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integrate ite-normalized derivatives

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2020-06-05 17:28:48 -07:00
parent 4dbf7b183d
commit 1b9fcc7098
4 changed files with 86 additions and 212 deletions
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174
src/ast/rewriter/seq_rewriter.cpp
View file

@ -2336,30 +2336,33 @@ expr_ref seq_rewriter::mk_der_op_rec(decl_kind k, expr* a, expr* b) {
expr* ca = nullptr, *a1 = nullptr, *a2 = nullptr;
expr* cb = nullptr, *b1 = nullptr, *b2 = nullptr;
expr_ref result(m());
auto mk_ite = [&](expr* c, expr* a, expr* b) {
return (a == b) ? a : m().mk_ite(c, a, b);
};
if (m().is_ite(a, ca, a1, a2)) {
if (m().is_ite(b, cb, b1, b2)) {
if (ca == cb) {
expr_ref r1 = mk_der_op(k, a1, b1);
expr_ref r2 = mk_der_op(k, a2, b2);
result = m().mk_ite(ca, r1, r2);
result = mk_ite(ca, r1, r2);
return result;
}
else if (ca->get_id() < cb->get_id()) {
expr_ref r1 = mk_der_op(k, a, b1);
expr_ref r2 = mk_der_op(k, a, b2);
result = m().mk_ite(cb, r1, r2);
result = mk_ite(cb, r1, r2);
return result;
}
}
expr_ref r1 = mk_der_op(k, a1, b);
expr_ref r2 = mk_der_op(k, a2, b);
result = m().mk_ite(ca, r1, r2);
result = mk_ite(ca, r1, r2);
return result;
}
if (m().is_ite(b, cb, b1, b2)) {
expr_ref r1 = mk_der_op(k, a, b1);
expr_ref r2 = mk_der_op(k, a, b2);
result = m().mk_ite(cb, r1, r2);
result = mk_ite(cb, r1, r2);
return result;
}
switch (k) {
@ -2413,6 +2416,7 @@ expr_ref seq_rewriter::mk_derivative_rec(expr* ele, expr* r) {
VERIFY(m_util.is_seq(seq_sort, ele_sort));
SASSERT(ele_sort == m().get_sort(ele));
expr* r1 = nullptr, *r2 = nullptr, *p = nullptr;
auto mk_empty = [&]() { return expr_ref(re().mk_empty(m().get_sort(r)), m()); };
unsigned lo = 0, hi = 0;
if (re().is_concat(r, r1, r2)) {
expr_ref is_n = is_nullable(r1);
@ -2422,7 +2426,8 @@ expr_ref seq_rewriter::mk_derivative_rec(expr* ele, expr* r) {
return result;
}
expr_ref dr2 = mk_derivative(ele, r2);
return mk_der_union(result, re_and(is_n, dr2));
is_n = re_predicate(is_n, seq_sort);
return mk_der_union(result, mk_der_concat(is_n, dr2));
}
else if (re().is_star(r, r1)) {
return mk_der_concat(mk_derivative(ele, r1), r);
@ -2459,8 +2464,7 @@ expr_ref seq_rewriter::mk_derivative_rec(expr* ele, expr* r) {
}
else if (re().is_loop(r, r1, lo, hi)) {
if (hi == 0) {
result = re().mk_empty(m().get_sort(r));
return result;
return mk_empty();
}
hi--;
if (lo > 0) {
@ -2470,20 +2474,17 @@ expr_ref seq_rewriter::mk_derivative_rec(expr* ele, expr* r) {
}
else if (re().is_full_seq(r) ||
re().is_empty(r)) {
result = r;
return result;
return expr_ref(r, m());
}
else if (re().is_to_re(r, r1)) {
// r1 is a string here (not a regexp)
expr_ref hd(m()), tl(m());
if (get_head_tail(r1, hd, tl)) {
// head must be equal; if so, derivative is tail
result = re_and(m().mk_eq(ele, hd), re().mk_to_re(tl));
return result;
return re_and(m().mk_eq(ele, hd), re().mk_to_re(tl));
}
else if (str().is_empty(r1)) {
result = re().mk_empty(m().get_sort(r));
return result;
return mk_empty();
}
else {
return expr_ref(re().mk_derivative(ele, r), m());
@ -2495,15 +2496,10 @@ expr_ref seq_rewriter::mk_derivative_rec(expr* ele, expr* r) {
// This is analagous to the previous is_to_re case.
expr_ref hd(m()), tl(m());
if (get_head_tail_reversed(r2, hd, tl)) {
result = re_and(
m().mk_eq(ele, tl),
re().mk_reverse(re().mk_to_re(hd))
);
return result;
return re_and(m().mk_eq(ele, tl), re().mk_reverse(re().mk_to_re(hd)));
}
else if (str().is_empty(r2)) {
result = re().mk_empty(m().get_sort(r));
return result;
return mk_empty();
}
else {
return expr_ref(re().mk_derivative(ele, r), m());
@ -2516,32 +2512,27 @@ expr_ref seq_rewriter::mk_derivative_rec(expr* ele, expr* r) {
if (s1.length() == 1 && s2.length() == 1) {
r1 = m_util.mk_char(s1[0]);
r2 = m_util.mk_char(s2[0]);
result = m().mk_and(m_util.mk_le(r1, ele), m_util.mk_le(ele, r2));
result = re_predicate(result, seq_sort);
return result;
return mk_der_inter(re_predicate(m_util.mk_le(r1, ele), seq_sort),
re_predicate(m_util.mk_le(ele, r2), seq_sort));
}
else {
result = re().mk_empty(m().get_sort(r));
return result;
return mk_empty();
}
}
expr* e1 = nullptr, *e2 = nullptr;
if (str().is_unit(r1, e1) && str().is_unit(r2, e2)) {
result = m().mk_and(m_util.mk_le(e1, ele), m_util.mk_le(ele, e2));
result = re_predicate(result, seq_sort);
return result;
return mk_der_inter(re_predicate(m_util.mk_le(e1, ele), seq_sort),
re_predicate(m_util.mk_le(ele, e2), seq_sort));
}
}
else if (re().is_full_char(r)) {
result = re().mk_to_re(str().mk_empty(seq_sort));
return result;
return expr_ref(re().mk_to_re(str().mk_empty(seq_sort)), m());
}
else if (re().is_of_pred(r, p)) {
array_util array(m());
expr* args[2] = { p, ele };
result = array.mk_select(2, args);
result = re_predicate(result, seq_sort);
return result;
return re_predicate(result, seq_sort);
}
// stuck cases: re().is_derivative, variable, ...
// and re().is_reverse if the reverse is not applied to a string
@ -3196,7 +3187,6 @@ void seq_rewriter::elim_condition(expr* elem, expr_ref& cond) {
else
intersect(0, ch-1, ranges);
}
// TBD: case for negation of range (not (and (<= lo e) (<= e hi)))
else {
all_ranges = false;
break;
@ -3237,124 +3227,6 @@ void seq_rewriter::elim_condition(expr* elem, expr_ref& cond) {
}
}
void seq_rewriter::get_cofactors(expr* r, expr_ref_vector& conds, expr_ref_pair_vector& result) {
expr_ref cond(m()), th(m()), el(m());
if (has_cofactor(r, cond, th, el)) {
conds.push_back(cond);
get_cofactors(th, conds, result);
conds.pop_back();
conds.push_back(mk_not(m(), cond));
get_cofactors(el, conds, result);
conds.pop_back();
}
else {
cond = mk_and(conds);
result.push_back(cond, r);
}
}
bool seq_rewriter::has_cofactor(expr* r, expr_ref& cond, expr_ref& th, expr_ref& el) {
if (m().is_ite(r)) {
cond = to_app(r)->get_arg(0);
th = to_app(r)->get_arg(1);
el = to_app(r)->get_arg(2);
return true;
}
expr_ref_vector trail(m()), args_th(m()), args_el(m());
expr* c = nullptr, *tt = nullptr, *ee = nullptr;
cond = 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 = mk_app(a->get_decl(), args_th);
el = 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;

12
src/ast/rewriter/seq_rewriter.h
View file

@ -273,12 +273,13 @@ class seq_rewriter {
class seq_util::str& str() { return u().str; }
class seq_util::str const& str() const { return u().str; }
void get_cofactors(expr* r, expr_ref_vector& conds, expr_ref_pair_vector& result);
expr_ref is_nullable_rec(expr* r);
void intersect(unsigned lo, unsigned hi, svector<std::pair<unsigned, unsigned>>& ranges);
public:
seq_rewriter(ast_manager & m, params_ref const & p = params_ref()):
m_util(m), m_autil(m), m_re2aut(m), m_op_cache(m), m_es(m), m_lhs(m), m_rhs(m), m_coalesce_chars(true) {
m_util(m), m_autil(m), m_re2aut(m), m_op_cache(m), m_es(m),
m_lhs(m), m_rhs(m), m_coalesce_chars(true) {
}
ast_manager & m() const { return m_util.get_manager(); }
family_id get_fid() const { return m_util.get_family_id(); }
@ -320,14 +321,7 @@ public:
void add_seqs(expr_ref_vector const& ls, expr_ref_vector const& rs, expr_ref_pair_vector& new_eqs);
expr_ref is_nullable(expr* r);
expr_ref is_nullable_rec(expr* r);
bool has_cofactor(expr* r, expr_ref& cond, expr_ref& th, expr_ref& el);
void get_cofactors(expr* r, expr_ref_pair_vector& result) {
expr_ref_vector conds(m());
get_cofactors(r, conds, result);
}
// heuristic elimination of element from condition that comes form a derivative.
// special case optimization for conjunctions of equalities, disequalities and ranges.

103
src/smt/seq_regex.cpp
View file

@ -148,32 +148,6 @@ namespace smt {
m_to_propagate.push_back(lit);
}
// s in R[if(p,R1,R2)] & p => s in R[R1]
// s in R[if(p,R1,R2)] & ~p => s in R[R2]
bool seq_regex::unfold_cofactors(expr_ref& r, literal_vector& conds) {
expr_ref cond(m), tt(m), el(m);
while (seq_rw().has_cofactor(r, cond, tt, el)) {
rewrite(cond);
literal lcond = th.mk_literal(cond);
switch (ctx.get_assignment(lcond)) {
case l_true:
conds.push_back(~lcond);
r = tt;
break;
case l_false:
conds.push_back(lcond);
r = el;
break;
case l_undef:
ctx.mark_as_relevant(lcond);
return false;
}
rewrite(r);
}
return true;
}
/**
* Propagate the atom (accept s i r)
@ -198,19 +172,14 @@ namespace smt {
TRACE("seq", tout << "propagate " << mk_pp(e, m) << "\n";);
if (block_unfolding(lit, idx))
return true;
literal_vector conds;
conds.push_back(~lit);
if (!unfold_cofactors(d, conds))
return false;
if (re().is_empty(d)) {
th.add_axiom(conds);
if (re().is_empty(r)) {
th.add_axiom(~lit);
return true;
}
if (block_unfolding(lit, idx))
return true;
// s in R & len(s) <= i => nullable(R)
literal len_s_le_i = th.m_ax.mk_le(th.mk_len(s), idx);
switch (ctx.get_assignment(len_s_le_i)) {
@ -218,11 +187,9 @@ namespace smt {
ctx.mark_as_relevant(len_s_le_i);
return false;
case l_true:
is_nullable = seq_rw().is_nullable(d);
is_nullable = seq_rw().is_nullable(r);
rewrite(is_nullable);
conds.push_back(~len_s_le_i);
conds.push_back(th.mk_literal(is_nullable));
th.add_axiom(conds);
th.add_axiom(~lit, ~len_s_le_i, th.mk_literal(is_nullable));
return true;
case l_false:
break;
@ -230,14 +197,38 @@ namespace smt {
// (accept s i R) & len(s) > i => (accept s (+ i 1) D(nth(s, i), R)) or conds
expr_ref head = th.mk_nth(s, i);
d = re().mk_derivative(head, r);
d = re().mk_derivative(m.mk_var(0, m.get_sort(head)), r);
rewrite(d);
literal acc_next = th.mk_literal(sk().mk_accept(s, a().mk_int(idx + 1), d));
literal_vector conds;
conds.push_back(~lit);
conds.push_back(len_s_le_i);
conds.push_back(acc_next);
th.add_axiom(conds);
expr* cond = nullptr, *tt = nullptr, *el = nullptr;
var_subst subst(m);
expr_ref_vector sub(m);
sub.push_back(head);
// s in R[if(p,R1,R2)] & p => s in R[R1]
// s in R[if(p,R1,R2)] & ~p => s in R[R2]
while (m.is_ite(d, cond, tt, el)) {
literal lcond = th.mk_literal(subst(cond, sub));
switch (ctx.get_assignment(lcond)) {
case l_true:
conds.push_back(~lcond);
d = tt;
break;
case l_false:
conds.push_back(lcond);
d = el;
break;
case l_undef:
ctx.mark_as_relevant(lcond);
return false;
}
}
// at this point there should be no free variables as the ites are at top-level.
if (!re().is_empty(d))
conds.push_back(th.mk_literal(sk().mk_accept(s, a().mk_int(idx + 1), d)));
th.add_axiom(conds);
TRACE("seq", tout << "unfold " << head << "\n" << mk_pp(r, m) << "\n";);
return true;
}
@ -358,7 +349,7 @@ namespace smt {
if (null_lit != false_literal)
lits.push_back(null_lit);
expr_ref_pair_vector cofactors(m);
seq_rw().get_cofactors(d, cofactors);
get_cofactors(d, cofactors);
for (auto const& p : cofactors) {
if (is_member(p.second, u))
continue;
@ -375,6 +366,21 @@ namespace smt {
th.add_axiom(lits);
}
void seq_regex::get_cofactors(expr* r, expr_ref_vector& conds, expr_ref_pair_vector& result) {
expr* cond = nullptr, *th = nullptr, *el = nullptr;
if (m.is_ite(r, cond, th, el)) {
conds.push_back(cond);
get_cofactors(th, conds, result);
conds.pop_back();
conds.push_back(mk_not(m, cond));
get_cofactors(el, conds, result);
conds.pop_back();
}
else {
cond = mk_and(conds);
result.push_back(cond, r);
}
}
/*
is_empty(r, u) => ~is_nullable(r)
@ -398,10 +404,7 @@ namespace smt {
rewrite(d);
literal_vector lits;
expr_ref_pair_vector cofactors(m);
seq_rw().get_cofactors(d, cofactors);
// is_empty(r, u) => forall hd . cond => is_empty(r1, u union r)
get_cofactors(d, cofactors);
for (auto const& p : cofactors) {
if (is_member(p.second, u))
continue;

9
src/smt/seq_regex.h
View file

@ -63,12 +63,17 @@ namespace smt {
expr_ref unroll_non_empty(expr* r, expr_mark& seen, unsigned depth);
bool unfold_cofactors(expr_ref& r, literal_vector& conds);
bool is_member(expr* r, expr* u);
expr_ref symmetric_diff(expr* r1, expr* r2);
void get_cofactors(expr* r, expr_ref_vector& conds, expr_ref_pair_vector& result);
void get_cofactors(expr* r, expr_ref_pair_vector& result) {
expr_ref_vector conds(m);
get_cofactors(r, conds, result);
}
public:
seq_regex(theory_seq& th);