def make_skolems(fmla, ast, pol, univs):
global macro_dep_map
global strat_map
if isinstance(fmla, il.Not):
make_skolems(fmla.args[0], ast, not pol, univs)
if isinstance(fmla, il.Implies):
make_skolems(fmla.args[0], ast, not pol, univs)
make_skolems(fmla.args[1], ast, pol, univs)
is_e = il.is_exists(fmla)
is_a = il.is_forall(fmla)
if is_e and pol or is_a and not pol:
fvs = set(il.free_variables(fmla))
for u in univs:
if u in fvs:
for e in il.quantifier_vars(fmla):
macro_dep_map[e].add(strat_map[u])
if is_e and not pol or is_a and pol:
make_skolems(fmla.args[0], ast, pol,
univs + list(il.quantifier_vars(fmla)))
for arg in fmla.args:
make_skolems(arg, ast, pol, univs)
if isinstance(fmla, il.Ite):
make_skolems(fmla.args[0], ast, not pol, univs)
if isinstance(fmla, il.Iff) or (il.is_eq(fmla)
and il.is_boolean(fmla.args[0])):
make_skolems(fmla.args[0], ast, not pol, univs)
make_skolems(fmla.args[1], ast, not pol, univs)
def get_qa_arcs(fmla,ast,pol,univs,strat_map):
if isinstance(fmla,il.Not):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs,strat_map):
yield a
return
if isinstance(fmla,il.Implies):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs,strat_map):
yield a
for a in get_qa_arcs(fmla.args[1],ast,pol,univs,strat_map):
yield a
return
is_e = il.is_exists(fmla)
is_a = il.is_forall(fmla)
if is_e and pol or is_a and not pol:
fvs = set(il.free_variables(fmla))
for u in univs:
if u in fvs:
for e in il.quantifier_vars(fmla):
yield (find(strat_map[u]),find(strat_map[e]),ast)
if is_e and not pol or is_a and pol:
for a in get_qa_arcs(fmla.args[0],ast,pol,univs+list(il.quantifier_vars(fmla)),strat_map):
yield a
for arg in fmla.args:
for a in get_qa_arcs(arg,ast,pol,univs,strat_map):
yield a
if isinstance(fmla,il.Ite):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs,strat_map):
yield a
if isinstance(fmla,il.Iff) or (il.is_eq(fmla) and il.is_boolean(fmla.args[0])):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs,strat_map):
yield a
for a in get_qa_arcs(fmla.args[1],ast,not pol,univs,strat_map):
yield a
def get_qa_arcs(fmla,ast,pol,univs,strat_map):
if isinstance(fmla,il.Not):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs,strat_map):
yield a
return
if isinstance(fmla,il.Implies):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs,strat_map):
yield a
for a in get_qa_arcs(fmla.args[1],ast,pol,univs,strat_map):
yield a
return
is_e = il.is_exists(fmla)
is_a = il.is_forall(fmla)
if is_e and pol or is_a and not pol:
fvs = set(il.free_variables(fmla))
for u in univs:
if u in fvs:
for e in il.quantifier_vars(fmla):
yield (find(strat_map[u]),find(strat_map[e]),ast)
if is_e and not pol or is_a and pol:
for a in get_qa_arcs(fmla.args[0],ast,pol,univs+list(il.quantifier_vars(fmla)),strat_map):
yield a
for arg in fmla.args:
for a in get_qa_arcs(arg,ast,pol,univs,strat_map):
yield a
if isinstance(fmla,il.Ite):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs,strat_map):
yield a
if isinstance(fmla,il.Iff) or (il.is_eq(fmla) and il.is_boolean(fmla.args[0])):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs,strat_map):
yield a
for a in get_qa_arcs(fmla.args[1],ast,not pol,univs,strat_map):
yield a
def get_qa_arcs(fmla,ast,pol,univs):
if isinstance(fmla,il.Not):
for a in get_qa_arcs(fmla.args[0],ast,not pol,univs):
yield a
return
is_e = il.is_exists(fmla)
is_a = il.is_forall(fmla)
if is_e and pol or is_a and not pol:
for u in univs:
for e in il.quantifier_vars(fmla):
yield (u.sort,e.sort,ast)
if is_e and not pol or is_a and pol:
for a in get_qa_arcs(fmla.args[0],ast,pol,univs+list(il.quantifier_vars(fmla))):
yield a
for arg in fmla.args:
for a in get_qa_arcs(arg,ast,pol,univs):
yield a
def get_qa_arcs(fmla, ast, pol, univs):
if isinstance(fmla, il.Not):
for a in get_qa_arcs(fmla.args[0], ast, not pol, univs):
yield a
return
is_e = il.is_exists(fmla)
is_a = il.is_forall(fmla)
if is_e and pol or is_a and not pol:
for u in univs:
for e in il.quantifier_vars(fmla):
yield (u.sort, e.sort, ast)
if is_e and not pol or is_a and pol:
for a in get_qa_arcs(fmla.args[0], ast, pol,
univs + list(il.quantifier_vars(fmla))):
yield a
for arg in fmla.args:
for a in get_qa_arcs(arg, ast, pol, univs):
yield a
def property_tactic(self, decls, proof):
cut = proof.args[0]
goal = decls[0]
subgoal = goal_subst(goal, cut, cut.lineno)
lhs = proof.args[1]
if not isinstance(lhs, ia.NoneAST):
fmla = il.drop_universals(cut.formula)
if not il.is_exists(fmla) or len(fmla.variables) != 1:
raise IvyError(proof, 'property is not existential')
evar = list(fmla.variables)[0]
rng = evar.sort
vmap = dict((x.name, x) for x in lu.variables_ast(fmla))
used = set()
args = lhs.args
targs = []
for a in args:
if a.name in used:
raise IvyError(lhs, 'repeat parameter: {}'.format(a.name))
used.add(a.name)
if a.name in vmap:
v = vmap[a.name]
targs.append(v)
if not (il.is_topsort(a.sort) or a.sort != v.sort):
raise IvyError(lhs, 'bad sort for {}'.format(a.name))
else:
if il.is_topsort(a.sort):
raise IvyError(
lhs, 'cannot infer sort for {}'.format(a.name))
targs.append(a)
for x in vmap:
if x not in used:
raise IvyError(
lhs, '{} must be a parameter of {}'.format(x, lhs.rep))
dom = [x.sort for x in targs]
sym = il.Symbol(lhs.rep, il.FuncConstSort(*(dom + [rng])))
if sym in self.stale or sym in goal_defns(goal):
raise iu.IvyError(lhs, '{} is not fresh'.format(sym))
term = sym(*targs) if targs else sym
fmla = lu.substitute_ast(fmla.body, {evar.name: term})
cut = clone_goal(cut, [], fmla)
goal = goal_add_prem(goal, ia.ConstantDecl(sym), goal.lineno)
return [goal_add_prem(goal, cut, cut.lineno)] + decls[1:] + [subgoal]
