for %d" % (desc, split))
for (hyp, desc) in linear_eq_hyps_at_visit(tag, split, eqs, restrs, vc_offs(1))
]
def linear_eq_induct_step_checks (p, restrs, hyps, tag, split, eqs):
details = (split, (0, 1), eqs)
cont = split_visit_one_visit (tag, details, restrs, vc_offs (1))
# the 'trivial' hyp here ensures the representation includes a loop
# of the rhs when proving const equations on the lhs
hyps = ([pc_true_hyp (cont)] + hyps
+ [h for (h, _) in linear_eq_hyps_at_visit (tag, split,
eqs, restrs, vc_offs (0))])
return [(hyps, hyp, 'Induct check (%s) at inductive step for %d'
% (desc, split))
for (hyp, desc) in linear_eq_hyps_at_visit (tag, split, eqs,
restrs, vc_offs (1))]
def linear_eq_hyps_at_visit (tag, split, eqs, restrs, visit_num):
details = (split, (0, 1), eqs)
visit = split_visit_one_visit (tag, details, restrs, visit_num)
start = split_visit_one_visit (tag, details, restrs, vc_num (0))
from syntax import mk_word32, mk_plus, mk_var, word32T
def mksub (v):
return lambda exp: logic.var_subst (exp, {('%i', word32T) : v},
must_subst = False)
zsub = mksub (mk_word32 (0))
if visit_num.kind == 'Number':
isub = mksub (mk_word32 (visit_num.n))
else:
isub = mksub (mk_plus (mk_var ('%n', word32T),
mk_word32 (visit_num.n)))
hyps = [(Hyp ('PCImp', visit, start), '%s pc imp' % tag)]
hyps += [(eq_hyp ((zsub (exp), start), (isub (exp), visit),
(split, 0)), '%s const' % tag)
for exp in eqs if logic.inst_eq_at_visit (exp, visit_num)]
return hyps