def extract_equal(eq):
"""Transform equals in a triple: var index, value, mask"""
if isinstance(eq.children()[0], z3.BitVecNumRef):
rhs = eq.children()[0]
lhs = eq.children()[1]
else:
rhs = eq.children()[1]
lhs = eq.children()[0]
if z3.is_var(lhs):
return ResultItem(
var=z3.get_var_index(lhs),
value=rhs,
mask=None)
else:
kind = lhs.decl().kind()
if kind == z3.Z3_OP_EXTRACT:
[high, low] = lhs.params()
sort = lhs.children()[0].sort()
val = rhs.as_long() << low
mask = (1 << (high + 1)) - (1 << low)
return ResultItem(
var=z3.get_var_index(lhs.children()[0]),
value=z3.BitVecVal(val, sort),
mask=z3.BitVecVal(mask, sort))
else:
raise base.Z3NotWellFormed(
"Bad lhs for equal {}".format(eq))
def find_vars (ast):
"""Returns the set of all variables in a given expression"""
vars = list()
def add(expr):
if z3.is_var(expr):
vars.append(expr)
foreach_expr(add, ast)
return sorted(vars, lambda x, y: z3.get_var_index(x) - z3.get_var_index(y))
def extract_eq(expr):
kind = expr.decl().kind()
children = expr.children()
if kind == z3.Z3_OP_EQ:
lhs = children[0]
rhs = children[1]
if z3.is_var(lhs):
return z3.get_var_index(lhs), rhs
elif z3.is_var(rhs):
return z3.get_var_index(rhs), lhs
else:
return None
return None
def pp_var(self, a, d, xs):
idx = z3.get_var_index(a)
sz = len(xs)
if idx >= sz:
return seq1('Var', (to_format(idx),))
else:
return to_format(xs[sz - idx - 1])
def pp_var(self, a, d, xs):
idx = z3.get_var_index(a)
sz = len(xs)
if idx >= sz:
return seq1("Var", (to_format(idx),))
else:
return to_format(xs[sz - idx - 1])
def translate(self, expr, bound_variables=[]):
if z3.is_const(expr):
return self.mk_const(expr)
# raise Z3_Unexpected_Expression('Unrecognized constant')
elif z3.is_var(expr): # a de Bruijn indexed bound variable
bv_length = len(bound_variables)
return bound_variables[bv_length - z3.get_var_index(expr) - 1]
elif z3.is_app(expr):
args = [self.translate(expr.arg(i), bound_variables)
for i in range(expr.num_args())]
return self.mk_fun(expr.decl())(*args)
# else:
# raise Z3_Unexpected_Expression(expr)
elif z3.is_quantifier(expr):
num_vars = expr.num_vars()
# vars = [language.const_dict[expr.var_name(i)]
# for i in range(num_vars)]
vars = [const(expr.var_name(i), self.mk_sort(expr.var_sort(i))) \
for i in range(num_vars)]
new_bound_variables = bound_variables + vars
body = self.translate(expr.body(), new_bound_variables)
if expr.is_forall():
return forall(vars, body)
else:
return exists(vars, body)
elif z3.is_func_decl(expr):
return self.mk_fun(expr)
else:
print expr.kind
raise Z3_Unexpected_Expression(expr)
def translate(self, expr, bound_variables=[]):
if z3.is_const(expr):
return self.mk_const(expr)
# raise Z3_Unexpected_Expression('Unrecognized constant')
elif z3.is_var(expr): # a de Bruijn indexed bound variable
bv_length = len(bound_variables)
return bound_variables[bv_length - z3.get_var_index(expr) - 1]
elif z3.is_app(expr):
args = [self.translate(expr.arg(i), bound_variables)
for i in range(expr.num_args())]
return self.mk_fun(expr.decl())(*args)
# else:
# raise Z3_Unexpected_Expression(expr)
elif z3.is_quantifier(expr):
num_vars = expr.num_vars()
# vars = [language.const_dict[expr.var_name(i)]
# for i in range(num_vars)]
vars = [const(expr.var_name(i), self.mk_sort(expr.var_sort(i))) \
for i in range(num_vars)]
new_bound_variables = bound_variables + vars
body = self.translate(expr.body(), new_bound_variables)
if expr.is_forall():
return forall(vars, body)
else:
return exists(vars, body)
elif z3.is_func_decl(expr):
return self.mk_fun(expr)
else:
print expr.kind
raise Z3_Unexpected_Expression(expr)
def pp_var(self, a, d, xs):
idx = z3.get_var_index(a)
sz = len(xs)
if idx >= sz:
# 957 is the greek letter nu
return to_format('ν<sub>%s</sub>' % idx, 1)
else:
return to_format(xs[sz - idx - 1])
def pp_var(self, a, d, xs):
idx = z3.get_var_index(a)
sz = len(xs)
if idx >= sz:
# 957 is the greek letter nu
return to_format("ν<sub>%s</sub>" % idx, 1)
else:
return to_format(xs[sz - idx - 1])
def convert(t, values):
if z3.is_int_value(t):
return t.as_long()
if z3.is_app(t):
func = globals()[t.decl().name()]
return func(
*[convert(t.arg(i), values) for i in range(t.num_args())])
elif z3.is_var(t):
return values[z3.get_var_index(t)]
def check_chc_head(expr):
if u_predicate(expr):
decl = expr.decl()
if decl is not None:
known_vars = Set([])
for kid in expr.children():
if not z3.is_var(kid):
raise Exception("illegal head: " +
"argument {} is not a variable {}".format(
expr.sexpr(), kid.sexpr()))
index = z3.get_var_index(kid)
if index in known_vars:
raise Exception("illegal head: non-distinct arguments, " +
"{} is used twice in {}".format(
kid.sexpr(), expr.sexpr()))
known_vars.add(z3.get_var_index(kid))
return False
elif expr == z3.BoolVal(False):
return True
else:
raise Exception("illegal head: {}".format(expr.sexpr()))
def rec_go(formula, var_list, reduction_type, q_type, bit_places, polarity):
"""Recursively go through the formula and apply approximations.
"""
# Constant
if z3.is_const(formula):
pass
# Variable
elif z3.is_var(formula):
order = - z3.get_var_index(formula) - 1
# Process if it is bit-vector variable
if type(formula) == z3.BitVecRef:
# Update max bit-vector width
global max_bit_width
if max_bit_width < formula.size():
max_bit_width = formula.size()
# Approximate if var is quantified in the right way
if var_list[order][1] == q_type:
formula = approximate(formula, reduction_type, bit_places)
# Quantified formula
elif type(formula) == z3.QuantifierRef:
formula = qform_process(formula,
list(var_list),
reduction_type,
q_type,
bit_places,
polarity)
# Complex formula
else:
formula = cform_process(formula,
list(var_list),
reduction_type,
q_type,
bit_places,
polarity)
return formula
def bound_var_sort (quant, var):
if z3.is_var (var):
var = z3.get_var_index ()
return quant.var_sort (quant.num_vars () - 1 - var)
def var_name(self,rule,i):
""" yields the name of a variable """
if z3.is_var(i): i = z3.get_var_index()
# (variables are numbered backwards within the predicates)
return rule.var_name(rule.num_vars()-1-i)
def bound_var_sort (quant, var):
if z3.is_var (var):
var = z3.get_var_index ()
return quant.var_sort (quant.num_vars () - 1 - var)
def var_name(self, rule, i):
""" yields the name of a variable """
if z3.is_var(i):
i = z3.get_var_index()
# (variables are numbered backwards within the predicates)
return rule.var_name(rule.num_vars() - 1 - i)