def predicates(expr):
"""Return a list of Z3 predicate names satisfied by expr.
If expr is an application, the list will include the Z3_OP_* that
expr is an application of.
This is for debugging purposes. Real code should use the
appropriate predicate functions directly.
"""
res = set()
for pred_name in dir(z3):
if not pred_name.startswith("is_"):
continue
if pred_name == "is_app_of":
continue
pred = getattr(z3, pred_name)
if pred(expr):
res.add(pred_name)
if z3.is_app(expr):
for op_name in dir(z3):
if not op_name.startswith("Z3_OP_"):
continue
if z3.is_app_of(expr, getattr(z3, op_name)):
res.add(op_name)
return res
def f(_cache, e, seen):
def f_cache(e):
return _cache(f, e, seen)
if z3.is_app_of(e, z3.Z3_OP_UMINUS):
return f_cache((-1) * (e.arg(0)))
elif z3.is_sub(e):
return f_cache(e.arg(0) + (-1) * e.arg(1))
elif z3.is_app(e) and e.num_args() == 2:
c1 = f_cache(e.arg(0))
c2 = f_cache(e.arg(1))
if z3.is_add(e):
return c1 + c2
elif z3.is_mul(e):
if z3.is_add(c1):
c11 = c1.arg(0)
c12 = c1.arg(1)
return f_cache(c11 * c2 + c12 * c2)
elif z3.is_add(c2):
c21 = c2.arg(0)
c22 = c2.arg(1)
return f_cache(c1 * c21 + c1 * c22)
else:
return c1 * c2
else:
return e
else:
return e
def is_atom(a):
"""
Check if the input formula is an atom. In FOL, atoms are
defined as atom := t1 = t2 | R(t1,..,tn) where ti are terms.
In addition, this function also allows Bool variable to
be terms (in propositional logic, a bool variable is considered term)
Example:
>>> from z3 import *
>>> is_atom(3)
False
>>> is_atom(Bool('b'))
True
>>> is_atom(Int('x'))
False
>>> is_atom(TRUE)
False
>>> is_atom(FALSE)
False
>>> is_atom(Int('x') + Int('y') > 3)
True
>>> is_atom(Bool('x') == TRUE)
True
>>> is_atom(Int('x') == 3)
True
>>> is_atom(IntVal(3))
False
>>> is_atom(Not(TRUE))
False
>>> is_atom(Or(TRUE,FALSE))
False
>>> is_atom(Or(Bool('b'),Bool('y')))
False
"""
if not is_bool(a):
return False
if is_expr_val(a):
return False
if is_expr_var(a):
return True
return is_app(a) and a.decl().kind() not in CONNECTIVE_OPS and\
all(is_term(c) for c in a.children())
def partial_leaf_substitution(expr, substitution_dict):
"""Replaces consts/vars in `expr` according to `substitution_dict`.
If a const/var is not in `substitution_dict.keys()`, it remains
unchanged.
>>> a, b, c = sl.list.locs("a b c")
>>> subst = {b : c}
>>> partial_leaf_substitution(sl.sepcon(sl.list("a"), sl.list("b")), subst)
sl.sepcon(sl.list(a), sl.list(c))
>>> i, j = Ints("i j")
>>> subst = {sl.alpha : i, sl.beta : j}
>>> partial_leaf_substitution(sl.alpha < sl.beta, subst)
i < j
"""
if z3.is_const(expr) or z3.is_var(expr):
return substitution_dict.get(expr, expr)
elif z3.is_app(expr):
new_args = [
partial_leaf_substitution(child, substitution_dict)
for child in expr.children()
]
return replace_args(expr, new_args)
else:
assert (z3.is_quantifier(expr))
new_arg = partial_leaf_substitution(expr.body(), substitution_dict)
return replace_args(expr, new_arg)
def infix_args_core(self, a, d, xs, r):
sz = len(r)
k = a.decl().kind()
p = self.get_precedence(k)
first = True
for child in a.children():
child_pp = self.pp_expr(child, d + 1, xs)
child_k = None
if z3.is_app(child):
child_k = child.decl().kind()
if k == child_k and (self.is_assoc(k) or (first and self.is_left_assoc(k))):
self.infix_args_core(child, d, xs, r)
sz = len(r)
if sz > self.max_args:
return
elif self.is_infix_unary(child_k):
child_p = self.get_precedence(child_k)
if p > child_p or (_is_add(k) and _is_sub(child_k)) or (_is_sub(k) and first and _is_add(child_k)):
r.append(child_pp)
else:
r.append(self.add_paren(child_pp))
sz = sz + 1
elif z3.is_quantifier(child):
r.append(self.add_paren(child_pp))
else:
r.append(child_pp)
sz = sz + 1
if sz > self.max_args:
r.append(self.pp_ellipses())
return
first = False
def infix_args_core(self, a, d, xs, r):
sz = len(r)
k = a.decl().kind()
p = self.get_precedence(k)
first = True
for child in a.children():
child_pp = self.pp_expr(child, d+1, xs)
child_k = None
if z3.is_app(child):
child_k = child.decl().kind()
if k == child_k and (self.is_assoc(k) or (first and self.is_left_assoc(k))):
self.infix_args_core(child, d, xs, r)
sz = len(r)
if sz > self.max_args:
return
elif self.is_infix_unary(child_k):
child_p = self.get_precedence(child_k)
if p > child_p or (_is_add(k) and _is_sub(child_k)) or (_is_sub(k) and first and _is_add(child_k)):
r.append(child_pp)
else:
r.append(self.add_paren(child_pp))
sz = sz + 1
elif z3.is_quantifier(child):
r.append(self.add_paren(child_pp))
else:
r.append(child_pp)
sz = sz + 1
if sz > self.max_args:
r.append(self.pp_ellipses())
return
first = False
def fixedpoint(M, bad):
fp = z3.Fixedpoint()
options = {'engine':'spacer'}
fp.set(**options)
xs = M.variables()
xsp = M.variables('prime')
sorts = M.sorts() + [z3.BoolSort()]
inv = z3.Function('inv', *sorts)
err = z3.Function('err', z3.BoolSort())
fp.register_relation(inv)
fp.register_relation(err)
for zi in xs + xsp:
fp.declare_var(zi)
inv_xs = inv(*xs)
inv_xsp = inv(*xsp)
fp.rule(inv_xs, M.init(xs))
fp.rule(inv_xsp, M.tr(xs, xsp) + [inv_xs])
fp.rule(err(), bad(xs) + [inv_xs])
if fp.query(err) == z3.unsat:
inv = fp.get_answer()
assert inv.is_forall()
body = inv.body()
assert z3.is_eq(body)
fapp = body.arg(0)
assert (z3.is_app(fapp))
args = [fapp.arg(i) for i in range(body.num_args())]
assert len(args) == len(xs)
expr = (body.arg(1))
return (z3.unsat, args, expr)
else:
return (z3.sat, None, None)
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 visitor_app(e):
if z3.is_app(e) and e.decl().kind() == z3.Z3_OP_UNINTERPRETED:
if e.num_args() > 0:
yield e
for ch in e.children():
for e0 in visitor_app(ch):
yield e0
def elim_bool_ite(exp):
if z3.is_quantifier(exp):
(qvars, matrix) = strip_qblock(exp)
matrix = elim_bool_ite(matrix)
if exp.is_forall():
e = z3.ForAll(qvars, matrix)
else:
e = z3.Exists(qvars, matrix)
return e
if not z3.is_bool(exp): return exp
if z3.is_true(exp) or z3.is_false(exp): return exp
assert z3.is_app(exp)
decl = exp.decl()
args = map(elim_bool_ite, exp.children())
# need to worry about And and Or because they can take >2 args and
# decl(*args) doesn't seem to work with the py interface
if z3.is_and(exp):
return z3.And(*args)
elif z3.is_or(exp):
return z3.Or(*args)
elif is_ite(exp):
impl1 = z3.Implies(args[0], args[1])
impl2 = z3.Implies(z3.Not(args[0]), args[2])
return z3.And(impl1, impl2)
else:
return decl(*args)
def _update(self):
if not self.has_formula():
return
rels = list()
find_all_uninterp_consts(self._formula, rels)
self._rels = frozenset(rels)
body = self._formula
if z3.is_quantifier(body):
body, self._bound_constants = ground_quantifier(body)
if z3.is_implies(body):
self._head = body.arg(1)
body = body.arg(0)
if z3.is_and(body):
body = body.children()
else:
body = [body]
else:
self._head = body
body = []
if len(body) > 0:
self._body = body
for i in range(len(body)):
f = body[i]
if z3.is_app(f) and f.decl() in self._rels:
self._uninterp_sz += 1
else:
break
assert (self._head is not None)
def pp_power_arg(self, arg, d, xs):
r = self.pp_expr(arg, d + 1, xs)
k = None
if z3.is_app(arg):
k = arg.decl().kind()
if self.is_infix_unary(k) or (z3.is_rational_value(arg) and arg.denominator_as_long() != 1):
return self.add_paren(r)
else:
return r
def pp_power_arg(self, arg, d, xs):
r = self.pp_expr(arg, d+1, xs)
k = None
if z3.is_app(arg):
k = arg.decl().kind()
if self.is_infix_unary(k) or (z3.is_rational_value(arg) and arg.denominator_as_long() != 1):
return self.add_paren(r)
else:
return r
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 unique_eq_terms_on_const(const, exp, eq_terms=None, done_exp=None):
def insert(e):
found = False
for t in eq_terms:
if z3.eq(t, e):
found = True
break
if not found:
eq_terms.append(e)
return True
return False
def process_eq(e1, e2):
if z3.eq(e1, const):
ret_val = z3.simplify(e2)
else:
assert z3.is_app(e1)
if not (z3.is_app_of(e1, z3.Z3_OP_ADD)
or z3.is_app_of(e1, z3.Z3_OP_SUB)):
return None
is_add = z3.is_app_of(e1, z3.Z3_OP_ADD)
arg0 = e1.arg(0)
arg1 = e1.arg(1)
if z3.eq(arg1, const):
if is_add: ret_val = z3.simplify(e2 - arg0)
else: ret_val = z3.simplify(arg0 - e2)
else:
if is_add: ret_val = process_eq(arg0, e2 - arg1)
else: ret_val = process_eq(arg0, e2 + arg1)
return ret_val
if eq_terms is None: eq_terms = []
if done_exp is None: done_exp = []
for e in done_exp:
if e.eq(exp): return # sub-dag is already processed
if z3.is_eq(exp):
arg0 = exp.arg(0)
arg1 = exp.arg(1)
if has_const(arg1, const):
arg0, arg1 = arg1, arg0 # swap
if has_const(arg0, const):
t = process_eq(arg0, arg1)
if t is not None:
if insert(t): yield (t, exp)
else: yield (None, exp)
elif z3.is_app(exp):
for i in range(exp.num_args()):
for (t, eq) in unique_eq_terms_on_const(const, exp.arg(i),
eq_terms, done_exp):
yield (t, eq)
done_exp.append(exp)
def pp_expr(self, a, d, xs):
self.visited = self.visited + 1
if d > self.max_depth or self.visited > self.max_visited:
return self.pp_ellipses()
if z3.is_app(a):
return self.pp_app(a, d, xs)
elif z3.is_quantifier(a):
return self.pp_quantifier(a, d, xs)
elif z3.is_var(a):
return self.pp_var(a, d, xs)
else:
return to_format(self.pp_unknown())
def pp_expr(self, a, d, xs):
self.visited = self.visited + 1
if d > self.max_depth or self.visited > self.max_visited:
return self.pp_ellipses()
if z3.is_app(a):
return self.pp_app(a, d, xs)
elif z3.is_quantifier(a):
return self.pp_quantifier(a, d, xs)
elif z3.is_var(a):
return self.pp_var(a, d, xs)
else:
return to_format(self.pp_unknown())
def f(_cache, e, seen):
def f_cache(e):
return _cache(f, e, seen)
r = []
if z3.is_app(e):
if e.decl().kind() in Z3_LOGICAL_OPS + Z3_REL_OPS:
for c in e.children():
r = r + f_cache(c)
elif z3.is_arith(e):
e = cls._distribute_mul_over_add(e)
r = r + cls._get_add_terms(e)
return r
def visitor(e, seen):
if e in seen:
return
seen[e] = True
yield e
if is_app(e):
for ch in e.children():
for e in visitor(ch, seen):
yield e
return
if is_quantifier(e):
for e in visitor(e.body(), seen):
yield e
return
def existVars(self, v1, v2):
"""
create a list of variables to be bound
"""
v1_str = [str(v) for v in v1]
v2_filtered = list()
for v in v2:
if z3.is_not(v):
v2_filtered.append(v.children()[0])
elif z3.is_app(v) and not z3.is_not(v):
v2_filtered.append(v)
for v in v2_filtered:
if str(v) not in v1_str: v1.append(v)
return v1
def fp_add_cover(fp, pred, lemma, level=-1):
# no trivial lemmas
if z3.is_true(lemma): return
assert (z3.is_app(pred))
sub = []
for i in range(0, pred.num_args()):
arg = pred.arg(i)
sub.append((arg, z3.Var(i, arg.decl().range())))
tlemma = z3.substitute(lemma, sub)
if verbose:
print "Lemma for ", pred.decl(), ": ", tlemma
fp.add_cover(level, pred.decl(), tlemma)
def variables_in_expression(expression):
expressions = [expression]
variables = []
while len(expressions) > 0:
expression = expressions.pop(0)
if z3.is_const(expression):
if not z3.is_bool_or_int_value(expression):
variables.append(expression)
elif z3.is_app(expression):
if expression.decl().kind() == z3.Z3_OP_UNINTERPRETED:
variables.append(expression.decl())
for i in range(expression.num_args()):
expressions.append(expression.arg(i))
return variables
def existVars(self, v1, v2):
"""
create a list of variables to be bound
"""
v1_str = [str(v) for v in v1]
v2_filtered = list()
for v in v2:
if z3.is_not(v):
v2_filtered.append(v.children()[0])
elif z3.is_app(v) and not z3.is_not(v):
v2_filtered.append(v)
for v in v2_filtered:
if str(v) not in v1_str : v1.append(v)
return v1
def fp_add_cover (fp, pred, lemma, level=-1):
# no trivial lemmas
if z3.is_true (lemma): return
assert (z3.is_app (pred))
sub = []
for i in range (0, pred.num_args ()):
arg = pred.arg (i)
sub.append ((arg,
z3.Var (i, arg.decl ().range ())))
tlemma = z3.substitute (lemma, sub)
if verbose:
print "Lemma for ", pred.decl (), ": ", tlemma
fp.add_cover (level, pred.decl (), tlemma)
def is_function_symbol(s: z3.ExprRef) -> bool:
if not z3.is_app(s):
return False
if z3.is_const(s):
return False
func = s.decl()
if func.range() == z3.BoolSort():
# predicate symbol
return False
if func.name().lower() == 'if':
return False
return True
def getLength1(M, bad):
fp = z3.Fixedpoint()
options = {'engine':'spacer'}
fp.set(**options)
Mp = TransitionSystem('prime')
# addCounter(M)
# addCounter(Mp)
xs = M.variables
xsp = Mp.variables
trx = [xsp[i]==M.tr[i] for i in range(len(xs))]
sorts = M.sorts + [z3.BoolSort()]
inv = z3.Function('inv', *sorts)
err = z3.Function('err', z3.BoolSort())
fp.register_relation(inv)
fp.register_relation(err)
for x in xs + xsp:
fp.declare_var(x)
inv_xs = inv(*xs)
inv_xsp = inv(*xsp)
fp.rule(inv_xs, M.init)
fp.rule(inv_xsp, trx + [inv_xs])
fp.rule(err(), bad(xs) + [inv_xs])
r = fp.query(err) == z3.unsat
if r:
inv = fp.get_answer()
print("INV:")
print(inv)
assert inv.is_forall()
body = inv.body()
# assert z3.is_eq(body)
print("BODY:", body)
fapp = body.arg(0)
print("FAPP: ", fapp)
assert (z3.is_app(fapp))
args = [fapp.arg(i) for i in range(body.num_args())]
assert len(args) == len(xs)
expr = (body.arg(1))
print(z3.unsat, args, expr)
return (z3.unsat, args, expr)
else:
return (z3.sat, len(fp.get_answer().children()), None) # Are you sure this is the correct length?
def bv_length(e):
li = [-1]
if e in seen:
return -1
if (z3.is_bv(e) and
z3.is_const(e) and
e.decl().kind() == z3.Z3_OP_UNINTERPRETED):
li.append(e.size())
seen.add(e)
if z3.is_app(e):
for ch in e.children():
li.append(bv_length(ch))
elif z3.is_quantifier(e):
for ch in e.body().children():
li.append(bv_length(ch))
return max(li)
def pp_unary(self, a, d, xs):
k = a.decl().kind()
p = self.get_precedence(k)
child = a.children()[0]
child_k = None
if z3.is_app(child):
child_k = child.decl().kind()
child_pp = self.pp_expr(child, d + 1, xs)
if k != child_k and self.is_infix_unary(child_k):
child_p = self.get_precedence(child_k)
if p <= child_p:
child_pp = self.add_paren(child_pp)
if z3.is_quantifier(child):
child_pp = self.add_paren(child_pp)
name = self.pp_name(a)
return compose(to_format(name), indent(_len(name), child_pp))
def pp_unary(self, a, d, xs):
k = a.decl().kind()
p = self.get_precedence(k)
child = a.children()[0]
child_k = None
if z3.is_app(child):
child_k = child.decl().kind()
child_pp = self.pp_expr(child, d+1, xs)
if k != child_k and self.is_infix_unary(child_k):
child_p = self.get_precedence(child_k)
if p <= child_p:
child_pp = self.add_paren(child_pp)
if z3.is_quantifier(child):
child_pp = self.add_paren(child_pp)
name = self.pp_name(a)
return compose(to_format(name), indent(_len(name), child_pp))
def unique_selects(exp, sel_keys=None):
def insert_and_yield(e):
k = exp_key(e)
if k not in sel_keys:
sel_keys.append(k)
yield e
if sel_keys is None: sel_keys = []
# post-order
if z3.is_app(exp):
for i in range(exp.num_args()): # args are the array and the idx
for sel in unique_selects(exp.arg(i), sel_keys):
yield sel
if z3.is_select(exp):
for sel in insert_and_yield(exp):
yield sel
def tagged_conditional_rewrite(s, rewriting_dict, leaf_fn, default_fn):
"""
Apply given rewriter to subexpressions of s bottom up
"""
todo = []
todo.append(s)
cache = {}
while todo:
n = todo[len(todo) - 1]
#print("Rewriting {}".format(n))
#print("Current cache: {}".format(cache))
if z3.is_var(n):
# No rewriting for variables
todo.pop()
# TODO: This is one difference => Could be added as leaf_fn to standard rewrite as well
cache[n] = leaf_fn(n)
elif z3.is_app(n):
# Add non-rewritten children to rewriting stack
processed_all_children = True
for arg in n.children():
if arg not in cache:
todo.append(arg)
processed_all_children = False
# All children haven been rewritten, so now rewrite n itself
if processed_all_children:
todo.pop()
new_args = [cache[arg] for arg in n.children()]
enabled_rewriter = rewriting_dict.get(n.decl())
if enabled_rewriter is not None:
cache[n] = enabled_rewriter(n, new_args)
else:
#cache[n] = replace_args(n, new_args)
cache[n] = default_fn(n, new_args)
else:
assert (z3.is_quantifier(n))
b = n.body()
if b in cache:
# The argument of the quantifier has already been rewritten
# Substitute this rewritten term
todo.pop()
# TODO: Another difference (but actually not even relevant in our setting). This could also be encapsulated in a function argument which could default to replace_args in the non-tagged setting
rewritten_arg, tag = cache[b]
cache[n] = (replace_args(n, [rewritten_arg]), tags)
else:
todo.append(b)
return cache[s]
def find_all_uninterp_consts(formula, res):
if z3.is_quantifier(formula):
formula = formula.body()
worklist = []
if z3.is_implies(formula):
worklist.append(formula.arg(1))
arg0 = formula.arg(0)
if z3.is_and(arg0):
worklist.extend(arg0.children())
else:
worklist.append(arg0)
else:
worklist.append(formula)
for t in worklist:
if z3.is_app(t) and t.decl().kind() == z3.Z3_OP_UNINTERPRETED:
res.append(t.decl())
def process_eq(e1, e2):
if z3.eq(e1, const):
ret_val = z3.simplify(e2)
else:
assert z3.is_app(e1)
if not (z3.is_app_of(e1, z3.Z3_OP_ADD)
or z3.is_app_of(e1, z3.Z3_OP_SUB)):
return None
is_add = z3.is_app_of(e1, z3.Z3_OP_ADD)
arg0 = e1.arg(0)
arg1 = e1.arg(1)
if z3.eq(arg1, const):
if is_add: ret_val = z3.simplify(e2 - arg0)
else: ret_val = z3.simplify(arg0 - e2)
else:
if is_add: ret_val = process_eq(arg0, e2 - arg1)
else: ret_val = process_eq(arg0, e2 + arg1)
return ret_val
def __init__ (self, vs):
if z3.is_app (vs):
vs = [vs]
self._saved_vs = vs
self._num_vars = len (vs)
num_vars = self._num_vars
self._vs = (z3.Ast * num_vars) ()
for i in range (num_vars):
self._vs [i] = vs[i].as_ast ()
self._pats = (z3.Pattern * 0) ()
self._num_pats = 0
self._num_no_pats = 0
self._no_pats = (z3.Ast * 0) ()
def __init__ (self, vs):
if z3.is_app (vs):
vs = [vs]
self._saved_vs = vs
self._num_vars = len (vs)
num_vars = self._num_vars
self._vs = (z3.Ast * num_vars) ()
for i in range (num_vars):
self._vs [i] = vs[i].as_ast ()
self._pats = (z3.Pattern * 0) ()
self._num_pats = 0
self._num_no_pats = 0
self._no_pats = (z3.Ast * 0) ()
def visit(self, e):
assert z3.is_ast(e)
if not z3.is_app(e):
raise Z3ExprDispatcherException('expr was not an application')
# Call the appropriate function application handler
app_kind = e.decl().kind()
if app_kind == z3.Z3_OP_UNINTERPRETED and e.num_args() == 0:
self.visit_variable(e)
return
try:
handler = self._z3_app_dispatcher_map[app_kind]
handler(e)
except KeyError as e:
msg = 'Handler for {} is missing from dispatch dictionary'.format(
app_kind)
raise NotImplementedError(msg)
def conditional_rewrite(s, rewriting_dict, default_fn=replace_args):
"""
Apply given rewriter to subexpressions of s bottom up
"""
todo = []
todo.append(s)
cache = {}
while todo:
n = todo[len(todo) - 1]
#print(n)
if z3.is_var(n):
# No rewriting for variables
todo.pop()
cache[n] = default_leaf_fn(n)
elif z3.is_app(n):
# Add non-rewritten children to rewriting stack
processed_all_children = True
for arg in n.children():
if arg not in cache:
todo.append(arg)
processed_all_children = False
# All children haven been rewritten, so now rewrite n itself
if processed_all_children:
todo.pop()
new_args = [cache[arg] for arg in n.children()]
enabled_rewriter = rewriting_dict.get(n.decl())
if enabled_rewriter is not None:
#print("Match for {}".format(n.decl()))
cache[n] = enabled_rewriter(n, new_args)
else:
#cache[n] = replace_args(n, new_args)
cache[n] = default_fn(n, new_args)
else:
assert (z3.is_quantifier(n))
b = n.body()
if b in cache:
# The argument of the quantifier has already been rewritten
# Substitute this rewritten term
todo.pop()
cache[n] = replace_args(n, [cache[b]])
else:
todo.append(b)
return cache[s]
def checkLength1(M, bad, count):
fp = z3.Fixedpoint()
options = {'engine': 'spacer'}
fp.set(**options)
addCounter(M)
xs = M.variables
sorts = M.sorts + [z3.BoolSort()]
inv = z3.Function('inv', *sorts)
err = z3.Bool('err')
fp.register_relation(inv)
fp.register_relation(err.decl())
fp.declare_var(*xs)
bad_state = [z3.And(bad(xs) + [xs[-1] == count])]
fp.rule(inv(*xs), M.init)
fp.rule(inv(*M.tr), inv(*xs))
fp.rule(err, bad_state + [inv(*xs)])
r = fp.query(err)
if r == z3.unsat:
inv = fp.get_answer()
print("INV:")
print(inv)
assert inv.is_forall()
body = inv.body()
assert z3.is_eq(body)
print("BODY:", body)
fapp = body.arg(0)
assert (z3.is_app(fapp))
args = [fapp.arg(i) for i in range(body.num_args())]
assert len(args) == len(xs)
expr = (body.arg(1))
print(z3.unsat, args, expr)
return (z3.unsat, args, expr)
else:
return (z3.sat, len(inv.children()), None)
def find_atomic_terms (exp, terms = list (), seen = set ()):
""" Finds all declarations in an expression """
if (z3.is_quantifier (exp)):
return find_atomic_terms (exp.body (), terms, seen)
if not (z3.is_app (exp)) : return terms
if z3AstRefKey (exp) in seen: return terms
seen.add (z3AstRefKey (exp))
decl = exp.decl ()
# atomic term
if decl.kind () == z3.Z3_OP_UNINTERPRETED:
if z3AstRefKey (decl) not in seen:
seen.add (z3AstRefKey (decl))
terms.append (decl)
# uninterpreted can also have kids
for k in exp.children (): find_atomic_terms (k, terms, seen)
return terms
def z3ExpChildGenerator (exp) :
if z3.is_app (exp) :
for i in range (exp.num_args ()) :
yield exp.arg (i)
def getFirstConjunct (exp) : assert z3.is_app (exp) if z3.is_and (exp) : return exp.arg (0) else : return exp