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seq

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2015-12-09 22:18:02 -08:00
parent c5a9d81d93
commit d58c219b54
2 changed files with 177 additions and 98 deletions
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267
src/smt/theory_seq.cpp
View file

@ -22,6 +22,7 @@ Revision History:
#include "smt_model_generator.h"
#include "theory_seq.h"
#include "seq_rewriter.h"
#include "ast_trail.h"
using namespace smt;
@ -118,7 +119,9 @@ theory_seq::theory_seq(ast_manager& m):
theory(m.mk_family_id("seq")),
m(m),
m_dam(m_dep_array_value_manager, m_alloc),
m_rep(m, m_dm),
m_rep(m, m_dm),
m_sort2len_fn(m),
m_factory(0),
m_ineqs(m),
m_exclude(m),
m_axioms(m),
@ -129,7 +132,7 @@ theory_seq::theory_seq(ast_manager& m):
m_rewrite(m),
m_util(m),
m_autil(m),
m_trail_stack(*this) {
m_trail_stack(*this) {
m_lhs.push_back(expr_array());
m_rhs.push_back(expr_array());
m_deps.push_back(enode_pair_dependency_array());
@ -506,6 +509,11 @@ bool theory_seq::internalize_term(app* term) {
!m_util.is_skolem(term)) {
set_incomplete(term);
}
expr* arg;
func_decl* fn;
if (m_util.str.is_length(term, arg) && !m_sort2len_fn.find(m.get_sort(arg), fn)) {
m_trail_stack.push(ast2ast_trail<theory_seq, sort, func_decl>(m_sort2len_fn, m.get_sort(arg), term->get_decl()));
}
return true;
}
@ -555,8 +563,7 @@ void theory_seq::collect_statistics(::statistics & st) const {
}
void theory_seq::init_model(model_generator & mg) {
m_factory = alloc(seq_factory, get_manager(),
get_family_id(), mg.get_model());
m_factory = alloc(seq_factory, get_manager(), get_family_id(), mg.get_model());
mg.register_factory(m_factory);
}
@ -575,7 +582,7 @@ model_value_proc * theory_seq::mk_value(enode * n, model_generator & mg) {
void theory_seq::set_incomplete(app* term) {
TRACE("seq", tout << "No support for: " << mk_pp(term, m) << "\n";);
if (!m_incomplete) {
m_trail_stack.push(value_trail<theory_seq,bool>(m_incomplete));
m_trail_stack.push(value_trail<theory_seq, bool>(m_incomplete));
m_incomplete = true;
}
}
@ -659,72 +666,73 @@ void theory_seq::create_axiom(expr_ref& e) {
}
/*
encode that s is not a proper prefix of xs
*/
expr_ref theory_seq::tightest_prefix(expr* s, expr* x) {
expr_ref s1 = mk_skolem(symbol("first"), s);
expr_ref c = mk_skolem(symbol("last"), s);
expr_ref fml(m);
fml = m.mk_and(m.mk_eq(s, m_util.str.mk_concat(s1, c)),
m.mk_eq(m_util.str.mk_length(c), m_autil.mk_int(1)),
m.mk_not(m_util.str.mk_contains(s, m_util.str.mk_concat(x, s1))));
return fml;
}
\brief nodes n1 and n2 are about to get merged.
if n1 occurs in the context of a length application,
then instantiate length axioms for each concatenation in the class of n2.
In this way we ensure that length respects concatenation.
*/
void theory_seq::new_eq_len_concat(enode* n1, enode* n2) {
context& ctx = get_context();
// TBD: walk use list of n1 for concat, walk use-list of n2 for length.
// instantiate length distributes over concatenation axiom.
SASSERT(n1->get_root() != n2->get_root());
if (!m_util.is_seq(n1->get_owner())) {
return;
}
func_decl* f_len = 0;
// TBD: extract length function for sort if it is used.
// TBD: add filter for already processed length equivalence classes
if (!f_len) {
if (!m_sort2len_fn.find(m.get_sort(n1->get_owner()), f_len)) {
return;
}
enode_vector::const_iterator it = ctx.begin_enodes_of(f_len);
enode* r1 = n1->get_root();
enode_vector::const_iterator it = ctx.begin_enodes_of(f_len);
enode_vector::const_iterator end = ctx.end_enodes_of(f_len);
bool has_concat = true;
for (; has_concat && it != end; ++it) {
if ((*it)->get_root() == n1->get_root()) {
enode* start2 = n2;
do {
if (m_util.str.is_concat(n2->get_owner())) {
has_concat = true;
add_len_concat_axiom(n2->get_owner());
}
n2 = n2->get_next();
}
while (n2 != start2);
}
bool has_len = false;
for (; !has_len && it != end; ++it) {
has_len = ((*it)->get_root() == r1);
}
if (!has_len) {
return;
}
enode* start2 = n2;
do {
if (m_util.str.is_concat(n2->get_owner())) {
expr_ref ln(m);
ln = m_util.str.mk_length(n2->get_owner());
add_len_axiom(ln);
}
n2 = n2->get_next();
}
while (n2 != start2);
}
void theory_seq::add_len_concat_axiom(expr* c) {
// or just internalize lc and have relevancy propagation create axiom?
expr *a, *b;
expr_ref la(m), lb(m), lc(m), fml(m);
VERIFY(m_util.str.is_concat(c, a, b));
la = m_util.str.mk_length(a);
lb = m_util.str.mk_length(b);
lc = m_util.str.mk_length(c);
fml = m.mk_eq(m_autil.mk_add(la, lb), lc);
create_axiom(fml);
/*
encode that s is not a proper prefix of xs1
where s1 is all of s, except the last element.
lit or s = "" or s = s1*c
lit or s = "" or len(c) = 1
lit or s = "" or !prefix(s, x*s1)
*/
void theory_seq::tightest_prefix(expr* s, expr* x, literal lit) {
expr_ref s1 = mk_skolem(symbol("first"), s);
expr_ref c = mk_skolem(symbol("last"), s);
expr_ref s1c(m_util.str.mk_concat(s1, c), m);
expr_ref lc(m_util.str.mk_length(c), m);
expr_ref one(m_autil.mk_int(1), m);
expr_ref emp(m_util.str.mk_empty(m.get_sort(s)), m);
literal s_eq_emp = mk_eq(s, emp, false);
add_axiom(lit, s_eq_emp, mk_eq(s, s1c, false));
add_axiom(lit, s_eq_emp, mk_eq(lc, one, false));
add_axiom(lit, s_eq_emp, ~mk_literal(m_util.str.mk_contains(s, m_util.str.mk_concat(x, s1))));
}
/*
let i = Index(s, t)
(!contains(s, t) -> i = -1)
(contains(s, t) & s = empty -> i = 0)
(contains(s, t) & s != empty -> t = xsy & tightest_prefix(s, x))
(s = empty -> i = 0)
(contains(s, t) & s != empty -> t = xsy)
(contains(s, t) -> tightest_prefix(s, x))
optional lemmas:
(len(s) > len(t) -> i = -1)
@ -733,43 +741,41 @@ void theory_seq::add_len_concat_axiom(expr* c) {
void theory_seq::add_indexof_axiom(expr* i) {
expr* s, *t;
VERIFY(m_util.str.is_index(i, s, t));
expr_ref cnt(m), fml(m), eq_empty(m);
expr_ref fml(m), emp(m), minus_one(m), zero(m), xsy(m);
expr_ref x = mk_skolem(m_contains_left_sym, s, t);
expr_ref y = mk_skolem(m_contains_right_sym, s, t);
eq_empty = m.mk_eq(s, m_util.str.mk_empty(m.get_sort(s)));
cnt = m_util.str.mk_contains(s, t);
fml = m.mk_or(cnt, m.mk_eq(i, m_autil.mk_int(-1)));
create_axiom(fml);
fml = m.mk_or(m.mk_not(cnt), m.mk_not(eq_empty), m.mk_eq(i, m_autil.mk_int(0)));
create_axiom(fml);
fml = m.mk_or(m.mk_not(cnt), eq_empty, m.mk_eq(t, m_util.str.mk_concat(x,s,y)));
create_axiom(fml);
fml = m.mk_or(m.mk_not(cnt), eq_empty, tightest_prefix(s, x));
create_axiom(fml);
minus_one = m_autil.mk_int(-1);
zero = m_autil.mk_int(0);
emp = m_util.str.mk_empty(m.get_sort(s));
xsy = m_util.str.mk_concat(x,s,y);
literal cnt = mk_literal(m_util.str.mk_contains(s, t));
literal eq_empty = mk_eq(s, emp, false);
add_axiom(cnt, mk_eq(i, minus_one, false));
add_axiom(~eq_empty, mk_eq(i, zero, false));
add_axiom(~cnt, eq_empty, mk_eq(t, xsy, false));
tightest_prefix(s, x, ~cnt);
}
/*
let r = replace(a, s, t)
(contains(s, a) -> r = xty & a = xsy & tightest_prefix(s,xs)) &
(contains(s, a) -> tightest_prefix(s,xs))
(contains(s, a) -> r = xty & a = xsy) &
(!contains(s, a) -> r = a)
*/
void theory_seq::add_replace_axiom(expr* r) {
expr* a, *s, *t;
VERIFY(m_util.str.is_replace(r, a, s, t));
expr_ref cnt(m), fml(m);
cnt = m_util.str.mk_contains(s, a);
expr_ref x = mk_skolem(m_contains_left_sym, s, a);
expr_ref y = mk_skolem(m_contains_right_sym, s, a);
fml = m.mk_or(m.mk_not(cnt), m.mk_eq(a, m_util.str.mk_concat(x, s, y)));
create_axiom(fml);
fml = m.mk_or(m.mk_not(cnt), m.mk_eq(r, m_util.str.mk_concat(x, t, y)));
create_axiom(fml);
fml = m.mk_or(m.mk_not(cnt), tightest_prefix(s, x));
create_axiom(fml);
fml = m.mk_or(cnt, m.mk_eq(r, a));
create_axiom(fml);
expr_ref xsy(m_util.str.mk_concat(x, t, y), m);
expr_ref xty(m_util.str.mk_concat(x, s, y), m);
literal cnt = mk_literal(m_util.str.mk_contains(s, a));
add_axiom(cnt, mk_eq(r, a, false));
add_axiom(~cnt, mk_eq(a, xsy, false));
add_axiom(~cnt, mk_eq(r, xty, false));
tightest_prefix(s, x, ~cnt);
}
/*
@ -781,27 +787,26 @@ void theory_seq::add_replace_axiom(expr* r) {
len(x) = rewrite(len(x))
*/
void theory_seq::add_len_axiom(expr* n) {
expr* x;
expr* x, *a, *b;
VERIFY(m_util.str.is_length(n, x));
expr_ref fml(m), eq1(m), eq2(m), nr(m);
eq1 = m.mk_eq(m_autil.mk_int(0), n);
eq2 = m.mk_eq(x, m_util.str.mk_empty(m.get_sort(x)));
fml = m_autil.mk_le(m_autil.mk_int(0), n);
create_axiom(fml);
fml = m.mk_or(m.mk_not(eq1), eq2);
create_axiom(fml);
fml = m.mk_or(m.mk_not(eq2), eq1);
create_axiom(fml);
nr = n;
m_rewrite(nr);
if (nr != n) {
fml = m.mk_eq(n, nr);
create_axiom(fml);
expr_ref zero(m), emp(m);
zero = m_autil.mk_int(0);
emp = m_util.str.mk_empty(m.get_sort(x));
literal eq1(mk_eq(zero, n, false));
literal eq2(mk_eq(x, emp, false));
add_axiom(mk_literal(m_autil.mk_le(zero, n)));
add_axiom(~eq1, eq2);
add_axiom(~eq2, eq1);
if (m_util.str.is_concat(n, a, b)) {
expr_ref _a(m_util.str.mk_length(a), m);
expr_ref _b(m_util.str.mk_length(b), m);
expr_ref a_p_b(m_autil.mk_add(_a, _b), m);
add_axiom(mk_eq(n, a_p_b, false));
}
}
/*
check semantics of extract.
TBD: check semantics of extract.
let e = extract(s, i, l)
@ -809,17 +814,73 @@ void theory_seq::add_len_axiom(expr* n) {
0 <= i < len(s) & l >= len(s) - i -> len(e) = len(s) - i
0 <= i < len(s) & 0 <= l < len(s) - i -> len(e) = l
0 <= i < len(s) & l < 0 -> len(e) = 0
i < 0 -> e = s
i >= len(s) -> e = empty
* i < 0 -> e = s
* i >= len(s) -> e = empty
*/
void theory_seq::add_extract_axiom(expr* e) {
expr* s, *i, *j;
VERIFY(m_util.str.is_extract(e, s, i, j));
expr_ref i_ge_0(m), i_le_j(m), j_lt_s(m);
NOT_IMPLEMENTED_YET();
expr* s, *i, *l;
VERIFY(m_util.str.is_extract(e, s, i, l));
expr_ref x(mk_skolem(symbol("extract_prefix"), s, e), m);
expr_ref ls(m_util.str.mk_length(s), m);
expr_ref lx(m_util.str.mk_length(x), m);
expr_ref le(m_util.str.mk_length(e), m);
expr_ref ls_minus_i(m_autil.mk_sub(ls, i), m);
expr_ref xe(m_util.str.mk_concat(x, e), m);
expr_ref zero(m_autil.mk_int(0), m);
literal i_ge_0 = mk_literal(m_autil.mk_ge(i, m_autil.mk_int(0)));
literal i_le_l = mk_literal(m_autil.mk_le(i, l));
literal i_ge_ls = mk_literal(m_autil.mk_ge(i, ls));
literal l_ge_ls = mk_literal(m_autil.mk_ge(l, ls));
literal l_ge_zero = mk_literal(m_autil.mk_ge(l, zero));
add_axiom(~i_ge_0, i_ge_ls, mk_literal(m_util.str.mk_prefix(xe, s)));
add_axiom(~i_ge_0, i_ge_ls, mk_eq(lx, i, false));
add_axiom(~i_ge_0, i_ge_ls, ~l_ge_ls, mk_eq(le, ls_minus_i, false));
add_axiom(~i_ge_0, i_ge_ls, l_ge_zero, mk_eq(le, zero, false));
}
/*
let e = at(s, i)
0 <= i < len(s) -> s = xey & len(x) = i & len(e) = 1
*/
void theory_seq::add_at_axiom(expr* e) {
expr* s, *i;
VERIFY(m_util.str.is_at(e, s, i));
expr_ref x(m), y(m), lx(m), le(m), xey(m), one(m), len_e(m), len_x(m);
x = mk_skolem(symbol("at_left"), s);
y = mk_skolem(symbol("at_right"), s);
xey = m_util.str.mk_concat(x, e, y);
one = m_autil.mk_int(1);
len_e = m_util.str.mk_length(e);
len_x = m_util.str.mk_length(x);
literal i_ge_0 = mk_literal(m_autil.mk_ge(i, m_autil.mk_int(0)));
literal i_ge_len_s = mk_literal(m_autil.mk_ge(i, m_util.str.mk_length(s)));
add_axiom(~i_ge_0, i_ge_len_s, mk_eq(s, xey, false));
add_axiom(~i_ge_0, i_ge_len_s, mk_eq(one, len_e, false));
add_axiom(~i_ge_0, i_ge_len_s, mk_eq(i, len_x, false));
}
literal theory_seq::mk_literal(expr* _e) {
expr_ref e(_e, m);
context& ctx = get_context();
ctx.internalize(e, false);
return ctx.get_literal(e);
}
void theory_seq::add_axiom(literal l1, literal l2, literal l3, literal l4) {
literal_vector lits;
if (l1 != null_literal) lits.push_back(l1);
if (l2 != null_literal) lits.push_back(l2);
if (l3 != null_literal) lits.push_back(l3);
if (l4 != null_literal) lits.push_back(l4);
get_context().mk_th_axiom(get_id(), lits.size(), lits.c_ptr());
}
void theory_seq::assert_axiom(expr_ref& e) {
@ -967,5 +1028,17 @@ void theory_seq::relevant_eh(app* n) {
if (m_util.str.is_length(n)) {
add_len_axiom(n);
}
else if (m_util.str.is_index(n)) {
add_indexof_axiom(n);
}
else if (m_util.str.is_replace(n)) {
add_replace_axiom(n);
}
else if (m_util.str.is_extract(n)) {
add_extract_axiom(n);
}
else if (m_util.str.is_at(n)) {
add_at_axiom(n);
}
}

8
src/smt/theory_seq.h
View file

@ -24,6 +24,7 @@ Revision History:
#include "theory_seq_empty.h"
#include "th_rewriter.h"
#include "union_find.h"
#include "ast_trail.h"
namespace smt {
@ -101,6 +102,7 @@ namespace smt {
vector<expr_array> m_lhs, m_rhs; // persistent sets of equalities.
vector<enode_pair_dependency_array> m_deps; // persistent sets of dependencies.
ast2ast_trailmap<sort, func_decl> m_sort2len_fn; // length functions per sort.
seq_factory* m_factory; // value factory
expr_ref_vector m_ineqs; // inequalities to check solution against
exclusion_table m_exclude; // set of asserted disequalities.
@ -168,15 +170,19 @@ namespace smt {
void assert_axiom(expr_ref& e);
void create_axiom(expr_ref& e);
void add_axiom(literal l1, literal l2 = null_literal, literal l3 = null_literal, literal l4 = null_literal);
void add_indexof_axiom(expr* e);
void add_replace_axiom(expr* e);
void add_extract_axiom(expr* e);
void add_len_concat_axiom(expr* c);
void add_len_axiom(expr* n);
void add_at_axiom(expr* n);
literal mk_literal(expr* n);
void tightest_prefix(expr* s, expr* x, literal lit);
void new_eq_len_concat(enode* n1, enode* n2);
expr_ref tightest_prefix(expr* s, expr* x);
expr_ref canonize(expr* e, enode_pair_dependency*& eqs);
expr_ref expand(expr* e, enode_pair_dependency*& eqs);
void add_dependency(enode_pair_dependency*& dep, enode* a, enode* b);