def split_hyps_at_visit (tags, split, restrs, visit):
(l_details, r_details, eqs, _, _) = split
(l_split, (l_seq_start, l_step), l_eqs) = l_details
(r_split, (r_seq_start, r_step), r_eqs) = r_details
(l_visit, r_visit) = split_visit_visits (tags, split, restrs, visit)
(l_start, r_start) = split_visit_visits (tags, split, restrs, vc_num (0))
(l_tag, r_tag) = tags
def mksub (v):
return lambda exp: logic.var_subst (exp, {('%i', word32T) : v},
must_subst = False)
def inst (exp):
return logic.inst_eq_at_visit (exp, visit)
zsub = mksub (mk_word32 (0))
if visit.kind == 'Number':
lsub = mksub (mk_word32 (visit.n))
else:
lsub = mksub (mk_plus (mk_var ('%n', word32T),
mk_word32 (visit.n)))
hyps = [(Hyp ('PCImp', l_visit, r_visit), 'pc imp'),
(Hyp ('PCImp', l_visit, l_start), '%s pc imp' % l_tag),
(Hyp ('PCImp', r_visit, r_start), '%s pc imp' % r_tag)]
hyps += [(eq_hyp ((zsub (l_exp), l_start), (lsub (l_exp), l_visit),
(l_split, r_split)), '%s const' % l_tag)
for l_exp in l_eqs if inst (l_exp)]
hyps += [(eq_hyp ((zsub (r_exp), r_start), (lsub (r_exp), r_visit),
(l_split, r_split)), '%s const' % r_tag)
for r_exp in r_eqs if inst (r_exp)]
hyps += [(eq_hyp ((lsub (l_exp), l_visit), (lsub (r_exp), r_visit),
(l_split, r_split)), 'eq')
for (l_exp, r_exp) in eqs
if inst (l_exp) and inst (r_exp)]
return hyps
def split_hyps_at_visit(tags, split, restrs, visit):
(l_details, r_details, eqs, _, _) = split
(l_split, (l_seq_start, l_step), l_eqs) = l_details
(r_split, (r_seq_start, r_step), r_eqs) = r_details
(l_visit, r_visit) = split_visit_visits(tags, split, restrs, visit)
(l_start, r_start) = split_visit_visits(tags, split, restrs, vc_num(0))
(l_tag, r_tag) = tags
def mksub(v):
return lambda exp: logic.var_subst(exp, {('%i', word32T): v},
must_subst=False)
def inst(exp):
return logic.inst_eq_at_visit(exp, visit)
zsub = mksub(mk_word32(0))
if visit.kind == 'Number':
lsub = mksub(mk_word32(visit.n))
else:
lsub = mksub(mk_plus(mk_var('%n', word32T), mk_word32(visit.n)))
hyps = [(Hyp('PCImp', l_visit, r_visit), 'pc imp'),
(Hyp('PCImp', l_visit, l_start), '%s pc imp' % l_tag),
(Hyp('PCImp', r_visit, r_start), '%s pc imp' % r_tag)]
hyps += [(eq_hyp((zsub(l_exp), l_start), (lsub(l_exp), l_visit),
(l_split, r_split)), '%s const' % l_tag)
for l_exp in l_eqs if inst(l_exp)]
hyps += [(eq_hyp((zsub(r_exp), r_start), (lsub(r_exp), r_visit),
(l_split, r_split)), '%s const' % r_tag)
for r_exp in r_eqs if inst(r_exp)]
hyps += [(eq_hyp((lsub(l_exp), l_visit), (lsub(r_exp), r_visit),
(l_split, r_split)), 'eq') for (l_exp, r_exp) in eqs
if inst(l_exp) and inst(r_exp)]
return hyps
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 build_compound_problem_with_links(call_stack, f):
funs = [get_body_addrs_fun(addr) for addr in call_stack] + [f]
(p, hyps, addr_map, tag_pairs) = build_compound_problem(funs)
call_tags = zip(tag_pairs[:-1], tag_pairs[1:])
call_hyps = [
get_call_link_hyps(p, addr_map[n], from_tp, to_tp) for (n, (from_tp, to_tp)) in zip(call_stack, call_tags)
]
wcet_hyps = []
from rep_graph import eq_hyp
for (entry, tag, _, inputs) in p.entries:
entry_vis = ((entry, ()), tag)
for f in target_objects.hooks("extra_wcet_assertions"):
for assn in f(inputs):
wcet_hyps.append(eq_hyp((assn, entry_vis), (syntax.true_term, entry_vis)))
return (p, hyps + [h for hs in call_hyps for h in hs] + wcet_hyps, addr_map)
def ident_callables (fname, callees, idents):
from solver import to_smt_expr, smt_expr
from syntax import mk_not, mk_and, true_term
auto_callables = dict ([((ident, f, true_term), True)
for ident in idents.get (fname, [true_term])
for f in callees if f not in idents])
if not [f for f in callees if f in idents]:
return auto_callables
fun = functions[fname]
p = fun.as_problem (problem.Problem, name = 'Target')
check_ns = [(n, ident, cond) for n in p.nodes
if p.nodes[n].kind == 'Call'
if p.nodes[n].fname in idents
for (ident, cond) in ident_conds (p.nodes[n].fname, idents)]
p.do_analysis ()
assert check_ns
rep = rep_graph.mk_graph_slice (p, fast = True)
err_hyp = rep_graph.pc_false_hyp ((default_n_vc (p, 'Err'), 'Target'))
callables = auto_callables
nhyps = mk_not_callable_hyps (p)
for (ident, cond) in ident_conds (fname, idents):
renames = p.entry_exit_renames (tags = ['Target'])
cond = syntax.rename_expr (cond, renames['Target_IN'])
entry = p.get_entry ('Target')
e_vis = ((entry, ()), 'Target')
hyps = [err_hyp, rep_graph.eq_hyp ((cond, e_vis),
(true_term, e_vis))]
for (n, ident2, cond2) in check_ns:
k = (ident, p.nodes[n].fname, ident2)
(inp_env, _, _) = rep.get_func (default_n_vc (p, n))
pc = rep.get_pc (default_n_vc (p, n))
cond2 = to_smt_expr (cond2, inp_env, rep.solv)
if rep.test_hyp_whyps (mk_not (mk_and (pc, cond2)),
hyps + nhyps):
callables[k] = False
else:
callables[k] = True
return callables
def inst_eqs(p, restrs, eqs, tag_map={}):
addr_map = {}
if not tag_map:
tag_map = dict([(tag, tag) for tag in p.tags()])
for (pair_tag, p_tag) in tag_map.iteritems():
addr_map[pair_tag + '_IN'] = ((p.get_entry(p_tag), ()), p_tag)
addr_map[pair_tag + '_OUT'] = (('Ret', restrs), p_tag)
renames = p.entry_exit_renames(tag_map.values())
for (pair_tag, p_tag) in tag_map.iteritems():
renames[pair_tag + '_IN'] = renames[p_tag + '_IN']
renames[pair_tag + '_OUT'] = renames[p_tag + '_OUT']
hyps = []
for (lhs, rhs) in eqs:
vals = [(rename_expr(x, renames[x_addr]), addr_map[x_addr])
for (x, x_addr) in (lhs, rhs)]
hyps.append(eq_hyp(vals[0], vals[1]))
return hyps
def inst_eqs (p, restrs, eqs, tag_map = {}):
addr_map = {}
if not tag_map:
tag_map = dict ([(tag, tag) for tag in p.tags ()])
for (pair_tag, p_tag) in tag_map.iteritems ():
addr_map[pair_tag + '_IN'] = ((p.get_entry (p_tag), ()), p_tag)
addr_map[pair_tag + '_OUT'] = (('Ret', restrs), p_tag)
renames = p.entry_exit_renames (tag_map.values ())
for (pair_tag, p_tag) in tag_map.iteritems ():
renames[pair_tag + '_IN'] = renames[p_tag + '_IN']
renames[pair_tag + '_OUT'] = renames[p_tag + '_OUT']
hyps = []
for (lhs, rhs) in eqs:
vals = [(rename_expr (x, renames[x_addr]), addr_map[x_addr])
for (x, x_addr) in (lhs, rhs)]
hyps.append (eq_hyp (vals[0], vals[1]))
return hyps
def build_compound_problem_with_links(call_stack, f):
funs = [get_body_addrs_fun(addr) for addr in call_stack] + [f]
(p, hyps, addr_map, tag_pairs) = build_compound_problem(funs)
call_tags = zip(tag_pairs[:-1], tag_pairs[1:])
call_hyps = [
get_call_link_hyps(p, addr_map[n], from_tp, to_tp)
for (n, (from_tp, to_tp)) in zip(call_stack, call_tags)
]
wcet_hyps = []
from rep_graph import eq_hyp
for (entry, tag, _, inputs) in p.entries:
entry_vis = ((entry, ()), tag)
for f in target_objects.hooks('extra_wcet_assertions'):
for assn in f(inputs):
wcet_hyps.append(
eq_hyp((assn, entry_vis), (syntax.true_term, entry_vis)))
return (p, hyps + [h for hs in call_hyps
for h in hs] + wcet_hyps, addr_map)
def ident_callables(fname, callees, idents):
from solver import to_smt_expr, smt_expr
from syntax import mk_not, mk_and, true_term
auto_callables = dict([((ident, f, true_term), True)
for ident in idents.get(fname, [true_term])
for f in callees if f not in idents])
if not [f for f in callees if f in idents]:
return auto_callables
fun = functions[fname]
p = fun.as_problem(problem.Problem, name='Target')
check_ns = [(n, ident, cond) for n in p.nodes if p.nodes[n].kind == 'Call'
if p.nodes[n].fname in idents
for (ident, cond) in ident_conds(p.nodes[n].fname, idents)]
p.do_analysis()
assert check_ns
rep = rep_graph.mk_graph_slice(p, fast=True)
err_hyp = rep_graph.pc_false_hyp((default_n_vc(p, 'Err'), 'Target'))
callables = auto_callables
nhyps = mk_not_callable_hyps(p)
for (ident, cond) in ident_conds(fname, idents):
renames = p.entry_exit_renames(tags=['Target'])
cond = syntax.rename_expr(cond, renames['Target_IN'])
entry = p.get_entry('Target')
e_vis = ((entry, ()), 'Target')
hyps = [err_hyp, rep_graph.eq_hyp((cond, e_vis), (true_term, e_vis))]
for (n, ident2, cond2) in check_ns:
k = (ident, p.nodes[n].fname, ident2)
(inp_env, _, _) = rep.get_func(default_n_vc(p, n))
pc = rep.get_pc(default_n_vc(p, n))
cond2 = to_smt_expr(cond2, inp_env, rep.solv)
if rep.test_hyp_whyps(mk_not(mk_and(pc, cond2)), hyps + nhyps):
callables[k] = False
else:
callables[k] = True
return callables
def leaf_condition_checks(p, restrs, hyps):
'''checks of the final refinement conditions'''
nrerr_pc_hyp = non_r_err_pc_hyp(p.pairing.tags, restrs)
hyps = [nrerr_pc_hyp] + hyps
[l_tag, r_tag] = p.pairing.tags
nlerr_pc = pc_false_hyp((('Err', restrs), l_tag))
# this 'hypothesis' ensures that the representation is built all
# the way to Ret. in particular this ensures that function relations
# are available to use in proving single-side equalities
ret_eq = eq_hyp((true_term, (('Ret', restrs), l_tag)),
(true_term, (('Ret', restrs), r_tag)))
### TODO: previously we considered the case where 'Ret' was unreachable
### (as a result of unsatisfiable hyps) and proved a simpler property.
### we might want to restore this
(_, out_eqs) = p.pairing.eqs
checks = [(hyps + [nlerr_pc, ret_eq], hyp, 'Leaf eq check')
for hyp in inst_eqs(p, restrs, out_eqs)]
return [(hyps + [ret_eq], nlerr_pc, 'Leaf path-cond imp')] + checks
def leaf_condition_checks (p, restrs, hyps):
'''checks of the final refinement conditions'''
nrerr_pc_hyp = non_r_err_pc_hyp (p.pairing.tags, restrs)
hyps = [nrerr_pc_hyp] + hyps
[l_tag, r_tag] = p.pairing.tags
nlerr_pc = pc_false_hyp ((('Err', restrs), l_tag))
# this 'hypothesis' ensures that the representation is built all
# the way to Ret. in particular this ensures that function relations
# are available to use in proving single-side equalities
ret_eq = eq_hyp ((true_term, (('Ret', restrs), l_tag)),
(true_term, (('Ret', restrs), r_tag)))
### TODO: previously we considered the case where 'Ret' was unreachable
### (as a result of unsatisfiable hyps) and proved a simpler property.
### we might want to restore this
(_, out_eqs) = p.pairing.eqs
checks = [(hyps + [nlerr_pc, ret_eq], hyp, 'Leaf eq check') for hyp in
inst_eqs (p, restrs, out_eqs)]
return [(hyps + [ret_eq], nlerr_pc, 'Leaf path-cond imp')] + checks
def loop_eq_hyps_at_visit(tag, split, eqs, restrs, visit_num, use_if_at=False):
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))
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),
use_if_at=use_if_at), '%s const' % tag) for exp in eqs
if logic.inst_eq_at_visit(exp, visit_num)]
return hyps
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
def add_recursion_ident (f, group, idents, extra_unfolds):
from syntax import mk_eq, mk_implies, mk_var
p = problem.Problem (None, name = 'Recursion Test')
chain = []
tag = 'fun0'
p.add_entry_function (functions[f], tag)
p.do_analysis ()
assns = []
recursion_last_assns[0] = assns
while True:
res = find_unknown_recursion (p, group, idents, tag, assns,
extra_unfolds)
if res == None:
break
if p.nodes[res].fname not in group:
problem.inline_at_point (p, res)
continue
fname = p.nodes[res].fname
chain.append (fname)
tag = 'fun%d' % len (chain)
(args, _, entry) = p.add_entry_function (functions[fname], tag)
p.do_analysis ()
assns += function_link_assns (p, res, tag)
if chain == []:
return None
recursion_trace.append (' created fun chain %s' % chain)
word_args = [(i, mk_var (s, typ))
for (i, (s, typ)) in enumerate (args)
if typ.kind == 'Word']
rep = rep_graph.mk_graph_slice (p, fast = True)
(_, env) = rep.get_node_pc_env ((entry, ()))
m = {}
res = rep.test_hyp_whyps (syntax.false_term, assns, model = m)
assert m
if find_unknown_recursion (p, group, idents, tag, [], []) == None:
idents.setdefault (fname, [])
idents[fname].append (syntax.true_term)
recursion_trace.append (' found final ident for %s' % fname)
return syntax.true_term
assert word_args
recursion_trace.append (' scanning for ident for %s' % fname)
for (i, arg) in word_args:
(nm, typ) = functions[fname].inputs[i]
arg_smt = solver.to_smt_expr (arg, env, rep.solv)
val = search.eval_model_expr (m, rep.solv, arg_smt)
if not rep.test_hyp_whyps (mk_eq (arg_smt, val), assns):
recursion_trace.append (' discarded %s = 0x%x, not stable' % (nm, val.val))
continue
entry_vis = ((entry, ()), tag)
ass = rep_graph.eq_hyp ((arg, entry_vis), (val, entry_vis))
res = find_unknown_recursion (p, group, idents, tag,
assns + [ass], [])
if res:
fname2 = p.nodes[res].fname
recursion_trace.append (' discarded %s, allows recursion to %s' % (nm, fname2))
continue
eq = syntax.mk_eq (mk_var (nm, typ), val)
idents.setdefault (fname, [])
idents[fname].append (eq)
recursion_trace.append (' found ident for %s: %s' % (fname, eq))
return eq
assert not "identifying assertion found"
def mk_loop_counter_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))
return eq_hyp((mk_var('%n', word32T), visit), (mk_word32(n), visit),
(split, 0))
def init_true_hyp(p, tag, expr):
n = p.get_entry(tag)
vis = ((n, ()), tag)
assert expr.typ == syntax.boolT, expr
return rep_graph.eq_hyp((expr, vis), (syntax.true_term, vis))
def add_recursion_ident(f, group, idents, extra_unfolds):
from syntax import mk_eq, mk_implies, mk_var
p = problem.Problem(None, name='Recursion Test')
chain = []
tag = 'fun0'
p.add_entry_function(functions[f], tag)
p.do_analysis()
assns = []
recursion_last_assns[0] = assns
while True:
res = find_unknown_recursion(p, group, idents, tag, assns,
extra_unfolds)
if res == None:
break
if p.nodes[res].fname not in group:
problem.inline_at_point(p, res)
continue
fname = p.nodes[res].fname
chain.append(fname)
tag = 'fun%d' % len(chain)
(args, _, entry) = p.add_entry_function(functions[fname], tag)
p.do_analysis()
assns += function_link_assns(p, res, tag)
if chain == []:
return None
recursion_trace.append(' created fun chain %s' % chain)
word_args = [(i, mk_var(s, typ)) for (i, (s, typ)) in enumerate(args)
if typ.kind == 'Word']
rep = rep_graph.mk_graph_slice(p, fast=True)
(_, env) = rep.get_node_pc_env((entry, ()))
m = {}
res = rep.test_hyp_whyps(syntax.false_term, assns, model=m)
assert m
if find_unknown_recursion(p, group, idents, tag, [], []) == None:
idents.setdefault(fname, [])
idents[fname].append(syntax.true_term)
recursion_trace.append(' found final ident for %s' % fname)
return syntax.true_term
assert word_args
recursion_trace.append(' scanning for ident for %s' % fname)
for (i, arg) in word_args:
(nm, typ) = functions[fname].inputs[i]
arg_smt = solver.to_smt_expr(arg, env, rep.solv)
val = search.eval_model_expr(m, rep.solv, arg_smt)
if not rep.test_hyp_whyps(mk_eq(arg_smt, val), assns):
recursion_trace.append(' discarded %s = 0x%x, not stable' %
(nm, val.val))
continue
entry_vis = ((entry, ()), tag)
ass = rep_graph.eq_hyp((arg, entry_vis), (val, entry_vis))
res = find_unknown_recursion(p, group, idents, tag, assns + [ass], [])
if res:
fname2 = p.nodes[res].fname
recursion_trace.append(
' discarded %s, allows recursion to %s' % (nm, fname2))
continue
eq = syntax.mk_eq(mk_var(nm, typ), val)
idents.setdefault(fname, [])
idents[fname].append(eq)
recursion_trace.append(' found ident for %s: %s' % (fname, eq))
return eq
assert not "identifying assertion found"
def get_necessary_split_opts (p, head, restrs, hyps, tags = None, iters = None):
if not tags:
tags = p.pairing.tags
[l_tag, r_tag] = tags
assert p.node_tags[head][0] == l_tag
l_seq_vs = get_interesting_linear_series_exprs (p, head)
if not l_seq_vs:
return None
r_seq_vs = {}
for n in init_loops_to_split (p, restrs):
if p.node_tags[n][0] == r_tag:
vs = get_interesting_linear_series_exprs (p, n)
r_seq_vs.update (vs)
if not r_seq_vs:
return None
rep = rep_graph.mk_graph_slice (p, fast = True)
def vis (n, i):
if n != p.loop_id (n):
i = i + 1
return (n, tuple ([(p.loop_id (n), vc_num (i))]) + restrs)
smt = lambda expr, n, i: rep.to_smt_expr (expr, vis (n, i))
smt_pc = lambda n, i: rep.get_pc (vis (n, i))
# remove duplicates by concretising
l_seq_vs = dict ([(smt (expr, n, 2), (kind, n, expr))
for n in l_seq_vs for (kind, expr) in l_seq_vs[n]]).values ()
r_seq_vs = dict ([(smt (expr, n, 2), (kind, n, expr))
for n in r_seq_vs for (kind, expr) in r_seq_vs[n]]).values ()
if iters == None:
if [n for n in p.loop_body (head) if p.nodes[n].kind == 'Call']:
iters = 5
else:
iters = 8
r_seq_end = 1 + 2 * iters
l_seq_end = 1 + iters
l_seq_ineq = 1 + max ([1 << n for n in range (iters)
if 1 << n <= iters])
hyps = hyps + [rep_graph.pc_triv_hyp ((vis (n, r_seq_end), r_tag))
for n in set ([n for (_, n, _) in r_seq_vs])]
hyps = hyps + [rep_graph.pc_triv_hyp ((vis (n, l_seq_end), l_tag))
for n in set ([n for (_, n, _) in l_seq_vs])]
ex_restrs = [(n, rep_graph.vc_upto (r_seq_end + 1))
for n in set ([p.loop_id (n) for (_, n, _) in r_seq_vs])]
hyps = hyps + [check.non_r_err_pc_hyp (tags,
restr_others (p, restrs + tuple (ex_restrs), 2))]
necessary_split_opts_trace[:] = []
necessary_split_opts_long_trace[:] = []
for (kind, n, expr) in sorted (l_seq_vs):
rel_r_seq_vs = [v for v in r_seq_vs if v[0] == kind]
if not rel_r_seq_vs:
necessary_split_opts_trace.append ((n, 'NoneRelevant'))
continue
m = {}
eq = mk_eq (smt (expr, n, 1), smt (expr, n, l_seq_ineq))
ex_hyps = [rep_graph.pc_true_hyp ((vis (n, i), l_tag))
for i in range (1, l_seq_end + 1)]
res = rep.test_hyp_whyps (eq, hyps + ex_hyps, model = m)
necessary_split_opts_long_trace.append ((n, eq, hyps + ex_hyps,
res, m, smt, smt_pc, (kind, n, expr), r_seq_vs, iters))
if not m:
necessary_split_opts_trace.append ((n, None))
continue
seq_eq = get_linear_seq_eq (rep, m, smt, smt_pc,
(kind, n, expr), r_seq_vs, iters)
necessary_split_opts_trace.append ((n, ('Seq', seq_eq)))
if not seq_eq:
continue
((n2, expr2), (l_start, l_step), (r_start, r_step)) = seq_eq
eqs = [rep_graph.eq_hyp ((expr,
(vis (n, l_start + (i * l_step)), l_tag)),
(expr2, (vis (n2, r_start + (i * r_step)), r_tag)))
for i in range (10)
if l_start + (i * l_step) <= l_seq_end
if r_start + (i * r_step) <= r_seq_end]
eq = foldr1 (mk_and, map (rep.interpret_hyp, eqs))
if rep.test_hyp_whyps (eq, hyps):
mk_i = lambda i: (l_start + (i * l_step), l_step)
mk_j = lambda j: (r_start + (j * r_step), r_step)
return [([mk_i (0)], [mk_j (0)]),
([mk_i (0), mk_i (1)], [mk_j (0), mk_j (1)])]
n_vcs = entry_path_no_loops (rep, l_tag, m, head)
path_hyps = [rep_graph.pc_true_hyp ((n_vc, l_tag)) for n_vc in n_vcs]
if rep.test_hyp_whyps (eq, hyps + path_hyps):
# immediate case split on difference between entry paths
checks = [(hyps, eq_hyp, 'eq') for eq_hyp in eqs]
return derive_case_split (rep, n_vcs, checks)
necessary_split_opts_trace.append ((n, 'Seq check failed'))
return None