Many resources are needed to download a project. Please understand that we have to compensate our server costs. Thank you in advance. Project price only 1 $
You can buy this project and download/modify it how often you want.
/*++
Copyright (c) 2020 Microsoft Corporation
Module Name:
seq_regex.cpp
Abstract:
Solver for regexes
Author:
Nikolaj Bjorner (nbjorner) 2020-5-22
Margus Veanes 2021
--*/
#include "smt/seq_regex.h"
#include "smt/theory_seq.h"
#include "ast/expr_abstract.h"
#include "ast/ast_util.h"
#include "ast/for_each_expr.h"
#include
namespace smt {
seq_regex::seq_regex(theory_seq& th):
th(th),
ctx(th.get_context()),
m(th.get_manager()),
m_state_to_expr(m),
m_state_graph(state_graph::state_pp(this, pp_state)) { }
seq_util& seq_regex::u() { return th.m_util; }
class seq_util::rex& 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; }
arith_util& seq_regex::a() { return th.m_autil; }
void seq_regex::rewrite(expr_ref& e) { th.m_rewrite(e); }
/**
* is_string_equality holds of str.in_re s R,
*
* s in (all ++ x ++ all ++ y ++ all)
* =>
* s = fresh1 ++ x ++ fresh2 ++ y ++ fresh3
*
* TBD General rewrite possible:
*
* s in (R ++ Q)
* =>
* s = x ++ y and x in R and y in Q
*/
bool seq_regex::is_string_equality(literal lit) {
expr* s = nullptr, *r = nullptr;
expr* e = ctx.bool_var2expr(lit.var());
expr_ref id(a().mk_int(e->get_id()), m);
VERIFY(str().is_in_re(e, s, r));
sort* seq_sort = s->get_sort();
vector patterns;
auto mk_cont = [&](unsigned idx) {
return sk().mk("seq.cont", id, a().mk_int(idx), seq_sort);
};
unsigned idx = 0;
if (seq_rw().is_re_contains_pattern(r, patterns)) {
expr_ref_vector ts(m);
ts.push_back(mk_cont(idx));
for (auto const& p : patterns) {
ts.append(p);
ts.push_back(mk_cont(++idx));
}
expr_ref t = th.mk_concat(ts, seq_sort);
th.propagate_eq(lit, s, t, true);
return true;
}
return false;
}
/**
* Propagate the atom (str.in_re s r)
*
* Propagation implements the following inference rules
*
* (not (str.in_re s r)) => (str.in_re s (complement r))
* (str.in_re s r) => r != {}
*
* (str.in_re s r) => (accept s 0 r)
*/
void seq_regex::propagate_in_re(literal lit) {
expr* s = nullptr, *r = nullptr;
expr* e = ctx.bool_var2expr(lit.var());
VERIFY(str().is_in_re(e, s, r));
TRACE("seq_regex", tout << "propagate in RE: " << lit.sign() << " " << mk_pp(e, m) << std::endl;);
STRACE("seq_regex_brief", tout << "PIR(" << mk_pp(s, m) << ","
<< state_str(r) << ") ";);
// 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);
if (lit == nlit) {
// is-nullable doesn't simplify for regexes with uninterpreted subterms
th.add_unhandled_expr(fml);
}
th.propagate_lit(nullptr, 1, &lit, nlit);
return;
}
if (coallesce_in_re(lit)) {
TRACE("seq_regex", tout
<< "simplified conjunctions to an intersection" << std::endl;);
STRACE("seq_regex_brief", tout << "coallesce_in_re ";);
return;
}
if (is_string_equality(lit)) {
TRACE("seq_regex", tout
<< "simplified regex using string equality" << std::endl;);
STRACE("seq_regex_brief", tout << "string_eq ";);
return;
}
// Convert a non-ground sequence into an additional regex and
// strengthen the original regex constraint into an intersection
// for example:
// (x ++ "a" ++ y) in b*
// is coverted to
// (x ++ "a" ++ y) in intersect((.* ++ "a" ++ .*), b*)
expr_ref _r_temp_owner(m);
if (!m.is_value(s)) {
expr_ref s_approx = get_overapprox_regex(s);
if (!re().is_full_seq(s_approx)) {
r = re().mk_inter(r, s_approx);
_r_temp_owner = r;
TRACE("seq_regex", tout
<< "get_overapprox_regex(" << mk_pp(s, m)
<< ") = " << mk_pp(s_approx, m) << std::endl;);
STRACE("seq_regex_brief", tout
<< "overapprox=" << state_str(r) << " ";);
}
}
expr_ref zero(a().mk_int(0), m);
expr_ref acc(sk().mk_accept(s, zero, r), m);
literal acc_lit = th.mk_literal(acc);
TRACE("seq", tout << "propagate " << acc << "\n";);
//th.propagate_lit(nullptr, 1, &lit, acc_lit);
th.add_axiom(~lit, acc_lit);
}
/**
* Gets an overapproximating regex s_approx for the input string expression s.
* such that for any valuation v(s) of s, v(s) in L(s_approx).
* If the overapproximation is trivial then dotstar is returned.
*/
expr_ref seq_regex::get_overapprox_regex(expr* s) {
expr_ref s_to_re(re().mk_to_re(s), m);
expr_ref dotstar(re().mk_full_seq(s_to_re->get_sort()), m);
if (m.is_value(s))
return s_to_re;
if (str().is_concat(s)) {
expr_ref_vector es(m);
str().get_concat(s, es);
expr_ref s_approx(m), e_approx(m), last(m);
for (expr* e : es) {
e_approx = get_overapprox_regex(e);
if (!s_approx)
s_approx = e_approx;
else if (last != dotstar || e_approx != dotstar)
s_approx = re().mk_concat(s_approx, e_approx);
last = e_approx;
}
if (!s_approx)
s_approx = re().mk_epsilon(s->get_sort());
return s_approx;
}
expr* c = nullptr, *r1 = nullptr, *r2 = nullptr;
if (m.is_ite(s, c, r1, r2)) {
// if either branch approximates to .* then the result is also .*
expr_ref s_approx1 = get_overapprox_regex(r1);
if (re().is_full_seq(s_approx1))
return s_approx1;
expr_ref s_approx2 = get_overapprox_regex(r2);
if (re().is_full_seq(s_approx2))
return s_approx2;
return expr_ref(re().mk_union(s_approx1, s_approx2), m);
}
// TBD: other app expressions that can be approximated
return dotstar;
}
bool seq_regex::block_if_empty(expr* r, literal lit) {
auto info = re().get_info(r);
//if the minlength of the regex is UINT_MAX then the regex is a deadend
if (re().is_empty(r) || info.min_length == UINT_MAX) {
STRACE("seq_regex_brief", tout << "(empty) ";);
th.add_axiom(~lit);
return true;
}
if (info.interpreted) {
update_state_graph(r);
if (m_state_graph.is_dead(get_state_id(r))) {
STRACE("seq_regex_brief", tout << "(dead) ";);
th.add_axiom(~lit);
return true;
}
}
return false;
}
/**
* Propagate the atom (accept s i r)
*
* Propagation triggers updating the state graph for dead state detection:
* (accept s i r) => update_state_graph(r)
* (accept s i r) & dead(r) => false
*
* Propagation is also blocked under certain conditions to throttle
* state space exploration past a certain point: see block_unfolding
*
* Otherwise, propagation implements the following inference rules:
*
* Rule 1. (accept s i r) => len(s) >= i + min_len(r)
* Rule 2. (accept s i r) & len(s) <= i => nullable(r)
* (only necessary if min_len fails and returns 0 for non-nullable r)
* Rule 3. (accept s i r) and len(s) > i =>
* (accept s (i + 1) (derivative s[i] r)
*
* Acceptance of a derivative is unfolded into a disjunction over
* all derivatives. Effectively, this implements the following rule:
* (accept s i (ite c r1 r2)) => (ite c (accept s i r1) (accept s i r2))
*/
void seq_regex::propagate_accept(literal lit) {
SASSERT(!lit.sign());
expr* s = nullptr, *i = nullptr, *r = nullptr;
expr* e = ctx.bool_var2expr(lit.var());
unsigned idx = 0;
VERIFY(sk().is_accept(e, s, i, idx, r));
TRACE("seq_regex", tout << "propagate accept: "
<< mk_pp(e, m) << std::endl;);
STRACE("seq_regex_brief", tout << std::endl
<< "PA(" << mk_pp(s, m) << "@" << idx
<< "," << state_str(r) << ") ";);
if (block_if_empty(r, lit))
return;
if (block_unfolding(lit, idx)) {
STRACE("seq_regex_brief", tout << "(blocked) ";);
return;
}
STRACE("seq_regex_brief", tout << "(unfold) ";);
// Rule 1: use min_length to prune search
unsigned min_len = re().min_length(r);
unsigned min_len_plus_i = u().max_plus(min_len, idx);
literal len_s_ge_min = th.m_ax.mk_ge(th.mk_len(s), min_len_plus_i);
// Acc(s,i,r) ==> |s| >= i + minlength(r)
th.propagate_lit(nullptr, 1, &lit, len_s_ge_min);
// Axiom equivalent to the above: th.add_axiom(~lit, len_s_ge_min);
// Rule 2: nullable check
literal len_s_le_i = th.m_ax.mk_le(th.mk_len(s), idx);
if (min_len == 0) {
expr_ref is_nullable = is_nullable_wrapper(r);
if (m.is_false(is_nullable)) {
STRACE("seq_regex", tout
<< "Warning: min_length returned 0 for non-nullable regex"
<< std::endl;);
STRACE("seq_regex_brief", tout
<< " (Warning: min_length returned 0 for"
<< " non-nullable regex)";);
// since nullable(r) = false:
// Acc(s,i,r) ==> |s|>i
th.propagate_lit(nullptr, 1, &lit, ~len_s_le_i);
}
else if (!m.is_true(is_nullable)) {
// is_nullable did not simplify
STRACE("seq_regex", tout
<< "Warning: is_nullable did not simplify to true or false"
<< std::endl;);
STRACE("seq_regex_brief", tout
<< " (Warning: is_nullable did not simplify)";);
literal is_nullable_lit = th.mk_literal(is_nullable);
ctx.mark_as_relevant(is_nullable_lit);
// Acc(s,i,r) & |s|<=i ==> nullable(r)
th.add_axiom(~lit, ~len_s_le_i, is_nullable_lit);
//TODO: what if is_nullable contains an in_re
if (str().is_in_re(is_nullable))
th.add_unhandled_expr(is_nullable);
}
}
// Rule 3: derivative unfolding
literal_vector accept_next;
expr_ref s_i = th.mk_nth(s, i);
expr_ref deriv(m);
deriv = mk_derivative_wrapper(s_i, r);
STRACE("seq_regex", tout
<< "mk_derivative_wrapper: " << re().to_str(deriv) << std::endl;);
expr_ref accept_deriv(m);
accept_deriv = mk_deriv_accept(s, idx + 1, deriv);
accept_next.push_back(~lit);
accept_next.push_back(len_s_le_i);
accept_next.push_back(th.mk_literal(accept_deriv));
// Acc(s, i, r) => (|s|<=i or Acc(s, i+1, D(s_i,r)))
// where Acc(s, i+1, ite(c, t, f)) = ite(c, Acc(s, i+1, t), Acc(s, i+1, t))
// and Acc(s, i+1, r U s) = Acc(s, i+1, r) or Acc(s, i+1, s)
th.add_axiom(accept_next);
}
/**
* Put a limit to the unfolding of s.
*/
bool seq_regex::block_unfolding(literal lit, unsigned i) {
return
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),
true);
}
/**
* Combine a conjunction of membership relations for the same string
* within the same Regex.
*/
bool seq_regex::coallesce_in_re(literal lit) {
return false; // disabled
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;
enode* n1 = th.ensure_enode(entry.m_s);
enode* n2 = th.ensure_enode(s);
if (n1->get_root() != n2->get_root())
continue;
if (entry.m_re == regex)
continue;
th.m_trail_stack.push(vector_value_trail(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) << std::endl;);
regex = re().mk_inter(entry.m_re, regex);
rewrite(regex);
lits.push_back(~entry.m_lit);
if (n1 != n2)
lits.push_back(~th.mk_eq(n1->get_expr(), n2->get_expr(), false));
}
m_s_in_re.push_back(s_in_re(lit, s, regex));
th.get_trail_stack().push(push_back_vector>(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)));
th.add_axiom(lits);
return true;
}
expr_ref seq_regex::symmetric_diff(expr* r1, expr* r2) {
expr_ref r(m);
if (r1 == r2)
r = re().mk_empty(r1->get_sort());
else if (re().is_empty(r1))
r = r2;
else if (re().is_empty(r2))
r = r1;
else
r = re().mk_union(re().mk_diff(r1, r2), re().mk_diff(r2, r1));
rewrite(r);
return r;
}
/*
Wrapper around calls to is_nullable from the seq rewriter.
TODO: clean up the following:
Note: the is_nullable_wrapper and mk_derivative_wrapper actually use
different sequence rewriters; these are at:
m_seq_rewrite
(returned by seq_rw())
th.m_rewrite.m_imp->m_cfg.m_seq_rw
(private, can't be accessed directly)
As a result operations are cached separately for the nullable
and derivative calls.
*/
expr_ref seq_regex::is_nullable_wrapper(expr* r) {
STRACE("seq_regex", tout << "nullable: " << mk_pp(r, m) << std::endl;);
expr_ref result = seq_rw().is_nullable(r);
//TODO: rewrite seems unnecessary here
rewrite(result);
STRACE("seq_regex", tout << "nullable result: " << mk_pp(result, m) << std::endl;);
STRACE("seq_regex_brief", tout << "n(" << state_str(r) << ")="
<< mk_pp(result, m) << " ";);
return result;
}
/*
First creates a derivatrive of r wrt x=(:var 0) and then replaces x by ele.
This will create a cached entry for the generic derivative of r that is independent of ele.
*/
expr_ref seq_regex::mk_derivative_wrapper(expr* ele, expr* r) {
STRACE("seq_regex", tout << "derivative(" << mk_pp(ele, m) << "): " << mk_pp(r, m) << std::endl;);
// Uses canonical variable (:var 0) for the derivative element
// Substitute (:var 0) with the actual element
expr_ref der = seq_rw().mk_derivative(r);
var_subst subst(m);
der = subst(der, ele);
STRACE("seq_regex", tout << "derivative result: " << mk_pp(der, m) << std::endl;);
STRACE("seq_regex_brief", tout << "d(" << state_str(r) << ")="
<< state_str(der) << " ";);
//TODO: simplify der further, if ele implies further simplifications
//e.g. if ele='b' then de(ite (x='a') t f) simplifies to t
return der;
}
void seq_regex::propagate_eq(expr* r1, expr* r2) {
TRACE("seq_regex", tout << "propagate EQ: " << mk_pp(r1, m) << ", " << mk_pp(r2, m) << std::endl;);
STRACE("seq_regex_brief", tout << "PEQ ";);
sort* seq_sort = nullptr;
VERIFY(u().is_re(r1, seq_sort));
expr_ref r = symmetric_diff(r1, r2);
if (re().is_empty(r))
//trivially true
return;
expr_ref emp(re().mk_empty(r->get_sort()), m);
expr_ref f(m.mk_fresh_const("re.char", seq_sort), m);
expr_ref is_empty = sk().mk_is_empty(r, r, f);
// is_empty : (re,re,seq) -> Bool is a Skolem function
// f is a fresh internal Skolem constant of sort seq
// the literal is satisfiable when emptiness check succeeds
// meaning that r is not nullable and
// that all derivatives of r (if any) are also empty
// TBD: rewrite to use state_graph
th.add_axiom(~th.mk_eq(r1, r2, false), th.mk_literal(is_empty));
}
void seq_regex::propagate_ne(expr* r1, expr* r2) {
TRACE("seq_regex", tout << "propagate NEQ: " << mk_pp(r1, m) << ", " << mk_pp(r2, m) << std::endl;);
STRACE("seq_regex_brief", tout << "PNEQ ";);
sort* seq_sort = nullptr;
VERIFY(u().is_re(r1, seq_sort));
expr_ref r = symmetric_diff(r1, r2);
expr_ref emp(re().mk_empty(r->get_sort()), m);
expr_ref n(m.mk_fresh_const("re.char", seq_sort), m);
expr_ref is_non_empty = sk().mk_is_non_empty(r, r, n);
th.add_axiom(th.mk_eq(r1, r2, false), th.mk_literal(is_non_empty));
}
bool seq_regex::is_member(expr* r, expr* u) {
expr* u2 = nullptr;
while (re().is_union(u, u, u2)) {
if (r == u2)
return true;
}
return r == u;
}
/**
* is_non_empty(r, u) => nullable or \/_i (c_i and is_non_empty(r_i, u union r))
*
* for each (c_i, r_i) in cofactors (min-terms)
*
* is_non_empty(r_i, u union r) := false if r_i in u
*
*/
void seq_regex::propagate_is_non_empty(literal lit) {
expr* e = ctx.bool_var2expr(lit.var()), *r = nullptr, *u = nullptr, *n = nullptr;
VERIFY(sk().is_is_non_empty(e, r, u, n));
if (block_if_empty(r, lit))
return;
TRACE("seq_regex", tout << "propagate nonempty: " << mk_pp(e, m) << std::endl;);
STRACE("seq_regex_brief", tout
<< std::endl << "PNE(" << expr_id_str(e) << "," << state_str(r)
<< "," << expr_id_str(u) << "," << expr_id_str(n) << ") ";);
expr_ref is_nullable = is_nullable_wrapper(r);
if (m.is_true(is_nullable))
return;
literal null_lit = th.mk_literal(is_nullable);
expr_ref hd = mk_first(r, n);
expr_ref d(m);
d = mk_derivative_wrapper(hd, r);
literal_vector lits;
lits.push_back(~lit);
if (null_lit != false_literal)
lits.push_back(null_lit);
expr_ref_pair_vector cofactors(m);
get_cofactors(d, cofactors);
for (auto const& p : cofactors) {
if (is_member(p.second, u))
continue;
expr_ref cond(p.first, m);
seq_rw().elim_condition(hd, cond);
rewrite(cond);
if (m.is_false(cond))
continue;
expr_ref next_non_empty = sk().mk_is_non_empty(p.second, re().mk_union(u, p.second), n);
if (!m.is_true(cond))
next_non_empty = m.mk_and(cond, next_non_empty);
lits.push_back(th.mk_literal(next_non_empty));
}
th.add_axiom(lits);
}
/*
Given a string s, index i, and a derivative r, return an
expression that is equivalent to
accept s i r
but which pushes accept s i r into the leaves
Input r is of type regex; output is of type bool.
Example:
mk_deriv_accept(s, i, (ite a r1 r2) u (ite b r3 r4))
= (or (ite a (accept s i r1) (accept s i r2))
(ite b (accept s i r3) (accept s i r4)))
*/
expr_ref seq_regex::mk_deriv_accept(expr* s, unsigned i, expr* r) {
vector to_visit;
to_visit.push_back(r);
obj_map re_to_accept;
expr_ref_vector _temp_bool_owner(m); // temp owner for bools we create
bool s_is_longer_than_i = str().min_length(s) > i;
expr* i_int = a().mk_int(i);
_temp_bool_owner.push_back(i_int);
// DFS, avoids duplicating derivative construction that has already been done
while (to_visit.size() > 0) {
expr* e = to_visit.back();
expr* econd = nullptr, *e1 = nullptr, *e2 = nullptr;
if (!re_to_accept.contains(e)) {
// First visit: add children
STRACE("seq_regex_verbose", tout << "1";);
if (m.is_ite(e, econd, e1, e2) ||
re().is_union(e, e1, e2)) {
to_visit.push_back(e1);
to_visit.push_back(e2);
}
// Mark first visit by adding nullptr to the map
re_to_accept.insert(e, nullptr);
}
else if (re_to_accept.find(e) == nullptr) {
// Second visit: set value
STRACE("seq_regex_verbose", tout << "2";);
to_visit.pop_back();
if (m.is_ite(e, econd, e1, e2)) {
expr* b1 = re_to_accept.find(e1);
expr* b2 = re_to_accept.find(e2);
expr* b = m.is_true(econd) || b1 == b2 ? b1 : m.is_false(econd) ? b2 : m.mk_ite(econd, b1, b2);
_temp_bool_owner.push_back(b);
re_to_accept.find(e) = b;
}
else if (re().is_empty(e) || (s_is_longer_than_i && re().is_epsilon(e)))
{
// s[i..] in [] <==> false, also: s[i..] in () <==> false when |s|>i
re_to_accept.find(e) = m.mk_false();
}
else if (re().is_full_seq(e) || (s_is_longer_than_i && re().is_dot_plus(e)))
{
// s[i..] in .* <==> true, also: s[i..] in .+ <==> true when |s|>i
re_to_accept.find(e) = m.mk_true();
}
else if (re().is_union(e, e1, e2)) {
expr* b1 = re_to_accept.find(e1);
expr* b2 = re_to_accept.find(e2);
expr* b = m.is_false(b1) || b1 == b2 ? b2 : m.is_false(b2) ? b1 : m.mk_or(b1, b2);
_temp_bool_owner.push_back(b);
re_to_accept.find(e) = b;
}
else {
expr_ref acc_leaf = sk().mk_accept(s, i_int, e);
_temp_bool_owner.push_back(acc_leaf);
re_to_accept.find(e) = acc_leaf;
STRACE("seq_regex_verbose", tout
<< "mk_deriv_accept: added accept leaf: "
<< mk_pp(acc_leaf, m) << std::endl;);
}
}
else {
STRACE("seq_regex_verbose", tout << "3";);
// Remaining visits: skip
to_visit.pop_back();
}
}
// Finalize
expr_ref result(m);
result = re_to_accept.find(r); // Assigns ownership of all exprs in
// re_to_accept for after this completes
rewrite(result);
return result;
}
/*
Return a list of all target regexes in the derivative of a regex r,
ignoring the conditions along each path.
The derivative construction uses (:var 0) and tries
to eliminate unsat condition paths but it does not perform
full satisfiability checks and it is not guaranteed
that all targets are actually reachable
*/
void seq_regex::get_derivative_targets(expr* r, expr_ref_vector& targets) {
// constructs the derivative wrt (:var 0)
expr_ref d(seq_rw().mk_derivative(r), m);
// use DFS to collect all the targets (leaf regexes) in d.
expr* _1 = nullptr, * e1 = nullptr, * e2 = nullptr;
obj_hashtable::entry* _2 = nullptr;
vector workset;
workset.push_back(d);
obj_hashtable done;
done.insert(d);
while (workset.size() > 0) {
expr* e = workset.back();
workset.pop_back();
if (m.is_ite(e, _1, e1, e2) || re().is_union(e, e1, e2)) {
if (done.insert_if_not_there_core(e1, _2))
workset.push_back(e1);
if (done.insert_if_not_there_core(e2, _2))
workset.push_back(e2);
}
else if (!re().is_empty(e))
targets.push_back(e);
}
}
/*
Return a list of all (cond, leaf) pairs in a given derivative
expression r.
Note: this implementation is inefficient: it simply collects all expressions under an if and
iterates over all combinations.
This method is still used by:
propagate_is_empty
propagate_is_non_empty
*/
void seq_regex::get_cofactors(expr* r, expr_ref_pair_vector& result) {
obj_hashtable ifs;
expr* cond = nullptr, * r1 = nullptr, * r2 = nullptr;
for (expr* e : subterms::ground(expr_ref(r, m)))
if (m.is_ite(e, cond, r1, r2))
ifs.insert(cond);
expr_ref_vector rs(m);
vector conds;
conds.push_back(expr_ref_vector(m));
rs.push_back(r);
for (expr* c : ifs) {
unsigned sz = conds.size();
expr_safe_replace rep1(m);
expr_safe_replace rep2(m);
rep1.insert(c, m.mk_true());
rep2.insert(c, m.mk_false());
expr_ref r2(m);
for (unsigned i = 0; i < sz; ++i) {
expr_ref_vector cs = conds[i];
cs.push_back(mk_not(m, c));
conds.push_back(cs);
conds[i].push_back(c);
expr_ref r1(rs.get(i), m);
rep1(r1, r2);
rs[i] = r2;
rep2(r1, r2);
rs.push_back(r2);
}
}
for (unsigned i = 0; i < conds.size(); ++i) {
expr_ref conj = mk_and(conds[i]);
expr_ref r(rs.get(i), m);
ctx.get_rewriter()(r);
if (!m.is_false(conj) && !re().is_empty(r))
result.push_back(conj, r);
}
}
/*
is_empty(r, u) => ~is_nullable(r)
is_empty(r, u) => (forall x . ~cond(x)) or is_empty(r1, u union r) for (cond, r) in min-terms(D(x,r))
is_empty(r, u) is true if r is a member of u
*/
void seq_regex::propagate_is_empty(literal lit) {
expr* e = ctx.bool_var2expr(lit.var()), *r = nullptr, *u = nullptr, *n = nullptr;
VERIFY(sk().is_is_empty(e, r, u, n));
expr_ref is_nullable = is_nullable_wrapper(r);
TRACE("seq_regex", tout << "propagate empty: " << mk_pp(e, m) << std::endl;);
STRACE("seq_regex_brief", tout
<< std::endl << "PE(" << expr_id_str(e) << "," << state_str(r)
<< "," << expr_id_str(u) << "," << expr_id_str(n) << ") ";);
if (m.is_true(is_nullable)) {
th.add_axiom(~lit);
return;
}
th.add_axiom(~lit, ~th.mk_literal(is_nullable));
expr_ref hd = mk_first(r, n);
expr_ref d(m);
d = mk_derivative_wrapper(hd, r);
literal_vector lits;
expr_ref_pair_vector cofactors(m);
get_cofactors(d, cofactors);
for (auto const& p : cofactors) {
if (is_member(p.second, u))
continue;
expr_ref cond(p.first, m);
seq_rw().elim_condition(hd, cond);
rewrite(cond);
if (m.is_false(cond))
continue;
lits.reset();
lits.push_back(~lit);
if (!m.is_true(cond)) {
expr_ref ncond(mk_not(m, cond), m);
lits.push_back(th.mk_literal(mk_forall(m, hd, ncond)));
}
expr_ref is_empty1 = sk().mk_is_empty(p.second, re().mk_union(u, p.second), n);
lits.push_back(th.mk_literal(is_empty1));
th.add_axiom(lits);
}
}
expr_ref seq_regex::mk_first(expr* r, expr* n) {
sort* elem_sort = nullptr, *seq_sort = nullptr;
VERIFY(u().is_re(r, seq_sort));
VERIFY(u().is_seq(seq_sort, elem_sort));
return sk().mk("re.first", n, a().mk_int(r->get_id()), elem_sort);
}
/**
* Dead state elimination using the state_graph class
*/
unsigned seq_regex::get_state_id(expr* e) {
// Assign increasing IDs starting from 1
if (!m_expr_to_state.contains(e)) {
m_state_to_expr.push_back(e);
unsigned new_id = m_state_to_expr.size();
m_expr_to_state.insert(e, new_id);
STRACE("seq_regex_brief", tout << "new(" << expr_id_str(e)
<< ")=" << state_str(e) << " ";);
STRACE("seq_regex", tout
<< "New state ID: " << new_id
<< " = " << mk_pp(e, m) << std::endl;);
SASSERT(get_expr_from_id(new_id) == e);
}
return m_expr_to_state.find(e);
}
expr* seq_regex::get_expr_from_id(unsigned id) {
SASSERT(id >= 1);
SASSERT(id <= m_state_to_expr.size());
return m_state_to_expr.get(id - 1);
}
bool seq_regex::can_be_in_cycle(expr *r1, expr *r2) {
// TBD: This can be used to optimize the state graph:
// return false here if it is known that r1 -> r2 can never be
// in a cycle. There are various easy syntactic checks on r1 and r2
// that can be used to infer this (e.g. star height, or length if
// both are star-free).
// This check need not be sound, but if it is not, some dead states
// will be missed.
return true;
}
/*
Update the state graph with expression r and all its derivatives.
*/
bool seq_regex::update_state_graph(expr* r) {
unsigned r_id = get_state_id(r);
if (m_state_graph.is_done(r_id)) return false;
if (m_state_graph.get_size() >= m_max_state_graph_size) {
STRACE("seq_regex", tout << "Warning: ignored state graph update -- max size of seen states reached!" << std::endl;);
STRACE("seq_regex_brief", tout << "(MAX SIZE REACHED) ";);
return false;
}
STRACE("seq_regex", tout << "Updating state graph for regex "
<< mk_pp(r, m) << ") ";);
STRACE("state_graph",
if (!m_state_graph.is_seen(r_id))
tout << std::endl << "state(" << r_id << ") = " << re().to_str(r) << std::endl << "info(" << r_id << ") = " << re().get_info(r) << std::endl;);
// Add state
m_state_graph.add_state(r_id);
STRACE("seq_regex", tout << "Updating state graph for regex "
<< mk_pp(r, m) << ") " << std::endl;);
STRACE("seq_regex_brief", tout << std::endl << "USG("
<< state_str(r) << ") ";);
expr_ref r_nullable = is_nullable_wrapper(r);
if (m.is_true(r_nullable)) {
m_state_graph.mark_live(r_id);
}
else {
// Add edges to all derivatives
expr_ref_vector derivatives(m);
STRACE("seq_regex_verbose", tout
<< "getting all derivs: " << r_id << " " << std::endl;);
get_derivative_targets(r, derivatives);
for (auto const& dr: derivatives) {
unsigned dr_id = get_state_id(dr);
STRACE("seq_regex_verbose", tout
<< std::endl << " traversing deriv: " << dr_id << " ";);
STRACE("state_graph",
if (!m_state_graph.is_seen(dr_id))
tout << "state(" << dr_id << ") = " << re().to_str(dr) << std::endl << "info(" << dr_id << ") = " << re().get_info(dr) << std::endl;);
// Add state
m_state_graph.add_state(dr_id);
bool maybecycle = can_be_in_cycle(r, dr);
m_state_graph.add_edge(r_id, dr_id, maybecycle);
}
m_state_graph.mark_done(r_id);
}
STRACE("seq_regex", m_state_graph.display(tout););
STRACE("seq_regex_brief", tout << std::endl;);
STRACE("seq_regex_brief", m_state_graph.display(tout););
return true;
}
std::string seq_regex::state_str(expr* e) {
if (m_expr_to_state.contains(e))
return std::to_string(get_state_id(e));
else
return expr_id_str(e);
}
std::string seq_regex::expr_id_str(expr* e) {
return std::string("id") + std::to_string(e->get_id());
}
}
