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more rewrite rules
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@NikolajBjorner
NikolajBjorner committed Feb 18, 2021
1 parent bcad4d9 commit e63dc7e
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Showing 5 changed files with 150 additions and 39 deletions.
49 changes: 41 additions & 8 deletions src/ast/rewriter/seq_axioms.cpp
View file
Expand Up @@ -127,31 +127,34 @@ namespace seq {
auto s = purify(_s);
auto i = purify(_i);
auto l = purify(_l);
if (is_tail(s, i, l)) {
if (is_tail(s, _i, _l)) {
tail_axiom(e, s);
return;
}
if (is_drop_last(s, i, l)) {
if (is_drop_last(s, _i, _l)) {
drop_last_axiom(e, s);
return;
}
if (is_extract_prefix0(s, i, l)) {
if (is_extract_prefix0(s, _i, _l)) {
extract_prefix_axiom(e, s, l);
return;
}
if (is_extract_suffix(s, _i, _l)) {
return;
}
expr_ref x = m_sk.mk_pre(s, i);
expr_ref ls = mk_len(s);
expr_ref ls = mk_len(_s);
expr_ref lx = mk_len(x);
expr_ref le = mk_len(e);
expr_ref ls_minus_i_l(mk_sub(mk_sub(ls, i), l), m);
expr_ref ls_minus_i_l(mk_sub(mk_sub(ls, _i), _l), m);
expr_ref y = m_sk.mk_post(s, a.mk_add(i, l));
expr_ref xe = mk_concat(x, e);
expr_ref xey = mk_concat(x, e, y);
expr_ref zero(a.mk_int(0), m);

expr_ref i_ge_0 = mk_ge(i, 0);
expr_ref i_le_ls = mk_le(mk_sub(i, ls), 0);
expr_ref ls_le_i = mk_le(mk_sub(ls, i), 0);
expr_ref i_ge_0 = mk_ge(_i, 0);
expr_ref i_le_ls = mk_le(mk_sub(_i, ls), 0);
expr_ref ls_le_i = mk_le(mk_sub(ls, _i), 0);
expr_ref ls_ge_li = mk_ge(ls_minus_i_l, 0);
expr_ref l_ge_0 = mk_ge(l, 0);
expr_ref l_le_0 = mk_le(l, 0);
Expand Down Expand Up @@ -224,13 +227,21 @@ namespace seq {
return a.is_numeral(i, i1) && i1.is_zero();
}

bool axioms::is_extract_suffix(expr* s, expr* i, expr* l) {
expr_ref len(a.mk_add(l, i), m);
m_rewrite(len);
return seq.str.is_length(len, l) && l == s;
}


/*
s = ey
l <= 0 => e = empty
0 <= l <= len(s) => len(e) = l
len(s) < l => e = s
*/
void axioms::extract_prefix_axiom(expr* e, expr* s, expr* l) {

TRACE("seq", tout << "prefix " << mk_bounded_pp(e, m, 2) << " " << mk_bounded_pp(s, m, 2) << " " << mk_bounded_pp(l, m, 2) << "\n";);
expr_ref le = mk_len(e);
expr_ref ls = mk_len(s);
Expand All @@ -244,6 +255,28 @@ namespace seq {
add_clause(l_le_s, mk_eq(e, s));
}

/*
s = xe
0 <= i <= len(s) => i = len(x)
i < 0 => e = empty
i > len(s) => e = empty
*/
void axioms::extract_suffix_axiom(expr* e, expr* s, expr* i) {
TRACE("seq", tout << "suffix " << mk_bounded_pp(e, m, 2) << " " << mk_bounded_pp(s, m, 2) << "\n";);
expr_ref x = m_sk.mk_pre(s, i);
expr_ref lx = mk_len(x);
expr_ref ls = mk_len(s);
expr_ref xe = mk_concat(x, e);
expr_ref emp = mk_eq_empty(e);
expr_ref i_ge_0 = mk_ge(i, 0);
expr_ref i_le_s = mk_le(mk_sub(i, ls), 0);
add_clause(mk_eq(s, xe));
add_clause(~i_ge_0, ~i_le_s, mk_eq(i, lx));
add_clause(i_ge_0, emp);
add_clause(i_le_s, emp);
}


/*
encode that s is not contained in of xs1
where s1 is all of s, except the last element.
Expand Down
2 changes: 2 additions & 0 deletions src/ast/rewriter/seq_axioms.h
View file
Expand Up @@ -62,10 +62,12 @@ namespace seq {
bool is_drop_last(expr* s, expr* i, expr* l);
bool is_tail(expr* s, expr* i, expr* l);
bool is_extract_prefix0(expr* s, expr* i, expr* l);
bool is_extract_suffix(expr* s, expr* i, expr* l);

void tail_axiom(expr* e, expr* s);
void drop_last_axiom(expr* e, expr* s);
void extract_prefix_axiom(expr* e, expr* s, expr* l);
void extract_suffix_axiom(expr* e, expr* s, expr* l);
void tightest_prefix(expr* s, expr* x);

public:
Expand Down
126 changes: 96 additions & 30 deletions src/ast/rewriter/seq_rewriter.cpp
View file
Expand Up @@ -966,7 +966,6 @@ br_status seq_rewriter::mk_seq_extract(expr* a, expr* b, expr* c, expr_ref& resu
bool constantBase = str().is_string(a, s);
bool constantPos = m_autil.is_numeral(b, pos);
bool constantLen = m_autil.is_numeral(c, len);
bool lengthPos = str().is_length(b) || m_autil.is_add(b);
sort* a_sort = a->get_sort();

sign sg;
Expand All @@ -988,6 +987,12 @@ br_status seq_rewriter::mk_seq_extract(expr* a, expr* b, expr* c, expr_ref& resu
return BR_DONE;
}

unsigned len_a;
if (constantPos && max_length(a, len_a) && rational(len_a) <= pos) {
result = str().mk_empty(a_sort);
return BR_DONE;
}

constantPos &= pos.is_unsigned();
constantLen &= len.is_unsigned();

Expand All @@ -1013,20 +1018,21 @@ br_status seq_rewriter::mk_seq_extract(expr* a, expr* b, expr* c, expr_ref& resu
return BR_DONE;
}

auto reassemble = [&](rational const& p, expr_ref_vector const& xs) {
expr_ref r(m_autil.mk_int(p), m());
for (expr* e : xs)
r = m_autil.mk_add(r, str().mk_length(e));
return r;
};

// extract(a + b + c, len(a + b), s) -> extract(c, 0, s)
// extract(a + b + c, len(a) + len(b), s) -> extract(c, 0, s)
if (lengthPos) {

m_lhs.reset();
expr_ref_vector lens(m());
str().get_concat(a, m_lhs);
TRACE("seq", tout << m_lhs << " " << pos << " " << lens << "\n";);
if (!get_lengths(b, lens, pos) || pos.is_neg()) {
return BR_FAILED;
}

expr_ref_vector lens(m());
if (get_lengths(b, lens, pos) && pos >= 0) {
unsigned i = 0;
for (; i < m_lhs.size(); ++i) {
expr* lhs = m_lhs.get(i);
for (; i < as.size(); ++i) {
expr* lhs = as.get(i);
if (lens.contains(lhs)) {
lens.erase(lhs);
}
Expand All @@ -1037,32 +1043,54 @@ br_status seq_rewriter::mk_seq_extract(expr* a, expr* b, expr* c, expr_ref& resu
break;
}
}
if (i == 0) return BR_FAILED;
expr_ref t1(m()), t2(m());
t1 = str().mk_concat(m_lhs.size() - i, m_lhs.c_ptr() + i, a->get_sort());
t2 = m_autil.mk_int(pos);
for (expr* rhs : lens) {
t2 = m_autil.mk_add(t2, str().mk_length(rhs));
if (i != 0) {
expr_ref t1(m());
t1 = str().mk_concat(as.size() - i, as.c_ptr() + i, a->get_sort());
expr_ref t2 = reassemble(pos, lens);
result = str().mk_substr(t1, t2, c);
TRACE("seq", tout << result << "\n";);
return BR_REWRITE2;
}
result = str().mk_substr(t1, t2, c);
TRACE("seq", tout << result << "\n";);
return BR_REWRITE2;
}


if (!constantPos) {
return BR_FAILED;
}
unsigned _pos = pos.get_unsigned();

// (extract s 0 (len s)) = s
expr* a2 = nullptr;
if (_pos == 0 && str().is_length(c, a2)) {
m_lhs.reset();
str().get_concat(a, m_lhs);
if (!m_lhs.empty() && m_lhs.get(0) == a2) {
result = a2;
// extract(a + b + c, 0, len(a) + len(b)) -> c
if (pos.is_zero()) {
lens.reset();
if (!get_lengths(c, lens, pos) || pos.is_neg())
return BR_FAILED;
unsigned i = 0;
for (; i < as.size(); ++i) {
expr* lhs = as.get(i);
if (lens.contains(lhs)) {
lens.erase(lhs);
}
else if (str().is_unit(lhs) && pos.is_pos()) {
pos -= rational(1);
}
else {
break;
}
}
if (i == as.size()) {
result = a;
return BR_DONE;
}
else if (i != 0) {
expr_ref t1(m()), t2(m());
t1 = str().mk_concat(as.size() - i, as.c_ptr() + i, a->get_sort());
t2 = reassemble(pos, lens);
result = str().mk_substr(t1, b, t2);
as[i] = result;
result = str().mk_concat(i + 1, as.c_ptr(), a->get_sort());
TRACE("seq", tout << result << "\n";);
return BR_REWRITE2;
}
}

expr* a1 = nullptr, *b1 = nullptr, *c1 = nullptr;
Expand Down Expand Up @@ -1123,16 +1151,23 @@ br_status seq_rewriter::mk_seq_extract(expr* a, expr* b, expr* c, expr_ref& resu
}

bool seq_rewriter::get_lengths(expr* e, expr_ref_vector& lens, rational& pos) {
expr* arg = nullptr;
expr* arg = nullptr, *e1 = nullptr, *e2 = nullptr;
rational pos1;
if (m_autil.is_add(e)) {
for (expr* arg1 : *to_app(e)) {
if (!get_lengths(arg1, lens, pos)) return false;
if (!get_lengths(arg1, lens, pos))
return false;
}
}
else if (str().is_length(e, arg)) {
lens.push_back(arg);
}
else if (m_autil.is_mul(e, e1, e2) && m_autil.is_numeral(e1, pos1) && str().is_length(e2, arg) && pos1 <= 10) {
while (pos1 > 0) {
lens.push_back(arg);
pos1 -= rational(1);
}
}
else if (m_autil.is_numeral(e, pos1)) {
pos += pos1;
}
Expand Down Expand Up @@ -4496,6 +4531,37 @@ bool seq_rewriter::min_length(expr_ref_vector const& es, unsigned& len) {
return bounded;
}

bool seq_rewriter::max_length(expr* e, unsigned& len) {
if (str().is_unit(e)) {
len = 1;
return true;
}
if (str().is_at(e)) {
len = 1;
return true;
}
zstring s;
if (str().is_string(e, s)) {
len = s.length();
return true;
}
if (str().is_empty(e)) {
len = 0;
return true;
}
if (str().is_concat(e)) {
unsigned l = 0;
len = 0;
for (expr* arg : *to_app(e)) {
if (!max_length(arg, l))
return false;
len += l;
}
return true;
}
return false;
}

bool seq_rewriter::is_string(unsigned n, expr* const* es, zstring& s) const {
zstring s1;
expr* e;
Expand Down
1 change: 1 addition & 0 deletions src/ast/rewriter/seq_rewriter.h
View file
Expand Up @@ -282,6 +282,7 @@ class seq_rewriter {
bool reduce_itos(expr_ref_vector& ls, expr_ref_vector& rs, expr_ref_pair_vector& eqs);
bool reduce_eq_empty(expr* l, expr* r, expr_ref& result);
bool min_length(expr_ref_vector const& es, unsigned& len);
bool max_length(expr* e, unsigned& len);
expr* concat_non_empty(expr_ref_vector& es);

bool is_string(unsigned n, expr* const* es, zstring& s) const;
Expand Down
11 changes: 10 additions & 1 deletion src/util/rational.h
View file
Expand Up @@ -500,7 +500,16 @@ inline bool operator>(int a, rational const & b) {
}


inline bool operator!=(rational const & a, int b) {
inline bool operator>=(rational const& a, int b) {
return a >= rational(b);
}

inline bool operator>=(int a, rational const& b) {
return rational(a) >= b;
}


inline bool operator!=(rational const& a, int b) {
return !(a == rational(b));
}

Expand Down

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