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 formula_to_z3_int(fmla):
# print "formula_to_z3_int: {} : {}".format(fmla,type(fmla))
if ivy_logic.is_atom(fmla):
return atom_to_z3(fmla)
if isinstance(fmla, ivy_logic.Definition) and ivy_logic.is_enumerated(fmla.args[0]) and not use_z3_enums:
return encode_equality(*fmla.args)
args = [formula_to_z3_int(arg) for arg in fmla.args]
if isinstance(fmla, ivy_logic.And):
return z3.And(args)
if isinstance(fmla, ivy_logic.Or):
return z3.Or(args)
if isinstance(fmla, ivy_logic.Not):
return z3.Not(args[0])
if isinstance(fmla, ivy_logic.Definition):
return my_eq(args[0], args[1])
if isinstance(fmla, ivy_logic.Iff):
return my_eq(args[0], args[1])
if isinstance(fmla, ivy_logic.Implies):
return z3.Implies(args[0], args[1])
if isinstance(fmla, ivy_logic.Ite):
return z3.If(args[0], args[1], args[2])
if ivy_logic.is_quantifier(fmla):
variables = ivy_logic.quantifier_vars(fmla)
q = z3.ForAll if ivy_logic.is_forall(fmla) else z3.Exists
res = q([term_to_z3(v) for v in variables], args[0])
# print "res = {}".format(res)
return res
if ivy_logic.is_individual(fmla):
return term_to_z3(fmla)
print "bad fmla: {!r}".format(fmla)
assert False
def formula_to_z3_int(fmla):
# print "formula_to_z3_int: {} : {}".format(fmla,type(fmla))
if ivy_logic.is_atom(fmla):
return atom_to_z3(fmla)
if isinstance(fmla, ivy_logic.Definition) and ivy_logic.is_enumerated(
fmla.args[0]):
return encode_equality(*fmla.args)
args = [formula_to_z3_int(arg) for arg in fmla.args]
if isinstance(fmla, ivy_logic.And):
return z3.And(args)
if isinstance(fmla, ivy_logic.Or):
return z3.Or(args)
if isinstance(fmla, ivy_logic.Not):
return z3.Not(args[0])
if isinstance(fmla, ivy_logic.Definition):
return my_eq(args[0], args[1])
if isinstance(fmla, ivy_logic.Iff):
return my_eq(args[0], args[1])
if isinstance(fmla, ivy_logic.Implies):
return z3.Implies(args[0], args[1])
if isinstance(fmla, ivy_logic.Ite):
return z3.If(args[0], args[1], args[2])
if ivy_logic.is_quantifier(fmla):
variables = ivy_logic.quantifier_vars(fmla)
q = z3.forall if ivy_logic.is_forall(fmla) else z3.Exists
res = q([term_to_z3(v) for v in variables], args[0])
# print "res = {}".format(res)
return res
if ivy_logic.is_individual(fmla):
return term_to_z3(fmla)
print "bad fmla: {!r}".format(fmla)
assert False
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 qe(self,expr,sort_constants):
if il.is_quantifier(expr):
old = self.syms.get(expr,None)
if old is not None:
return old
res = self.fresh(expr)
consts = [sort_constants[x.sort] for x in expr.variables]
values = itertools.product(*consts)
maps = [dict(zip(expr.variables,v)) for v in values]
insts = [normalize(il.substitute(expr.body,m)) for m in maps]
# for i in insts:
# print ' {}'.format(i)
for inst in insts:
c = il.Implies(res,inst) if il.is_forall(expr) else il.Implies(inst,res)
self.fmlas.append(c)
return res
return clone_normal(expr,[self.qe(e,sort_constants) for e in expr.args])
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
