From e63dc7efc2f14e04522c430b3da52afcc4a4d0be Mon Sep 17 00:00:00 2001
From: Nikolaj Bjorner <nbjorner@microsoft.com>
Date: Wed, 17 Feb 2021 17:31:46 -0800
Subject: [PATCH] more rewrite rules
---
src/ast/rewriter/seq_axioms.cpp | 49 ++++++++++--
src/ast/rewriter/seq_axioms.h | 2 +
src/ast/rewriter/seq_rewriter.cpp | 126 +++++++++++++++++++++++-------
src/ast/rewriter/seq_rewriter.h | 1 +
src/util/rational.h | 11 ++-
5 files changed, 150 insertions(+), 39 deletions(-)
diff --git a/src/ast/rewriter/seq_axioms.cpp b/src/ast/rewriter/seq_axioms.cpp
index 5798df110..e7a4da35c 100644
--- a/src/ast/rewriter/seq_axioms.cpp
+++ b/src/ast/rewriter/seq_axioms.cpp
@@ -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);
@@ -224,6 +227,13 @@ 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
@@ -231,6 +241,7 @@ namespace seq {
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);
@@ -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.
diff --git a/src/ast/rewriter/seq_axioms.h b/src/ast/rewriter/seq_axioms.h
index be15a8166..16b166c62 100644
--- a/src/ast/rewriter/seq_axioms.h
+++ b/src/ast/rewriter/seq_axioms.h
@@ -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:
diff --git a/src/ast/rewriter/seq_rewriter.cpp b/src/ast/rewriter/seq_rewriter.cpp
index 362ee43e2..f2b22f41b 100644
--- a/src/ast/rewriter/seq_rewriter.cpp
+++ b/src/ast/rewriter/seq_rewriter.cpp
@@ -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;
@@ -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();
@@ -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);
}
@@ -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;
@@ -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;
}
@@ -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;
diff --git a/src/ast/rewriter/seq_rewriter.h b/src/ast/rewriter/seq_rewriter.h
index d503ba022..314a83d4f 100644
--- a/src/ast/rewriter/seq_rewriter.h
+++ b/src/ast/rewriter/seq_rewriter.h
@@ -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;
diff --git a/src/util/rational.h b/src/util/rational.h
index e0a76d9ee..7bf800294 100644
--- a/src/util/rational.h
+++ b/src/util/rational.h
@@ -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));
}