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initial pass at using derivatives in regex unfolding

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2020-05-23 11:52:53 -07:00
parent b7b8ed23fb
commit eb3f20832e
11 changed files with 694 additions and 228 deletions

View file

@ -410,78 +410,78 @@ void seq_rewriter::get_param_descrs(param_descrs & r) {
}
br_status seq_rewriter::mk_bool_app(func_decl* f, unsigned n, expr* const* args, expr_ref& result) {
switch (f->get_decl_kind()) {
case OP_AND:
return mk_bool_app_helper(true, n, args, result);
case OP_OR:
return mk_bool_app_helper(false, n, args, result);
default:
return BR_FAILED;
}
switch (f->get_decl_kind()) {
case OP_AND:
return mk_bool_app_helper(true, n, args, result);
case OP_OR:
return mk_bool_app_helper(false, n, args, result);
default:
return BR_FAILED;
}
}
br_status seq_rewriter::mk_bool_app_helper(bool is_and, unsigned n, expr* const* args, expr_ref& result) {
bool found = false;
expr* arg = nullptr;
for (unsigned i = 0; i < n && !found; ++i) {
found = m_util.str.is_in_re(args[i]) || (m().is_not(args[i], arg) && m_util.str.is_in_re(arg));
}
if (!found) return BR_FAILED;
obj_map<expr, expr*> in_re, not_in_re;
bool found_pair = false;
for (unsigned i = 0; i < n; ++i) {
expr* args_i = args[i];
expr* x = nullptr;
expr* y = nullptr;
expr* z = nullptr;
if (m_util.str.is_in_re(args_i, x, y)) {
if (in_re.find(x, z)) {
in_re[x] = is_and ? m_util.re.mk_inter(z, y) : m_util.re.mk_union(z, y);
found_pair = true;
}
else {
in_re.insert(x, y);
}
found_pair |= not_in_re.contains(x);
}
else if (m().is_not(args_i, arg) && m_util.str.is_in_re(arg, x, y)) {
bool found = false;
expr* arg = nullptr;
for (unsigned i = 0; i < n && !found; ++i) {
found = m_util.str.is_in_re(args[i]) || (m().is_not(args[i], arg) && m_util.str.is_in_re(arg));
}
if (!found) return BR_FAILED;
obj_map<expr, expr*> in_re, not_in_re;
bool found_pair = false;
for (unsigned i = 0; i < n; ++i) {
expr* args_i = args[i];
expr* x = nullptr;
expr* y = nullptr;
expr* z = nullptr;
if (m_util.str.is_in_re(args_i, x, y)) {
if (in_re.find(x, z)) {
in_re[x] = is_and ? re().mk_inter(z, y) : re().mk_union(z, y);
found_pair = true;
}
else {
in_re.insert(x, y);
}
found_pair |= not_in_re.contains(x);
}
else if (m().is_not(args_i, arg) && m_util.str.is_in_re(arg, x, y)) {
if (not_in_re.find(x, z)) {
not_in_re[x] = is_and ? m_util.re.mk_union(z, y) : m_util.re.mk_inter(z, y);
not_in_re[x] = is_and ? re().mk_union(z, y) : re().mk_inter(z, y);
found_pair = true;
}
else {
not_in_re.insert(x, y);
}
found_pair |= in_re.contains(x);
}
}
if (!found_pair) {
return BR_FAILED;
}
ptr_buffer<expr> new_args;
for (auto const & kv : in_re) {
expr* x = kv.m_key;
expr* y = kv.m_value;
expr* z = nullptr;
if (not_in_re.find(x, z)) {
expr* z_c = m_util.re.mk_complement(z);
expr* w = is_and ? m_util.re.mk_inter(y, z_c) : m_util.re.mk_union(y, z_c);
new_args.push_back(m_util.re.mk_in_re(x, w));
}
else {
new_args.push_back(m_util.re.mk_in_re(x, y));
}
}
found_pair |= in_re.contains(x);
}
}
if (!found_pair) {
return BR_FAILED;
}
ptr_buffer<expr> new_args;
for (auto const & kv : in_re) {
expr* x = kv.m_key;
expr* y = kv.m_value;
expr* z = nullptr;
if (not_in_re.find(x, z)) {
expr* z_c = re().mk_complement(z);
expr* w = is_and ? re().mk_inter(y, z_c) : re().mk_union(y, z_c);
new_args.push_back(re().mk_in_re(x, w));
}
else {
new_args.push_back(re().mk_in_re(x, y));
}
}
for (auto const& kv : not_in_re) {
expr* x = kv.m_key;
expr* y = kv.m_value;
if (!in_re.contains(x)) {
new_args.push_back(m_util.re.mk_in_re(x, m_util.re.mk_complement(y)));
new_args.push_back(re().mk_in_re(x, re().mk_complement(y)));
}
}
for (unsigned i = 0; i < n; ++i) {
@ -490,9 +490,9 @@ br_status seq_rewriter::mk_bool_app_helper(bool is_and, unsigned n, expr* const*
new_args.push_back(arg);
}
}
result = is_and ? m().mk_and(new_args.size(), new_args.c_ptr()) : m().mk_or(new_args.size(), new_args.c_ptr());
return BR_REWRITE_FULL;
return BR_REWRITE_FULL;
}
br_status seq_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * const * args, expr_ref & result) {
@ -2066,14 +2066,14 @@ bool seq_rewriter::get_head_tail(expr* s, expr_ref& head, expr_ref& tail) {
expr_ref seq_rewriter::kleene_and(expr* cond, expr* r) {
if (m().is_true(cond))
return expr_ref(r, m());
expr* re_empty = m_util.re.mk_empty(m().get_sort(r));
expr* re_empty = re().mk_empty(m().get_sort(r));
if (m().is_false(cond))
return expr_ref(re_empty, m());
return expr_ref(m().mk_ite(cond, r, re_empty), m());
}
expr_ref seq_rewriter::kleene_predicate(expr* cond, sort* seq_sort) {
expr_ref re_with_empty(m_util.re.mk_to_re(m_util.str.mk_empty(seq_sort)), m());
expr_ref re_with_empty(re().mk_to_re(m_util.str.mk_empty(seq_sort)), m());
return kleene_and(cond, re_with_empty);
}
@ -2082,39 +2082,39 @@ expr_ref seq_rewriter::is_nullable(expr* r) {
expr* r1 = nullptr, *r2 = nullptr;
unsigned lo = 0, hi = 0;
expr_ref result(m());
if (m_util.re.is_concat(r, r1, r2) ||
m_util.re.is_intersection(r, r1, r2)) {
if (re().is_concat(r, r1, r2) ||
re().is_intersection(r, r1, r2)) {
result = mk_and(m(), is_nullable(r1), is_nullable(r2));
}
else if (m_util.re.is_union(r, r1, r2)) {
else if (re().is_union(r, r1, r2)) {
result = mk_or(m(), is_nullable(r1), is_nullable(r2));
}
else if (m_util.re.is_diff(r, r1, r2)) {
else if (re().is_diff(r, r1, r2)) {
result = mk_not(m(), is_nullable(r2));
result = mk_and(m(), is_nullable(r1), result);
}
else if (m_util.re.is_star(r) ||
m_util.re.is_opt(r) ||
m_util.re.is_full_seq(r) ||
(m_util.re.is_loop(r, r1, lo) && lo == 0) ||
(m_util.re.is_loop(r, r1, lo, hi) && lo == 0)) {
else if (re().is_star(r) ||
re().is_opt(r) ||
re().is_full_seq(r) ||
(re().is_loop(r, r1, lo) && lo == 0) ||
(re().is_loop(r, r1, lo, hi) && lo == 0)) {
result = m().mk_true();
}
else if (m_util.re.is_full_char(r) ||
m_util.re.is_empty(r) ||
m_util.re.is_of_pred(r) ||
m_util.re.is_range(r)) {
else if (re().is_full_char(r) ||
re().is_empty(r) ||
re().is_of_pred(r) ||
re().is_range(r)) {
result = m().mk_false();
}
else if (m_util.re.is_plus(r, r1) ||
(m_util.re.is_loop(r, r1, lo) && lo > 0) ||
(m_util.re.is_loop(r, r1, lo, hi) && lo > 0)) {
else if (re().is_plus(r, r1) ||
(re().is_loop(r, r1, lo) && lo > 0) ||
(re().is_loop(r, r1, lo, hi) && lo > 0)) {
result = is_nullable(r1);
}
else if (m_util.re.is_complement(r, r1)) {
else if (re().is_complement(r, r1)) {
result = mk_not(m(), is_nullable(r1));
}
else if (m_util.re.is_to_re(r, r1)) {
else if (re().is_to_re(r, r1)) {
sort* seq_sort = nullptr;
VERIFY(m_util.is_re(r, seq_sort));
expr* emptystr = m_util.str.mk_empty(seq_sort);
@ -2123,7 +2123,7 @@ expr_ref seq_rewriter::is_nullable(expr* r) {
else {
sort* seq_sort = nullptr;
VERIFY(m_util.is_re(r, seq_sort));
result = m_util.re.mk_in_re(m_util.str.mk_empty(seq_sort), r);
result = re().mk_in_re(m_util.str.mk_empty(seq_sort), r);
}
return result;
}
@ -2141,14 +2141,14 @@ expr_ref seq_rewriter::derivative(expr* elem, expr* r) {
expr* r1 = nullptr, * r2 = nullptr, *p = nullptr;
expr_ref dr1(m()), dr2(m()), result(m());
unsigned lo = 0, hi = 0;
if (m_util.re.is_concat(r, r1, r2)) {
if (re().is_concat(r, r1, r2)) {
expr_ref is_n = is_nullable(r1);
dr1 = derivative(elem, r1);
if (!dr1) {
result = dr1; // failed
}
else if (m().is_false(is_n)) {
result = m_util.re.mk_concat(dr1, r2);
result = re().mk_concat(dr1, r2);
}
else {
dr2 = derivative(elem, r2);
@ -2156,67 +2156,67 @@ expr_ref seq_rewriter::derivative(expr* elem, expr* r) {
result = dr2; // failed
}
else if (m().is_true(is_n)) {
result = m_util.re.mk_union(
m_util.re.mk_concat(dr1, r2),
result = re().mk_union(
re().mk_concat(dr1, r2),
dr2
);
}
else {
result = m_util.re.mk_union(
m_util.re.mk_concat(dr1, r2),
result = re().mk_union(
re().mk_concat(dr1, r2),
kleene_and(is_n, dr2)
);
}
}
}
else if (m_util.re.is_star(r, r1)) {
else if (re().is_star(r, r1)) {
result = derivative(elem, r1);
if (result) {
result = m_util.re.mk_concat(result, r);
result = re().mk_concat(result, r);
}
}
else if (m_util.re.is_plus(r, r1)) {
result = m_util.re.mk_star(r1);
else if (re().is_plus(r, r1)) {
result = re().mk_star(r1);
result = derivative(elem, result);
}
else if (m_util.re.is_union(r, r1, r2)) {
else if (re().is_union(r, r1, r2)) {
dr1 = derivative(elem, r1);
dr2 = derivative(elem, r2);
if (dr1 && dr2) {
result = m_util.re.mk_union(dr1, dr2);
result = re().mk_union(dr1, dr2);
}
}
else if (m_util.re.is_intersection(r, r1, r2)) {
else if (re().is_intersection(r, r1, r2)) {
dr1 = derivative(elem, r1);
dr2 = derivative(elem, r2);
if (dr1 && dr2) {
result = m_util.re.mk_inter(dr1, dr2);
result = re().mk_inter(dr1, dr2);
}
}
else if (m_util.re.is_opt(r, r1)) {
else if (re().is_opt(r, r1)) {
result = derivative(elem, r1);
}
else if (m_util.re.is_complement(r, r1)) {
else if (re().is_complement(r, r1)) {
result = derivative(elem, r1);
if (result) {
result = m_util.re.mk_complement(result);
result = re().mk_complement(result);
}
}
else if (m_util.re.is_loop(r, r1, lo)) {
else if (re().is_loop(r, r1, lo)) {
result = derivative(elem, r1);
if (result) {
if (lo > 0) {
lo--;
}
result = m_util.re.mk_concat(
result = re().mk_concat(
result,
m_util.re.mk_loop(r1, lo)
re().mk_loop(r1, lo)
);
}
}
else if (m_util.re.is_loop(r, r1, lo, hi)) {
else if (re().is_loop(r, r1, lo, hi)) {
if (hi == 0) {
result = m_util.re.mk_empty(m().get_sort(r));
result = re().mk_empty(m().get_sort(r));
}
else {
result = derivative(elem, r1);
@ -2225,18 +2225,18 @@ expr_ref seq_rewriter::derivative(expr* elem, expr* r) {
if (lo > 0) {
lo--;
}
result = m_util.re.mk_concat(
result = re().mk_concat(
result,
m_util.re.mk_loop(r1, lo, hi)
re().mk_loop(r1, lo, hi)
);
}
}
}
else if (m_util.re.is_full_seq(r) ||
m_util.re.is_empty(r)) {
else if (re().is_full_seq(r) ||
re().is_empty(r)) {
result = r;
}
else if (m_util.re.is_to_re(r, r1)) {
else if (re().is_to_re(r, r1)) {
// r1 is a string here (not a regexp)
expr_ref hd(m());
expr_ref tl(m());
@ -2244,14 +2244,14 @@ expr_ref seq_rewriter::derivative(expr* elem, expr* r) {
// head must be equal; if so, derivative is tail
result = kleene_and(
m().mk_eq(elem, hd),
m_util.re.mk_to_re(tl)
re().mk_to_re(tl)
);
}
else if (m_util.str.is_empty(r1)) {
result = m_util.re.mk_empty(m().get_sort(r));
result = re().mk_empty(m().get_sort(r));
}
}
else if (m_util.re.is_range(r, r1, r2)) {
else if (re().is_range(r, r1, r2)) {
// r1, r2 are sequences.
zstring s1, s2;
if (m_util.str.is_string(r1, s1) && m_util.str.is_string(r2, s2)) {
@ -2262,14 +2262,14 @@ expr_ref seq_rewriter::derivative(expr* elem, expr* r) {
result = kleene_predicate(result, seq_sort);
}
else {
result = m_util.re.mk_empty(m().get_sort(r));
result = re().mk_empty(m().get_sort(r));
}
}
}
else if (m_util.re.is_full_char(r)) {
result = m_util.re.mk_to_re(m_util.str.mk_empty(seq_sort));
else if (re().is_full_char(r)) {
result = re().mk_to_re(m_util.str.mk_empty(seq_sort));
}
else if (m_util.re.is_of_pred(r, p)) {
else if (re().is_of_pred(r, p)) {
array_util array(m());
expr* args[2] = { p, elem };
result = array.mk_select(2, args);
@ -2280,16 +2280,16 @@ expr_ref seq_rewriter::derivative(expr* elem, expr* r) {
br_status seq_rewriter::mk_str_in_regexp(expr* a, expr* b, expr_ref& result) {
if (m_util.re.is_empty(b)) {
if (re().is_empty(b)) {
result = m().mk_false();
return BR_DONE;
}
if (m_util.re.is_full_seq(b)) {
if (re().is_full_seq(b)) {
result = m().mk_true();
return BR_DONE;
}
expr* b1 = nullptr;
if (m_util.re.is_to_re(b, b1)) {
if (re().is_to_re(b, b1)) {
result = m().mk_eq(a, b1);
return BR_REWRITE1;
}
@ -2305,7 +2305,7 @@ br_status seq_rewriter::mk_str_in_regexp(expr* a, expr* b, expr_ref& result) {
if (get_head_tail(a, hd, tl)) {
expr_ref db = derivative(hd, b); // null if failed
if (db) {
result = m_util.re.mk_in_re(tl, db);
result = re().mk_in_re(tl, db);
return BR_REWRITE_FULL;
}
}
@ -2318,15 +2318,15 @@ br_status seq_rewriter::mk_str_to_regexp(expr* a, expr_ref& result) {
}
br_status seq_rewriter::mk_re_concat(expr* a, expr* b, expr_ref& result) {
if (m_util.re.is_full_seq(a) && m_util.re.is_full_seq(b)) {
if (re().is_full_seq(a) && re().is_full_seq(b)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_empty(a)) {
if (re().is_empty(a)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_empty(b)) {
if (re().is_empty(b)) {
result = b;
return BR_DONE;
}
@ -2339,47 +2339,47 @@ br_status seq_rewriter::mk_re_concat(expr* a, expr* b, expr_ref& result) {
return BR_DONE;
}
expr* a1 = nullptr, *b1 = nullptr;
if (m_util.re.is_to_re(a, a1) && m_util.re.is_to_re(b, b1)) {
result = m_util.re.mk_to_re(m_util.str.mk_concat(a1, b1));
if (re().is_to_re(a, a1) && re().is_to_re(b, b1)) {
result = re().mk_to_re(m_util.str.mk_concat(a1, b1));
return BR_REWRITE2;
}
if (m_util.re.is_star(a, a1) && m_util.re.is_star(b, b1) && a1 == b1) {
if (re().is_star(a, a1) && re().is_star(b, b1) && a1 == b1) {
result = a;
return BR_DONE;
}
if (m_util.re.is_star(a, a1) && a1 == b) {
result = m_util.re.mk_concat(b, a);
if (re().is_star(a, a1) && a1 == b) {
result = re().mk_concat(b, a);
return BR_DONE;
}
unsigned lo1, hi1, lo2, hi2;
if (m_util.re.is_loop(a, a1, lo1, hi1) && lo1 <= hi1 && m_util.re.is_loop(b, b1, lo2, hi2) && lo2 <= hi2 && a1 == b1) {
result = m_util.re.mk_loop(a1, lo1 + lo2, hi1 + hi2);
if (re().is_loop(a, a1, lo1, hi1) && lo1 <= hi1 && re().is_loop(b, b1, lo2, hi2) && lo2 <= hi2 && a1 == b1) {
result = re().mk_loop(a1, lo1 + lo2, hi1 + hi2);
return BR_DONE;
}
if (m_util.re.is_loop(a, a1, lo1) && m_util.re.is_loop(b, b1, lo2) && a1 == b1) {
result = m_util.re.mk_loop(a1, lo1 + lo2);
if (re().is_loop(a, a1, lo1) && re().is_loop(b, b1, lo2) && a1 == b1) {
result = re().mk_loop(a1, lo1 + lo2);
return BR_DONE;
}
for (unsigned i = 0; i < 2; ++i) {
// (loop a lo1) + (loop a lo2 hi2) = (loop a lo1 + lo2)
if (m_util.re.is_loop(a, a1, lo1) && m_util.re.is_loop(b, b1, lo2, hi2) && lo2 <= hi2 && a1 == b1) {
result = m_util.re.mk_loop(a1, lo1 + lo2);
if (re().is_loop(a, a1, lo1) && re().is_loop(b, b1, lo2, hi2) && lo2 <= hi2 && a1 == b1) {
result = re().mk_loop(a1, lo1 + lo2);
return BR_DONE;
}
// (loop a lo1 hi1) + a* = (loop a lo1)
if (m_util.re.is_loop(a, a1, lo1, hi1) && m_util.re.is_star(b, b1) && a1 == b1) {
result = m_util.re.mk_loop(a1, lo1);
if (re().is_loop(a, a1, lo1, hi1) && re().is_star(b, b1) && a1 == b1) {
result = re().mk_loop(a1, lo1);
return BR_DONE;
}
// (loop a lo1) + a* = (loop a lo1)
if (m_util.re.is_loop(a, a1, lo1) && m_util.re.is_star(b, b1) && a1 == b1) {
if (re().is_loop(a, a1, lo1) && re().is_star(b, b1) && a1 == b1) {
result = a;
return BR_DONE;
}
// (loop a lo1 hi1) + a = (loop a lo1+1 hi1+1)
if (m_util.re.is_loop(a, a1, lo1, hi1) && lo1 <= hi1 && a1 == b) {
result = m_util.re.mk_loop(a1, lo1+1, hi1+1);
if (re().is_loop(a, a1, lo1, hi1) && lo1 <= hi1 && a1 == b) {
result = re().mk_loop(a1, lo1+1, hi1+1);
return BR_DONE;
}
std::swap(a, b);
@ -2396,27 +2396,27 @@ br_status seq_rewriter::mk_re_union(expr* a, expr* b, expr_ref& result) {
result = a;
return BR_DONE;
}
if (m_util.re.is_empty(a)) {
if (re().is_empty(a)) {
result = b;
return BR_DONE;
}
if (m_util.re.is_empty(b)) {
if (re().is_empty(b)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_full_seq(a)) {
if (re().is_full_seq(a)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_full_seq(b)) {
if (re().is_full_seq(b)) {
result = b;
return BR_DONE;
}
if (m_util.re.is_star(a) && is_epsilon(b)) {
if (re().is_star(a) && is_epsilon(b)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_star(b) && is_epsilon(a)) {
if (re().is_star(b) && is_epsilon(a)) {
result = b;
return BR_DONE;
}
@ -2425,20 +2425,20 @@ br_status seq_rewriter::mk_re_union(expr* a, expr* b, expr_ref& result) {
br_status seq_rewriter::mk_re_complement(expr* a, expr_ref& result) {
expr* e1, *e2;
if (m_util.re.is_intersection(a, e1, e2)) {
result = m_util.re.mk_union(m_util.re.mk_complement(e1), m_util.re.mk_complement(e2));
if (re().is_intersection(a, e1, e2)) {
result = re().mk_union(re().mk_complement(e1), re().mk_complement(e2));
return BR_REWRITE2;
}
if (m_util.re.is_union(a, e1, e2)) {
result = m_util.re.mk_inter(m_util.re.mk_complement(e1), m_util.re.mk_complement(e2));
if (re().is_union(a, e1, e2)) {
result = re().mk_inter(re().mk_complement(e1), re().mk_complement(e2));
return BR_REWRITE2;
}
if (m_util.re.is_empty(a)) {
result = m_util.re.mk_full_seq(m().get_sort(a));
if (re().is_empty(a)) {
result = re().mk_full_seq(m().get_sort(a));
return BR_DONE;
}
if (m_util.re.is_full_seq(a)) {
result = m_util.re.mk_empty(m().get_sort(a));
if (re().is_full_seq(a)) {
result = re().mk_empty(m().get_sort(a));
return BR_DONE;
}
return BR_FAILED;
@ -2456,40 +2456,40 @@ br_status seq_rewriter::mk_re_inter(expr* a, expr* b, expr_ref& result) {
result = a;
return BR_DONE;
}
if (m_util.re.is_empty(a)) {
if (re().is_empty(a)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_empty(b)) {
if (re().is_empty(b)) {
result = b;
return BR_DONE;
}
if (m_util.re.is_full_seq(a)) {
if (re().is_full_seq(a)) {
result = b;
return BR_DONE;
}
if (m_util.re.is_full_seq(b)) {
if (re().is_full_seq(b)) {
result = a;
return BR_DONE;
}
expr* ac = nullptr, *bc = nullptr;
if ((m_util.re.is_complement(a, ac) && ac == b) ||
(m_util.re.is_complement(b, bc) && bc == a)) {
result = m_util.re.mk_empty(m().get_sort(a));
if ((re().is_complement(a, ac) && ac == b) ||
(re().is_complement(b, bc) && bc == a)) {
result = re().mk_empty(m().get_sort(a));
return BR_DONE;
}
if (m_util.re.is_to_re(b))
if (re().is_to_re(b))
std::swap(a, b);
expr* s = nullptr;
if (m_util.re.is_to_re(a, s)) {
result = m().mk_ite(m_util.re.mk_in_re(s, b), a, m_util.re.mk_empty(m().get_sort(a)));
if (re().is_to_re(a, s)) {
result = m().mk_ite(re().mk_in_re(s, b), a, re().mk_empty(m().get_sort(a)));
return BR_REWRITE2;
}
return BR_FAILED;
}
br_status seq_rewriter::mk_re_diff(expr* a, expr* b, expr_ref& result) {
result = m_util.re.mk_inter(a, m_util.re.mk_complement(b));
result = re().mk_inter(a, re().mk_complement(b));
return BR_REWRITE2;
}
@ -2505,21 +2505,21 @@ br_status seq_rewriter::mk_re_loop(func_decl* f, unsigned num_args, expr* const*
hi2 = np > 1 ? f->get_parameter(1).get_int() : lo2;
// (loop a 0 0) = ""
if (np == 2 && lo2 > hi2) {
result = m_util.re.mk_empty(m().get_sort(args[0]));
result = re().mk_empty(m().get_sort(args[0]));
return BR_DONE;
}
if (np == 2 && hi2 == 0) {
result = m_util.re.mk_to_re(m_util.str.mk_empty(m_util.re.to_seq(m().get_sort(args[0]))));
result = re().mk_to_re(m_util.str.mk_empty(re().to_seq(m().get_sort(args[0]))));
return BR_DONE;
}
// (loop (loop a lo) lo2) = (loop lo*lo2)
if (m_util.re.is_loop(args[0], a, lo) && np == 1) {
result = m_util.re.mk_loop(a, lo2 * lo);
if (re().is_loop(args[0], a, lo) && np == 1) {
result = re().mk_loop(a, lo2 * lo);
return BR_REWRITE1;
}
// (loop (loop a l l) h h) = (loop a l*h l*h)
if (m_util.re.is_loop(args[0], a, lo, hi) && np == 2 && lo == hi && lo2 == hi2) {
result = m_util.re.mk_loop(a, lo2 * lo, hi2 * hi);
if (re().is_loop(args[0], a, lo, hi) && np == 2 && lo == hi && lo2 == hi2) {
result = re().mk_loop(a, lo2 * lo, hi2 * hi);
return BR_REWRITE1;
}
// (loop a 1 1) = a
@ -2529,20 +2529,20 @@ br_status seq_rewriter::mk_re_loop(func_decl* f, unsigned num_args, expr* const*
}
// (loop a 0) = a*
if (np == 1 && lo2 == 0) {
result = m_util.re.mk_star(args[0]);
result = re().mk_star(args[0]);
return BR_DONE;
}
break;
case 2:
if (m_autil.is_numeral(args[1], n1) && n1.is_unsigned()) {
result = m_util.re.mk_loop(args[0], n1.get_unsigned());
result = re().mk_loop(args[0], n1.get_unsigned());
return BR_REWRITE1;
}
break;
case 3:
if (m_autil.is_numeral(args[1], n1) && n1.is_unsigned() &&
m_autil.is_numeral(args[2], n2) && n2.is_unsigned()) {
result = m_util.re.mk_loop(args[0], n1.get_unsigned(), n2.get_unsigned());
result = re().mk_loop(args[0], n1.get_unsigned(), n2.get_unsigned());
return BR_REWRITE1;
}
break;
@ -2554,7 +2554,7 @@ br_status seq_rewriter::mk_re_loop(func_decl* f, unsigned num_args, expr* const*
br_status seq_rewriter::mk_re_power(func_decl* f, expr* a, expr_ref& result) {
unsigned p = f->get_parameter(0).get_int();
result = m_util.re.mk_loop(a, p, p);
result = re().mk_loop(a, p, p);
return BR_REWRITE1;
}
@ -2570,45 +2570,45 @@ br_status seq_rewriter::mk_re_power(func_decl* f, expr* a, expr_ref& result) {
*/
br_status seq_rewriter::mk_re_star(expr* a, expr_ref& result) {
expr* b, *c, *b1, *c1;
if (m_util.re.is_star(a) || m_util.re.is_full_seq(a)) {
if (re().is_star(a) || re().is_full_seq(a)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_full_char(a)) {
result = m_util.re.mk_full_seq(m().get_sort(a));
if (re().is_full_char(a)) {
result = re().mk_full_seq(m().get_sort(a));
return BR_DONE;
}
if (m_util.re.is_empty(a)) {
if (re().is_empty(a)) {
sort* seq_sort = nullptr;
VERIFY(m_util.is_re(a, seq_sort));
result = m_util.re.mk_to_re(m_util.str.mk_empty(seq_sort));
result = re().mk_to_re(m_util.str.mk_empty(seq_sort));
return BR_DONE;
}
if (m_util.re.is_plus(a, b)) {
result = m_util.re.mk_star(b);
if (re().is_plus(a, b)) {
result = re().mk_star(b);
return BR_DONE;
}
if (m_util.re.is_union(a, b, c)) {
if (m_util.re.is_star(b, b1)) {
result = m_util.re.mk_star(m_util.re.mk_union(b1, c));
if (re().is_union(a, b, c)) {
if (re().is_star(b, b1)) {
result = re().mk_star(re().mk_union(b1, c));
return BR_REWRITE2;
}
if (m_util.re.is_star(c, c1)) {
result = m_util.re.mk_star(m_util.re.mk_union(b, c1));
if (re().is_star(c, c1)) {
result = re().mk_star(re().mk_union(b, c1));
return BR_REWRITE2;
}
if (is_epsilon(b)) {
result = m_util.re.mk_star(c);
result = re().mk_star(c);
return BR_REWRITE2;
}
if (is_epsilon(c)) {
result = m_util.re.mk_star(b);
result = re().mk_star(b);
return BR_REWRITE2;
}
}
if (m_util.re.is_concat(a, b, c) &&
m_util.re.is_star(b, b1) && m_util.re.is_star(c, c1)) {
result = m_util.re.mk_star(m_util.re.mk_union(b1, c1));
if (re().is_concat(a, b, c) &&
re().is_star(b, b1) && re().is_star(c, c1)) {
result = re().mk_star(re().mk_union(b1, c1));
return BR_REWRITE2;
}
@ -2630,11 +2630,11 @@ br_status seq_rewriter::mk_re_range(expr* lo, expr* hi, expr_ref& result) {
a+ = aa*
*/
br_status seq_rewriter::mk_re_plus(expr* a, expr_ref& result) {
if (m_util.re.is_empty(a)) {
if (re().is_empty(a)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_full_seq(a)) {
if (re().is_full_seq(a)) {
result = a;
return BR_DONE;
}
@ -2642,80 +2642,175 @@ br_status seq_rewriter::mk_re_plus(expr* a, expr_ref& result) {
result = a;
return BR_DONE;
}
if (m_util.re.is_plus(a)) {
if (re().is_plus(a)) {
result = a;
return BR_DONE;
}
if (m_util.re.is_star(a)) {
if (re().is_star(a)) {
result = a;
return BR_DONE;
}
result = m_util.re.mk_concat(a, m_util.re.mk_star(a));
result = re().mk_concat(a, re().mk_star(a));
return BR_REWRITE2;
}
br_status seq_rewriter::mk_re_opt(expr* a, expr_ref& result) {
sort* s = nullptr;
VERIFY(m_util.is_re(a, s));
result = m_util.re.mk_union(m_util.re.mk_to_re(m_util.str.mk_empty(s)), a);
result = re().mk_union(re().mk_to_re(m_util.str.mk_empty(s)), a);
return BR_REWRITE1;
}
bool seq_rewriter::has_cofactor(expr* r, expr_ref& cond, expr_ref& th, expr_ref& el) {
expr_ref_vector trail(m()), args_th(m()), args_el(m());
expr* c = nullptr, *tt = nullptr, *ee = nullptr;
obj_map<expr,expr*> cache_th, cache_el;
expr_mark no_cofactor, visited;
ptr_vector<expr> todo;
todo.push_back(r);
while (!todo.empty()) {
expr* e = todo.back();
if (visited.is_marked(e) || !is_app(e)) {
todo.pop_back();
continue;
}
app* a = to_app(e);
if (m().is_ite(e, c, tt, ee)) {
if (!cond) {
cond = c;
cache_th.insert(a, tt);
cache_el.insert(a, ee);
}
else if (cond == c) {
cache_th.insert(a, tt);
cache_el.insert(a, ee);
}
else {
no_cofactor.mark(a);
}
visited.mark(e, true);
todo.pop_back();
continue;
}
if (a->get_family_id() != u().get_family_id()) {
visited.mark(e, true);
no_cofactor.mark(e, true);
todo.pop_back();
continue;
}
switch (a->get_decl_kind()) {
case OP_RE_CONCAT:
case OP_RE_UNION:
case OP_RE_INTERSECT:
case OP_RE_COMPLEMENT:
break;
case OP_RE_STAR:
case OP_RE_LOOP:
default:
visited.mark(e, true);
no_cofactor.mark(e, true);
continue;
}
args_th.reset();
args_el.reset();
bool has_cof = false;
for (expr* arg : *a) {
if (no_cofactor.is_marked(arg)) {
args_th.push_back(arg);
args_el.push_back(arg);
}
else if (cache_th.contains(arg)) {
args_th.push_back(cache_th[arg]);
args_el.push_back(cache_el[arg]);
has_cof = true;
}
else {
todo.push_back(arg);
}
}
if (args_th.size() == a->get_num_args()) {
if (has_cof) {
th = m().mk_app(a->get_decl(), args_th);
el = m().mk_app(a->get_decl(), args_el);
trail.push_back(th);
trail.push_back(el);
cache_th.insert(a, th);
cache_el.insert(a, el);
}
else {
no_cofactor.mark(a, true);
}
visited.mark(e, true);
todo.pop_back();
}
}
SASSERT(cond == !no_cofactor.is_marked(r));
if (cond) {
th = cache_th[r];
el = cache_el[r];
return true;
}
else {
return false;
}
}
br_status seq_rewriter::reduce_re_is_empty(expr* r, expr_ref& result) {
expr* r1, *r2, *r3, *r4;
zstring s1, s2;
unsigned lo, hi;
auto eq_empty = [&](expr* r) { return m().mk_eq(r, m_util.re.mk_empty(m().get_sort(r))); };
if (m_util.re.is_union(r, r1, r2)) {
auto eq_empty = [&](expr* r) { return m().mk_eq(r, re().mk_empty(m().get_sort(r))); };
if (re().is_union(r, r1, r2)) {
result = m().mk_and(eq_empty(r1), eq_empty(r2));
return BR_REWRITE2;
}
if (m_util.re.is_star(r) ||
m_util.re.is_to_re(r) ||
m_util.re.is_full_char(r) ||
m_util.re.is_full_seq(r)) {
if (re().is_star(r) ||
re().is_to_re(r) ||
re().is_full_char(r) ||
re().is_full_seq(r)) {
result = m().mk_false();
return BR_DONE;
}
if (m_util.re.is_concat(r, r1, r2)) {
if (re().is_concat(r, r1, r2)) {
result = m().mk_or(eq_empty(r1), eq_empty(r2));
return BR_REWRITE2;
}
else if (m_util.re.is_range(r, r1, r2) &&
else if (re().is_range(r, r1, r2) &&
m_util.str.is_string(r1, s1) && m_util.str.is_string(r2, s2) &&
s1.length() == 1 && s2.length() == 1) {
result = m().mk_bool_val(s1[0] <= s2[0]);
return BR_DONE;
}
else if ((m_util.re.is_loop(r, r1, lo) ||
m_util.re.is_loop(r, r1, lo, hi)) && lo == 0) {
else if ((re().is_loop(r, r1, lo) ||
re().is_loop(r, r1, lo, hi)) && lo == 0) {
result = m().mk_false();
return BR_DONE;
}
else if (m_util.re.is_loop(r, r1, lo) ||
(m_util.re.is_loop(r, r1, lo, hi) && lo <= hi)) {
else if (re().is_loop(r, r1, lo) ||
(re().is_loop(r, r1, lo, hi) && lo <= hi)) {
result = eq_empty(r1);
return BR_REWRITE1;
}
// DNF expansion:
else if (m_util.re.is_intersection(r, r1, r2) && m_util.re.is_union(r1, r3, r4)) {
result = eq_empty(m_util.re.mk_union(m_util.re.mk_inter(r3, r2), m_util.re.mk_inter(r4, r2)));
// Partial DNF expansion:
else if (re().is_intersection(r, r1, r2) && re().is_union(r1, r3, r4)) {
result = eq_empty(re().mk_union(re().mk_inter(r3, r2), re().mk_inter(r4, r2)));
return BR_REWRITE3;
}
else if (m_util.re.is_intersection(r, r1, r2) && m_util.re.is_union(r2, r3, r4)) {
result = eq_empty(m_util.re.mk_union(m_util.re.mk_inter(r3, r1), m_util.re.mk_inter(r4, r1)));
else if (re().is_intersection(r, r1, r2) && re().is_union(r2, r3, r4)) {
result = eq_empty(re().mk_union(re().mk_inter(r3, r1), re().mk_inter(r4, r1)));
return BR_REWRITE3;
}
return BR_FAILED;
}
br_status seq_rewriter::reduce_re_eq(expr* l, expr* r, expr_ref& result) {
if (m_util.re.is_empty(l)) {
if (re().is_empty(l)) {
std::swap(l, r);
}
if (m_util.re.is_empty(r)) {
if (re().is_empty(r)) {
return reduce_re_is_empty(l, result);
}
return BR_FAILED;
@ -2996,9 +3091,9 @@ bool seq_rewriter::reduce_contains(expr* a, expr* b, expr_ref_vector& disj) {
}
if (m_util.str.is_string(b, s)) {
expr* all = m_util.re.mk_full_seq(m_util.re.mk_re(m().get_sort(b)));
disj.push_back(m_util.re.mk_in_re(m_util.str.mk_concat(m_lhs.size() - i, m_lhs.c_ptr() + i, sort_a),
m_util.re.mk_concat(all, m_util.re.mk_concat(m_util.re.mk_to_re(b), all))));
expr* all = re().mk_full_seq(re().mk_re(m().get_sort(b)));
disj.push_back(re().mk_in_re(m_util.str.mk_concat(m_lhs.size() - i, m_lhs.c_ptr() + i, sort_a),
re().mk_concat(all, re().mk_concat(re().mk_to_re(b), all))));
return true;
}
@ -3155,7 +3250,7 @@ bool seq_rewriter::reduce_by_length(expr_ref_vector& ls, expr_ref_vector& rs,
bool seq_rewriter::is_epsilon(expr* e) const {
expr* e1;
return m_util.re.is_to_re(e, e1) && m_util.str.is_empty(e1);
return re().is_to_re(e, e1) && m_util.str.is_empty(e1);
}
bool seq_rewriter::reduce_subsequence(expr_ref_vector& ls, expr_ref_vector& rs, expr_ref_pair_vector& eqs) {

View file

@ -135,10 +135,8 @@ class seq_rewriter {
// Support for regular expression derivatives
bool get_head_tail(expr* e, expr_ref& head, expr_ref& tail);
expr_ref is_nullable(expr* r);
expr_ref kleene_and(expr* cond, expr* r);
expr_ref kleene_predicate(expr* cond, sort* seq_sort);
expr_ref derivative(expr* hd, expr* r);
br_status mk_seq_unit(expr* e, expr_ref& result);
br_status mk_seq_concat(expr* a, expr* b, expr_ref& result);
@ -181,8 +179,7 @@ class seq_rewriter {
br_status reduce_re_eq(expr* a, expr* b, expr_ref& result);
br_status reduce_re_is_empty(expr* r, expr_ref& result);
br_status mk_bool_app_helper(bool is_and, unsigned n, expr* const* args, expr_ref& result);
br_status mk_bool_app_helper(bool is_and, unsigned n, expr* const* args, expr_ref& result);
bool cannot_contain_prefix(expr* a, expr* b);
bool cannot_contain_suffix(expr* a, expr* b);
@ -212,6 +209,11 @@ class seq_rewriter {
void remove_empty_and_concats(expr_ref_vector& es);
void remove_leading(unsigned n, expr_ref_vector& es);
class seq_util::re& re() { return u().re; }
class seq_util::re const& re() const { return u().re; }
class seq_util::str& str() { return u().str; }
class seq_util::str const& str() const { return u().str; }
public:
seq_rewriter(ast_manager & m, params_ref const & p = params_ref()):
m_util(m), m_autil(m), m_re2aut(m), m_es(m), m_lhs(m), m_rhs(m), m_coalesce_chars(true) {
@ -219,6 +221,7 @@ public:
ast_manager & m() const { return m_util.get_manager(); }
family_id get_fid() const { return m_util.get_family_id(); }
seq_util const& u() const { return m_util; }
seq_util& u() { return m_util; }
void updt_params(params_ref const & p);
static void get_param_descrs(param_descrs & r);
@ -241,6 +244,11 @@ public:
br_status mk_bool_app(func_decl* f, unsigned n, expr* const* args, expr_ref& result);
expr_ref derivative(expr* hd, expr* r);
expr_ref is_nullable(expr* r);
bool has_cofactor(expr* r, expr_ref& cond, expr_ref& th, expr_ref& el);
};

View file

@ -242,7 +242,7 @@ public:
bool is_re(sort* s) const { return is_sort_of(s, m_fid, RE_SORT); }
bool is_re(sort* s, sort*& seq) const { return is_sort_of(s, m_fid, RE_SORT) && (seq = to_sort(s->get_parameter(0).get_ast()), true); }
bool is_seq(expr* e) const { return is_seq(m.get_sort(e)); }
bool is_seq(sort* s, sort*& seq) { return is_seq(s) && (seq = to_sort(s->get_parameter(0).get_ast()), true); }
bool is_seq(sort* s, sort*& seq) const { return is_seq(s) && (seq = to_sort(s->get_parameter(0).get_ast()), true); }
bool is_re(expr* e) const { return is_re(m.get_sort(e)); }
bool is_re(expr* e, sort*& seq) const { return is_re(m.get_sort(e), seq); }
bool is_char(expr* e) const { return is_char(m.get_sort(e)); }

View file

@ -13,10 +13,11 @@ z3_add_component(smt
old_interval.cpp
qi_queue.cpp
seq_axioms.cpp
seq_skolem.cpp
seq_eq_solver.cpp
seq_ne_solver.cpp
seq_offset_eq.cpp
seq_regex.cpp
seq_skolem.cpp
seq_unicode.cpp
smt_almost_cg_table.cpp
smt_arith_value.cpp

View file

@ -96,6 +96,7 @@ def_module_params(module_name='smt',
('core.validate', BOOL, False, '[internal] validate unsat core produced by SMT context. This option is intended for debugging'),
('seq.split_w_len', BOOL, True, 'enable splitting guided by length constraints'),
('seq.validate', BOOL, False, 'enable self-validation of theory axioms created by seq theory'),
('seq.use_derivatives', BOOL, False, 'dev flag (not for users) enable derivative based unfolding of regex'),
('str.strong_arrangements', BOOL, True, 'assert equivalences instead of implications when generating string arrangement axioms'),
('str.aggressive_length_testing', BOOL, False, 'prioritize testing concrete length values over generating more options'),
('str.aggressive_value_testing', BOOL, False, 'prioritize testing concrete string constant values over generating more options'),

View file

@ -21,4 +21,5 @@ void theory_seq_params::updt_params(params_ref const & _p) {
smt_params_helper p(_p);
m_split_w_len = p.seq_split_w_len();
m_seq_validate = p.seq_validate();
m_seq_use_derivatives = p.seq_use_derivatives();
}

View file

@ -25,11 +25,13 @@ struct theory_seq_params {
*/
bool m_split_w_len;
bool m_seq_validate;
bool m_seq_use_derivatives;
theory_seq_params(params_ref const & p = params_ref()):
m_split_w_len(true),
m_seq_validate(false)
m_seq_validate(false),
m_seq_use_derivatives(false)
{
updt_params(p);
}

266
src/smt/seq_regex.cpp Normal file
View file

@ -0,0 +1,266 @@
/*++
Copyright (c) 2011 Microsoft Corporation
Module Name:
seq_regex.cpp
Abstract:
Solver for regexes
Author:
Nikolaj Bjorner (nbjorner) 2020-5-22
--*/
#include "smt/seq_regex.h"
#include "smt/theory_seq.h"
namespace smt {
seq_regex::seq_regex(theory_seq& th):
th(th),
ctx(th.get_context()),
m(th.get_manager())
{}
seq_util& seq_regex::u() { return th.m_util; }
class seq_util::re& seq_regex::re() { return th.m_util.re; }
class seq_util::str& seq_regex::str() { return th.m_util.str; }
seq_rewriter& seq_regex::seq_rw() { return th.m_seq_rewrite; }
seq_skolem& seq_regex::sk() { return th.m_sk; }
void seq_regex::rewrite(expr_ref& e) { th.m_rewrite(e); }
void seq_regex::propagate_in_re(literal lit) {
if (!propagate(lit))
m_to_propagate.push_back(lit);
}
bool seq_regex::propagate() {
bool change = false;
for (unsigned i = 0; !ctx.inconsistent() && i < m_to_propagate.size(); ++i) {
if (propagate(m_to_propagate[i])) {
m_to_propagate.erase_and_swap(i--);
change = true;
}
}
return change;
}
bool seq_regex::propagate(literal lit) {
expr* s = nullptr, *r = nullptr;
expr* e = ctx.bool_var2expr(lit.var());
VERIFY(str().is_in_re(e, s, r));
// only positive assignments of membership propagation are relevant.
if (lit.sign() && sk().is_tail(s))
return true;
// convert negative negative membership literals to positive
// ~(s in R) => s in C(R)
if (lit.sign()) {
expr_ref fml(re().mk_in_re(s, re().mk_complement(r)), m);
rewrite(fml);
literal nlit = th.mk_literal(fml);
th.propagate_lit(nullptr, 1, &lit, nlit);
return true;
}
if (!sk().is_tail(s) && coallesce_in_re(lit))
return true;
// TBD
// for !sk().is_tail(s):
// s in R => R != {}
if (block_unfolding(lit, s))
return true;
// s in R[if(p,R1,R2)] & p => s in R[R1]
// s in R[if(p,R1,R2)] & ~p => s in R[R2]
expr_ref cond(m), tt(m), el(m);
if (seq_rw().has_cofactor(r, cond, tt, el)) {
literal lcond = th.mk_literal(cond), next_lit;
switch (ctx.get_assignment(lcond)) {
case l_true: {
rewrite(tt);
literal lits[2] = { lit, lcond };
next_lit = th.mk_literal(re().mk_in_re(s, tt));
th.propagate_lit(nullptr, 2, lits, next_lit);
return true;
}
case l_false: {
rewrite(el);
next_lit = th.mk_literal(re().mk_in_re(s, el));
literal lits[2] = { lit, ~lcond };
th.propagate_lit(nullptr, 2, lits, next_lit);
return true;
}
case l_undef:
ctx.mark_as_relevant(lcond);
return false;
}
}
// s in R & s = "" => nullable(R)
literal is_empty = th.mk_eq(s, str().mk_empty(m.get_sort(s)), false);
expr_ref is_nullable = seq_rw().is_nullable(r);
rewrite(is_nullable);
th.add_axiom(~lit, ~is_empty, th.mk_literal(is_nullable));
switch (ctx.get_assignment(is_empty)) {
case l_undef:
ctx.mark_as_relevant(is_empty);
return false;
case l_true:
return true;
case l_false:
break;
}
// s in R & s != "" => s = head ++ tail
// s in R & s != "" => tail in D(head, R)
expr_ref head(m), tail(m), d(m);
expr* h = nullptr;
sk().decompose(s, head, tail);
if (!str().is_unit(head, h))
throw default_exception("expected a unit");
d = seq_rw().derivative(h, r);
if (!d)
throw default_exception("unable to expand derivative");
th.add_axiom(is_empty, th.mk_eq(s, th.mk_concat(head, tail), false));
th.add_axiom(~lit, is_empty, th.mk_literal(re().mk_in_re(tail, d)));
return true;
}
bool seq_regex::block_unfolding(literal lit, expr* s) {
expr* t = nullptr;
unsigned i = 0;
if (!sk().is_tail_u(s, t, i))
return false;
if (i > th.m_max_unfolding_depth &&
th.m_max_unfolding_lit != null_literal &&
ctx.get_assignment(th.m_max_unfolding_lit) == l_true &&
!ctx.at_base_level()) {
th.propagate_lit(nullptr, 1, &lit, ~th.m_max_unfolding_lit);
return true;
}
return false;
}
bool seq_regex::coallesce_in_re(literal lit) {
// initially disable this
return false;
expr* s = nullptr, *r = nullptr;
expr* e = ctx.bool_var2expr(lit.var());
VERIFY(str().is_in_re(e, s, r));
expr_ref regex(r, m);
literal_vector lits;
for (unsigned i = 0; i < m_s_in_re.size(); ++i) {
auto const& entry = m_s_in_re[i];
if (!entry.m_active)
continue;
if (th.get_root(entry.m_s) != th.get_root(s))
continue;
if (entry.m_re == regex)
continue;
th.m_trail_stack.push(vector_value_trail<theory_seq, s_in_re, true>(m_s_in_re, i));
m_s_in_re[i].m_active = false;
IF_VERBOSE(11, verbose_stream() << "intersect " << regex << " " <<
mk_pp(entry.m_re, m) << " " << mk_pp(s, m) << " " << mk_pp(entry.m_s, m) << "\n";);
regex = re().mk_inter(entry.m_re, regex);
rewrite(regex);
lits.push_back(~entry.m_lit);
enode* n1 = th.ensure_enode(entry.m_s);
enode* n2 = th.ensure_enode(s);
if (n1 != n2) {
lits.push_back(~th.mk_eq(n1->get_owner(), n2->get_owner(), false));
}
}
m_s_in_re.push_back(s_in_re(lit, s, regex));
th.get_trail_stack().push(push_back_vector<theory_seq, vector<s_in_re>>(m_s_in_re));
if (lits.empty())
return false;
lits.push_back(~lit);
lits.push_back(th.mk_literal(re().mk_in_re(s, regex)));
ctx.mk_th_axiom(th.get_id(), lits.size(), lits.c_ptr());
return true;
}
void seq_regex::propagate_is_empty(literal lit) {
// the dual version of unroll_non_empty, but
// skolem functions have to be eliminated or turned into
// universal quantifiers.
throw default_exception("emptiness checking of regex is TBD");
}
void seq_regex::propagate_is_nonempty(expr* r) {
sort* seq_sort = nullptr;
VERIFY(u().is_re(r, seq_sort));
literal lit = ~th.mk_eq(r, re().mk_empty(seq_sort), false);
expr_mark seen;
expr_ref non_empty = unroll_non_empty(r, seen, 0);
if (non_empty) {
rewrite(non_empty);
th.add_axiom(~lit, th.mk_literal(non_empty));
}
else {
// generally introduce predicate (re.nonempty r seen)
// with inference rules based on unroll_non_empty
throw default_exception("unrolling large regexes is TBD");
}
}
/**
nonempty(R union Q, Seen) = R = {} or Q = {}
nonempty(R[if(p,R1,R2)], Seen) = if(p, nonempty(R[R1], Seen), nonempty(R[R2], Seen)) (co-factor)
nonempty(R, Seen) = nullable(R) or (R not in Seen and nonempty(D(first(R),R), Seen u { R })) (derivative)
TBD: eliminate variables from p when possible to perform quantifier elimination.
p := first(R) == 'a'
then replace first(R) by 'a' in R[R1]
TBD:
empty(R, Seen) = R = {} if R does not contain a subterm in Seen and Seen is non-empty
first : RegEx -> Char is a skolem function
*/
expr_ref seq_regex::mk_first(expr* r) {
sort* elem_sort = nullptr, *seq_sort = nullptr;
VERIFY(u().is_re(r, seq_sort));
VERIFY(u().is_seq(seq_sort, elem_sort));
return expr_ref(m.mk_fresh_const("re.first", elem_sort), m);
// return sk().mk("re.first", r, elem_sort);
}
expr_ref seq_regex::unroll_non_empty(expr* r, expr_mark& seen, unsigned depth) {
if (seen.is_marked(r))
return expr_ref(m.mk_false(), m);
if (depth > 300)
return expr_ref(m);
expr_ref result(m), cond(m), th(m), el(m);
// TBD: try also rewriting
if (seq_rw().has_cofactor(r, cond, th, el)) {
th = unroll_non_empty(th, seen, depth + 1);
el = unroll_non_empty(el, seen, depth + 1);
if (th && el)
result = m.mk_ite(cond, th, el);
return result;
}
expr_ref hd = mk_first(r);
result = seq_rw().derivative(hd, r);
if (result) {
// TBD fast check if r is a subterm of result, if not, then
// loop instead of recurse
seen.mark(r, true);
result = unroll_non_empty(result, seen, depth + 1);
seen.mark(r, false);
}
return result;
}
}

77
src/smt/seq_regex.h Normal file
View file

@ -0,0 +1,77 @@
/*++
Copyright (c) 2011 Microsoft Corporation
Module Name:
seq_regex.h
Abstract:
Solver for regexes
Author:
Nikolaj Bjorner (nbjorner) 2020-5-22
--*/
#pragma once
#include "util/scoped_vector.h"
#include "ast/seq_decl_plugin.h"
#include "ast/rewriter/seq_rewriter.h"
#include "smt/smt_context.h"
#include "smt/seq_skolem.h"
namespace smt {
class theory_seq;
class seq_regex {
struct s_in_re {
literal m_lit;
expr* m_s;
expr* m_re;
bool m_active;
s_in_re(literal l, expr* s, expr* r):
m_lit(l), m_s(s), m_re(r), m_active(true) {}
};
theory_seq& th;
context& ctx;
ast_manager& m;
vector<s_in_re> m_s_in_re;
scoped_vector<literal> m_to_propagate;
seq_util& u();
class seq_util::re& re();
class seq_util::str& str();
seq_rewriter& seq_rw();
seq_skolem& sk();
void rewrite(expr_ref& e);
bool propagate(literal lit);
bool coallesce_in_re(literal lit);
bool block_unfolding(literal lit, expr* s);
expr_ref mk_first(expr* r);
expr_ref unroll_non_empty(expr* r, expr_mark& seen, unsigned depth);
public:
seq_regex(theory_seq& th);
bool propagate();
void propagate_in_re(literal lit);
void propagate_is_empty(literal lit);
void propagate_is_nonempty(expr* r);
};
};

View file

@ -299,6 +299,7 @@ theory_seq::theory_seq(context& ctx):
m_sk(m, m_rewrite),
m_ax(*this, m_rewrite),
m_unicode(*this),
m_regex(*this),
m_arith_value(m),
m_trail_stack(*this),
m_ls(m), m_rs(m),
@ -367,6 +368,10 @@ final_check_status theory_seq::final_check_eh() {
TRACEFIN("solve_nqs");
return FC_CONTINUE;
}
if (m_regex.propagate()) {
TRACEFIN("regex propagate");
return FC_CONTINUE;
}
if (check_contains()) {
++m_stats.m_propagate_contains;
TRACEFIN("propagate_contains");
@ -2617,6 +2622,7 @@ expr_ref theory_seq::add_elim_string_axiom(expr* n) {
}
void theory_seq::propagate_in_re(expr* n, bool is_true) {
TRACE("seq", tout << mk_pp(n, m) << " <- " << (is_true?"true":"false") << "\n";);
expr_ref tmp(n, m);
@ -3053,7 +3059,12 @@ void theory_seq::assign_eh(bool_var v, bool is_true) {
}
}
else if (m_util.str.is_in_re(e)) {
propagate_in_re(e, is_true);
if (ctx.get_fparams().m_seq_use_derivatives) {
m_regex.propagate_in_re(lit);
}
else {
propagate_in_re(e, is_true);
}
}
else if (m_sk.is_digit(e)) {
// no-op

View file

@ -34,11 +34,14 @@ Revision History:
#include "smt/seq_skolem.h"
#include "smt/seq_axioms.h"
#include "smt/seq_unicode.h"
#include "smt/seq_regex.h"
#include "smt/seq_offset_eq.h"
namespace smt {
class theory_seq : public theory {
friend class seq_regex;
struct assumption {
enode* n1, *n2;
literal lit;
@ -404,6 +407,7 @@ namespace smt {
seq_skolem m_sk;
seq_axioms m_ax;
seq_unicode m_unicode;
seq_regex m_regex;
arith_value m_arith_value;
th_trail_stack m_trail_stack;
stats m_stats;