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z3/src/ast/macros/macro_util.cpp
Nikolaj Bjorner 520ce9a5ee integrate lambda expressions 
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2018-06-26 07:23:04 -07:00

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/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
macro_util.cpp
Abstract:
Macro finding goodies.
They are used during preprocessing (MACRO_FINDER=true), and model building.
Author:
Leonardo de Moura (leonardo) 2010-12-15.
Revision History:
--*/
#include "ast/macros/macro_util.h"
#include "ast/occurs.h"
#include "ast/ast_util.h"
#include "ast/rewriter/var_subst.h"
#include "ast/ast_pp.h"
#include "ast/ast_ll_pp.h"
#include "ast/for_each_expr.h"
#include "ast/well_sorted.h"
#include "ast/rewriter/bool_rewriter.h"
macro_util::macro_util(ast_manager & m):
m_manager(m),
m_bv(m),
m_arith(m),
m_arith_rw(m),
m_bv_rw(m),
m_forbidden_set(nullptr),
m_curr_clause(nullptr) {
}
bool macro_util::is_bv(expr * n) const {
return m_bv.is_bv(n);
}
bool macro_util::is_bv_sort(sort * s) const {
return m_bv.is_bv_sort(s);
}
bool macro_util::is_add(expr * n) const {
return m_arith.is_add(n) || m_bv.is_bv_add(n);
}
bool macro_util::is_times_minus_one(expr * n, expr * & arg) const {
return m_arith_rw.is_times_minus_one(n, arg) || m_bv_rw.is_times_minus_one(n, arg);
}
bool macro_util::is_le(expr * n) const {
return m_arith.is_le(n) || m_bv.is_bv_ule(n) || m_bv.is_bv_sle(n);
}
bool macro_util::is_le_ge(expr * n) const {
return m_arith.is_ge(n) || m_arith.is_le(n) || m_bv.is_bv_ule(n) || m_bv.is_bv_sle(n);
}
bool macro_util::is_var_plus_ground(expr * n, bool & inv, var * & v, expr_ref & t) {
return m_arith_rw.is_var_plus_ground(n, inv, v, t) || m_bv_rw.is_var_plus_ground(n, inv, v, t);
}
bool macro_util::is_zero_safe(expr * n) const {
if (m_bv_rw.is_bv(n)) {
return m_bv.is_zero(n);
}
else {
return m_arith_rw.is_zero(n);
}
}
app * macro_util::mk_zero(sort * s) const {
if (m_bv.is_bv_sort(s)) {
return m_bv.mk_numeral(rational(0), s);
}
else {
return m_arith.mk_numeral(rational(0), s);
}
}
void macro_util::mk_sub(expr * t1, expr * t2, expr_ref & r) const {
if (is_bv(t1)) {
m_bv_rw.mk_sub(t1, t2, r);
}
else {
m_arith_rw.mk_sub(t1, t2, r);
}
}
void macro_util::mk_add(expr * t1, expr * t2, expr_ref & r) const {
if (is_bv(t1)) {
m_bv_rw.mk_add(t1, t2, r);
}
else {
m_arith_rw.mk_add(t1, t2, r);
}
}
void macro_util::mk_add(unsigned num_args, expr * const * args, sort * s, expr_ref & r) const {
switch (num_args) {
case 0:
r = mk_zero(s);
break;
case 1:
r = args[0];
break;
default:
if (m_bv.is_bv_sort(s)) {
r = args[0];
while (num_args >= 2) {
--num_args;
++args;
r = m_bv.mk_bv_add(r, args[0]);
}
}
else {
r = m_arith.mk_add(num_args, args);
}
break;
}
}
/**
\brief Return true if \c n is an application of the form
(f x_{k_1}, ..., x_{k_n})
where f is uninterpreted
n == num_decls
x_{k_i}'s are variables
and {k_1, ..., k_n } is equals to the set {0, ..., num_decls-1}
*/
bool macro_util::is_macro_head(expr * n, unsigned num_decls) const {
if (is_app(n) &&
!to_app(n)->get_decl()->is_associative() &&
to_app(n)->get_family_id() == null_family_id &&
to_app(n)->get_num_args() == num_decls) {
sbuffer<int> var2pos;
var2pos.resize(num_decls, -1);
for (unsigned i = 0; i < num_decls; i++) {
expr * c = to_app(n)->get_arg(i);
if (!is_var(c))
return false;
unsigned idx = to_var(c)->get_idx();
if (idx >= num_decls || var2pos[idx] != -1)
return false;
var2pos[idx] = i;
}
return true;
}
return false;
}
/**
\brief Return true if n is of the form
(= (f x_{k_1}, ..., x_{k_n}) t) OR
(iff (f x_{k_1}, ..., x_{k_n}) t)
where
is_macro_head((f x_{k_1}, ..., x_{k_n})) returns true AND
t does not contain f AND
f is not in forbidden_set
In case of success
head will contain (f x_{k_1}, ..., x_{k_n}) AND
def will contain t
*/
bool macro_util::is_left_simple_macro(expr * n, unsigned num_decls, app_ref & head, expr_ref & def) const {
if (m_manager.is_eq(n)) {
expr * lhs = to_app(n)->get_arg(0);
expr * rhs = to_app(n)->get_arg(1);
if (is_macro_head(lhs, num_decls) && !is_forbidden(to_app(lhs)->get_decl()) &&
!occurs(to_app(lhs)->get_decl(), rhs)) {
head = to_app(lhs);
def = rhs;
return true;
}
}
return false;
}
/**
\brief Return true if n is of the form
(= t (f x_{k_1}, ..., x_{k_n})) OR
(iff t (f x_{k_1}, ..., x_{k_n}))
where
is_macro_head((f x_{k_1}, ..., x_{k_n})) returns true AND
t does not contain f AND
f is not in forbidden_set
In case of success
head will contain (f x_{k_1}, ..., x_{k_n}) AND
def will contain t
*/
bool macro_util::is_right_simple_macro(expr * n, unsigned num_decls, app_ref & head, expr_ref & def) const {
if (m_manager.is_eq(n)) {
expr * lhs = to_app(n)->get_arg(0);
expr * rhs = to_app(n)->get_arg(1);
if (is_macro_head(rhs, num_decls) && !is_forbidden(to_app(rhs)->get_decl()) &&
!occurs(to_app(rhs)->get_decl(), lhs)) {
head = to_app(rhs);
def = lhs;
return true;
}
}
return false;
}
/**
\brief Return true if n contains f. The method ignores the sub-expression \c exception.
\remark n is a "polynomial".
*/
bool macro_util::poly_contains_head(expr * n, func_decl * f, expr * exception) const {
unsigned num_args;
expr * const * args;
if (is_add(n)) {
num_args = to_app(n)->get_num_args();
args = to_app(n)->get_args();
}
else {
num_args = 1;
args = &n;
}
for (unsigned i = 0; i < num_args; i++) {
expr * arg = args[i];
if (arg != exception && occurs(f, arg))
return true;
}
return false;
}
bool macro_util::is_arith_macro(expr * n, unsigned num_decls, app_ref & head, expr_ref & def, bool & inv) const {
// TODO: obsolete... we should move to collect_arith_macro_candidates
if (!m_manager.is_eq(n) && !m_arith.is_le(n) && !m_arith.is_ge(n))
return false;
expr * lhs = to_app(n)->get_arg(0);
expr * rhs = to_app(n)->get_arg(1);
if (!m_arith.is_numeral(rhs))
return false;
inv = false;
ptr_buffer<expr> args;
expr * h = nullptr;
unsigned lhs_num_args;
expr * const * lhs_args;
if (is_add(lhs)) {
lhs_num_args = to_app(lhs)->get_num_args();
lhs_args = to_app(lhs)->get_args();
}
else {
lhs_num_args = 1;
lhs_args = &lhs;
}
for (unsigned i = 0; i < lhs_num_args; i++) {
expr * arg = lhs_args[i];
expr * neg_arg;
if (h == nullptr &&
is_macro_head(arg, num_decls) &&
!is_forbidden(to_app(arg)->get_decl()) &&
!poly_contains_head(lhs, to_app(arg)->get_decl(), arg)) {
h = arg;
}
else if (h == nullptr && m_arith_rw.is_times_minus_one(arg, neg_arg) &&
is_macro_head(neg_arg, num_decls) &&
!is_forbidden(to_app(neg_arg)->get_decl()) &&
!poly_contains_head(lhs, to_app(neg_arg)->get_decl(), arg)) {
h = neg_arg;
inv = true;
}
else {
args.push_back(arg);
}
}
if (h == nullptr)
return false;
head = to_app(h);
expr_ref tmp(m_manager);
tmp = m_arith.mk_add(args.size(), args.c_ptr());
if (inv)
mk_sub(tmp, rhs, def);
else
mk_sub(rhs, tmp, def);
TRACE("macro_util", tout << def << "\n";);
return true;
}
/**
\brief Auxiliary function for is_pseudo_predicate_macro. It detects the pattern (= (f X) t)
*/
bool macro_util::is_pseudo_head(expr * n, unsigned num_decls, app_ref & head, app_ref & t) {
if (!m_manager.is_eq(n))
return false;
expr * lhs = to_app(n)->get_arg(0);
expr * rhs = to_app(n)->get_arg(1);
if (!is_ground(lhs) && !is_ground(rhs))
return false;
sort * s = m_manager.get_sort(lhs);
if (m_manager.is_uninterp(s))
return false;
sort_size sz = s->get_num_elements();
if (sz.is_finite() && sz.size() == 1)
return false;
if (is_macro_head(lhs, num_decls)) {
head = to_app(lhs);
t = to_app(rhs);
return true;
}
if (is_macro_head(rhs, num_decls)) {
head = to_app(rhs);
t = to_app(lhs);
return true;
}
return false;
}
/**
\brief Returns true if n if of the form (forall (X) (iff (= (f X) t) def[X]))
where t is a ground term, (f X) is the head.
*/
bool macro_util::is_pseudo_predicate_macro(expr * n, app_ref & head, app_ref & t, expr_ref & def) {
if (!is_forall(n))
return false;
TRACE("macro_util", tout << "processing: " << mk_pp(n, m_manager) << "\n";);
expr * body = to_quantifier(n)->get_expr();
unsigned num_decls = to_quantifier(n)->get_num_decls();
expr * lhs, *rhs;
if (!m_manager.is_iff(body, lhs, rhs))
return false;
if (is_pseudo_head(lhs, num_decls, head, t) &&
!is_forbidden(head->get_decl()) &&
!occurs(head->get_decl(), rhs)) {
def = rhs;
return true;
}
if (is_pseudo_head(rhs, num_decls, head, t) &&
!is_forbidden(head->get_decl()) &&
!occurs(head->get_decl(), lhs)) {
def = lhs;
return true;
}
return false;
}
/**
\brief A quasi-macro head is of the form f[X_1, ..., X_n],
where n == num_decls, f[X_1, ..., X_n] is a term starting with symbol f, f is uninterpreted,
contains all universally quantified variables as arguments.
Note that, some arguments of f[X_1, ..., X_n] may not be variables.
Examples of quasi-macros:
f(x_1, x_1 + x_2, x_2) for num_decls == 2
g(x_1, x_1) for num_decls == 1
Return true if \c n is a quasi-macro. Store the macro head in \c head, and the conditions to apply the macro in \c cond.
*/
bool macro_util::is_quasi_macro_head(expr * n, unsigned num_decls) const {
if (is_app(n) &&
to_app(n)->get_family_id() == null_family_id &&
to_app(n)->get_num_args() >= num_decls) {
unsigned num_args = to_app(n)->get_num_args();
sbuffer<bool> found_vars;
found_vars.resize(num_decls, false);
unsigned num_found_vars = 0;
for (unsigned i = 0; i < num_args; i++) {
expr * arg = to_app(n)->get_arg(i);
if (is_var(arg)) {
unsigned idx = to_var(arg)->get_idx();
if (idx >= num_decls)
return false;
if (found_vars[idx] == false) {
found_vars[idx] = true;
num_found_vars++;
}
}
else {
if (occurs(to_app(n)->get_decl(), arg))
return false;
}
}
return num_found_vars == num_decls;
}
return false;
}
/**
\brief Convert a quasi-macro head into a macro head, and store the conditions under
which it is valid in cond.
*/
void macro_util::quasi_macro_head_to_macro_head(app * qhead, unsigned & num_decls, app_ref & head, expr_ref & cond) const {
unsigned num_args = qhead->get_num_args();
sbuffer<bool> found_vars;
found_vars.resize(num_decls, false);
ptr_buffer<expr> new_args;
ptr_buffer<expr> new_conds;
unsigned next_var_idx = num_decls;
for (unsigned i = 0; i < num_args; i++) {
expr * arg = qhead->get_arg(i);
if (is_var(arg)) {
unsigned idx = to_var(arg)->get_idx();
SASSERT(idx < num_decls);
if (found_vars[idx] == false) {
found_vars[idx] = true;
new_args.push_back(arg);
continue;
}
}
var * new_var = m_manager.mk_var(next_var_idx, m_manager.get_sort(arg));
next_var_idx++;
expr * new_cond = m_manager.mk_eq(new_var, arg);
new_args.push_back(new_var);
new_conds.push_back(new_cond);
}
bool_rewriter(m_manager).mk_and(new_conds.size(), new_conds.c_ptr(), cond);
head = m_manager.mk_app(qhead->get_decl(), new_args.size(), new_args.c_ptr());
num_decls = next_var_idx;
}
/**
\brief Given a macro defined by head and def, stores an interpretation for head->get_decl() in interp.
This method assumes is_macro_head(head, head->get_num_args()) returns true,
and def does not contain head->get_decl().
See normalize_expr
*/
void macro_util::mk_macro_interpretation(app * head, unsigned num_decls, expr * def, expr_ref & interp) const {
SASSERT(is_macro_head(head, head->get_num_args()));
SASSERT(!occurs(head->get_decl(), def));
normalize_expr(head, num_decls, def, interp);
}
/**
\brief The variables in head may be in the wrong order.
Example: f(x_1, x_0) instead of f(x_0, x_1)
This method is essentially renaming the variables in t.
Suppose t is g(x_1, x_0 + x_1)
This method will store g(x_0, x_1 + x_0) in norm_t.
f(x_1, x_2) --> f(x_0, x_1)
f(x_3, x_2) --> f(x_0, x_1)
*/
void macro_util::normalize_expr(app * head, unsigned num_decls, expr * t, expr_ref & norm_t) const {
expr_ref_buffer var_mapping(m_manager);
var_mapping.resize(num_decls);
bool changed = false;
unsigned num_args = head->get_num_args();
TRACE("macro_util",
tout << "head: " << mk_pp(head, m_manager) << "\n";
tout << "applying substitution to:\n" << mk_bounded_pp(t, m_manager) << "\n";);
for (unsigned i = 0; i < num_args; i++) {
var * v = to_var(head->get_arg(i));
unsigned vi = v->get_idx();
SASSERT(vi < num_decls);
if (vi != i) {
changed = true;
var_ref new_var(m_manager.mk_var(i, v->get_sort()), m_manager);
var_mapping.setx(num_decls - vi - 1, new_var);
}
else
var_mapping.setx(num_decls - i - 1, v);
}
if (changed) {
// REMARK: t may have nested quantifiers... So, I must use the std order for variable substitution.
var_subst subst(m_manager, true);
TRACE("macro_util",
tout << "head: " << mk_pp(head, m_manager) << "\n";
tout << "applying substitution to:\n" << mk_ll_pp(t, m_manager) << "\nsubstitution:\n";
for (unsigned i = 0; i < var_mapping.size(); i++) {
if (var_mapping[i] != 0)
tout << "#" << i << " -> " << mk_ll_pp(var_mapping[i], m_manager);
});
norm_t = subst(t, var_mapping.size(), var_mapping.c_ptr());
}
else {
norm_t = t;
}
}
// -----------------------------
//
// "Hint" support
// See comment at is_hint_atom
// for a definition of what a hint is.
//
// -----------------------------
bool is_hint_head(expr * n, ptr_buffer<var> & vars) {
if (!is_app(n))
return false;
if (to_app(n)->get_decl()->is_associative() || to_app(n)->get_family_id() != null_family_id)
return false;
unsigned num_args = to_app(n)->get_num_args();
for (unsigned i = 0; i < num_args; i++) {
expr * arg = to_app(n)->get_arg(i);
if (is_var(arg))
vars.push_back(to_var(arg));
}
return !vars.empty();
}
/**
\brief Returns true if the variables in n is a subset of \c vars.
*/
bool vars_of_is_subset(expr * n, ptr_buffer<var> const & vars) {
if (is_ground(n))
return true;
obj_hashtable<expr> visited;
ptr_buffer<expr> todo;
todo.push_back(n);
while (!todo.empty()) {
expr * curr = todo.back();
todo.pop_back();
if (is_var(curr)) {
if (std::find(vars.begin(), vars.end(), to_var(curr)) == vars.end())
return false;
}
else if (is_app(curr)) {
unsigned num_args = to_app(curr)->get_num_args();
for (unsigned i = 0; i < num_args; i++) {
expr * arg = to_app(curr)->get_arg(i);
if (is_ground(arg))
continue;
if (visited.contains(arg))
continue;
visited.insert(arg);
todo.push_back(arg);
}
}
else {
SASSERT(is_quantifier(curr));
return false; // do no support nested quantifier... being conservative.
}
}
return true;
}
/**
\brief (= lhs rhs) is a hint atom if
lhs is of the form (f t_1 ... t_n)
and all variables occurring in rhs are direct arguments of lhs.
*/
bool is_hint_atom(expr * lhs, expr * rhs) {
ptr_buffer<var> vars;
if (!is_hint_head(lhs, vars))
return false;
return !occurs(to_app(lhs)->get_decl(), rhs) && vars_of_is_subset(rhs, vars);
}
void hint_to_macro_head(ast_manager & m, app * head, unsigned & num_decls, app_ref & new_head) {
unsigned num_args = head->get_num_args();
ptr_buffer<expr> new_args;
sbuffer<bool> found_vars;
found_vars.resize(num_decls, false);
unsigned next_var_idx = num_decls;
for (unsigned i = 0; i < num_args; i++) {
expr * arg = head->get_arg(i);
if (is_var(arg)) {
unsigned idx = to_var(arg)->get_idx();
SASSERT(idx < num_decls);
if (found_vars[idx] == false) {
found_vars[idx] = true;
new_args.push_back(arg);
continue;
}
}
var * new_var = m.mk_var(next_var_idx, m.get_sort(arg));
next_var_idx++;
new_args.push_back(new_var);
}
new_head = m.mk_app(head->get_decl(), new_args.size(), new_args.c_ptr());
num_decls = next_var_idx;
}
/**
\brief Return true if n can be viewed as a polynomial "hint" based on head.
That is, n (but the monomial exception) only uses the variables in head, and does not use
head->get_decl().
is_hint_head(head, vars) must also return true
*/
bool macro_util::is_poly_hint(expr * n, app * head, expr * exception) {
TRACE("macro_util", tout << "is_poly_hint n:\n" << mk_pp(n, m_manager) << "\nhead:\n" << mk_pp(head, m_manager) << "\nexception:\n";
if (exception) tout << mk_pp(exception, m_manager); else tout << "<null>";
tout << "\n";);
ptr_buffer<var> vars;
if (!is_hint_head(head, vars)) {
TRACE("macro_util", tout << "failed because head is not hint head\n";);
return false;
}
func_decl * f = head->get_decl();
unsigned num_args;
expr * const * args;
if (is_add(n)) {
num_args = to_app(n)->get_num_args();
args = to_app(n)->get_args();
}
else {
num_args = 1;
args = &n;
}
for (unsigned i = 0; i < num_args; i++) {
expr * arg = args[i];
if (arg != exception && (occurs(f, arg) || !vars_of_is_subset(arg, vars))) {
TRACE("macro_util", tout << "failed because of:\n" << mk_pp(arg, m_manager) << "\n";);
return false;
}
}
TRACE("macro_util", tout << "succeeded\n";);
return true;
}
// -----------------------------
//
// Macro candidates
//
// -----------------------------
macro_util::macro_candidates::macro_candidates(ast_manager & m):
m_defs(m),
m_conds(m) {
}
void macro_util::macro_candidates::reset() {
m_fs.reset();
m_defs.reset();
m_conds.reset();
m_ineq.reset();
m_satisfy.reset();
m_hint.reset();
}
void macro_util::macro_candidates::insert(func_decl * f, expr * def, expr * cond, bool ineq, bool satisfy_atom, bool hint) {
m_fs.push_back(f);
m_defs.push_back(def);
m_conds.push_back(cond);
m_ineq.push_back(ineq);
m_satisfy.push_back(satisfy_atom);
m_hint.push_back(hint);
}
// -----------------------------
//
// Macro util
//
// -----------------------------
void macro_util::insert_macro(app * head, unsigned num_decls, expr * def, expr * cond, bool ineq, bool satisfy_atom, bool hint, macro_candidates & r) {
expr_ref norm_def(m_manager);
expr_ref norm_cond(m_manager);
normalize_expr(head, num_decls, def, norm_def);
if (cond != nullptr)
normalize_expr(head, num_decls, cond, norm_cond);
else if (!hint)
norm_cond = m_manager.mk_true();
SASSERT(!hint || norm_cond.get() == 0);
r.insert(head->get_decl(), norm_def.get(), norm_cond.get(), ineq, satisfy_atom, hint);
}
void macro_util::insert_quasi_macro(app * head, unsigned num_decls, expr * def, expr * cond, bool ineq, bool satisfy_atom,
bool hint, macro_candidates & r) {
if (!is_macro_head(head, head->get_num_args())) {
app_ref new_head(m_manager);
expr_ref extra_cond(m_manager);
expr_ref new_cond(m_manager);
if (!hint) {
quasi_macro_head_to_macro_head(head, num_decls, new_head, extra_cond);
if (cond == nullptr)
new_cond = extra_cond;
else
bool_rewriter(m_manager).mk_and(cond, extra_cond, new_cond);
}
else {
hint_to_macro_head(m_manager, head, num_decls, new_head);
TRACE("macro_util",
tout << "hint macro head: " << mk_ismt2_pp(new_head, m_manager) << std::endl;
tout << "hint macro def: " << mk_ismt2_pp(def, m_manager) << std::endl; );
}
insert_macro(new_head, num_decls, def, new_cond, ineq, satisfy_atom, hint, r);
}
else {
insert_macro(head, num_decls, def, cond, ineq, satisfy_atom, hint, r);
}
}
bool macro_util::rest_contains_decl(func_decl * f, expr * except_lit) {
if (m_curr_clause == nullptr)
return false;
SASSERT(is_clause(m_manager, m_curr_clause));
unsigned num_lits = get_clause_num_literals(m_manager, m_curr_clause);
for (unsigned i = 0; i < num_lits; i++) {
expr * l = get_clause_literal(m_manager, m_curr_clause, i);
if (l != except_lit && occurs(f, l))
return true;
}
return false;
}
void macro_util::get_rest_clause_as_cond(expr * except_lit, expr_ref & extra_cond) {
if (m_curr_clause == nullptr)
return;
SASSERT(is_clause(m_manager, m_curr_clause));
expr_ref_buffer neg_other_lits(m_manager);
unsigned num_lits = get_clause_num_literals(m_manager, m_curr_clause);
for (unsigned i = 0; i < num_lits; i++) {
expr * l = get_clause_literal(m_manager, m_curr_clause, i);
if (l != except_lit) {
expr_ref neg_l(m_manager);
bool_rewriter(m_manager).mk_not(l, neg_l);
neg_other_lits.push_back(neg_l);
}
}
if (neg_other_lits.empty())
return;
bool_rewriter(m_manager).mk_and(neg_other_lits.size(), neg_other_lits.c_ptr(), extra_cond);
}
void macro_util::collect_poly_args(expr * n, expr * exception, ptr_buffer<expr> & args) {
args.reset();
unsigned num_args;
expr * const * _args;
if (is_add(n)) {
num_args = to_app(n)->get_num_args();
_args = to_app(n)->get_args();
}
else {
num_args = 1;
_args = &n;
}
for (unsigned i = 0; i < num_args; i++) {
expr * arg = _args[i];
if (arg != exception)
args.push_back(arg);
}
}
void macro_util::add_arith_macro_candidate(app * head, unsigned num_decls, expr * def, expr * atom, bool ineq, bool hint, macro_candidates & r) {
expr_ref cond(m_manager);
if (!hint)
get_rest_clause_as_cond(atom, cond);
insert_quasi_macro(head, num_decls, def, cond, ineq, true, hint, r);
}
void macro_util::collect_arith_macro_candidates(expr * lhs, expr * rhs, expr * atom, unsigned num_decls, bool is_ineq, macro_candidates & r) {
if (!is_add(lhs) && m_manager.is_eq(atom)) // this case is a simple macro.
return;
ptr_buffer<expr> args;
unsigned lhs_num_args;
expr * const * lhs_args;
if (is_add(lhs)) {
lhs_num_args = to_app(lhs)->get_num_args();
lhs_args = to_app(lhs)->get_args();
}
else {
lhs_num_args = 1;
lhs_args = &lhs;
}
for (unsigned i = 0; i < lhs_num_args; i++) {
expr * arg = lhs_args[i];
expr * neg_arg;
if (!is_app(arg))
continue;
func_decl * f = to_app(arg)->get_decl();
bool _is_arith_macro =
is_quasi_macro_head(arg, num_decls) &&
!is_forbidden(f) &&
!poly_contains_head(lhs, f, arg) &&
!occurs(f, rhs) &&
!rest_contains_decl(f, atom);
bool _is_poly_hint = !_is_arith_macro && is_poly_hint(lhs, to_app(arg), arg);
if (_is_arith_macro || _is_poly_hint) {
collect_poly_args(lhs, arg, args);
expr_ref rest(m_manager);
mk_add(args.size(), args.c_ptr(), m_manager.get_sort(arg), rest);
expr_ref def(m_manager);
mk_sub(rhs, rest, def);
// If is_poly_hint, rhs may contain variables that do not occur in to_app(arg).
// So, we should re-check.
if (!_is_poly_hint || is_poly_hint(def, to_app(arg), nullptr))
add_arith_macro_candidate(to_app(arg), num_decls, def, atom, is_ineq, _is_poly_hint, r);
}
else if (is_times_minus_one(arg, neg_arg) && is_app(neg_arg)) {
f = to_app(neg_arg)->get_decl();
bool _is_arith_macro =
is_quasi_macro_head(neg_arg, num_decls) &&
!is_forbidden(f) &&
!poly_contains_head(lhs, f, arg) &&
!occurs(f, rhs) &&
!rest_contains_decl(f, atom);
bool _is_poly_hint = !_is_arith_macro && is_poly_hint(lhs, to_app(neg_arg), arg);
if (_is_arith_macro || _is_poly_hint) {
collect_poly_args(lhs, arg, args);
expr_ref rest(m_manager);
mk_add(args.size(), args.c_ptr(), m_manager.get_sort(arg), rest);
expr_ref def(m_manager);
mk_sub(rest, rhs, def);
// If is_poly_hint, rhs may contain variables that do not occur in to_app(neg_arg).
// So, we should re-check.
if (!_is_poly_hint || is_poly_hint(def, to_app(neg_arg), nullptr))
add_arith_macro_candidate(to_app(neg_arg), num_decls, def, atom, is_ineq, _is_poly_hint, r);
}
}
}
}
void macro_util::collect_arith_macro_candidates(expr * atom, unsigned num_decls, macro_candidates & r) {
TRACE("macro_util", tout << "collect_arith_macro_candidates:\n" << mk_pp(atom, m_manager) << "\n";);
if (!m_manager.is_eq(atom) && !is_le_ge(atom))
return;
expr * lhs = to_app(atom)->get_arg(0);
expr * rhs = to_app(atom)->get_arg(1);
bool is_ineq = !m_manager.is_eq(atom);
collect_arith_macro_candidates(lhs, rhs, atom, num_decls, is_ineq, r);
collect_arith_macro_candidates(rhs, lhs, atom, num_decls, is_ineq, r);
}
/**
\brief Collect macro candidates for atom \c atom.
The candidates are stored in \c r.
The following post-condition holds:
for each i in [0, r.size() - 1]
we have a conditional macro of the form
r.get_cond(i) IMPLIES f(x_1, ..., x_n) = r.get_def(i)
where
f == r.get_fs(i) .., x_n), f is uninterpreted and x_1, ..., x_n are variables.
r.get_cond(i) and r.get_defs(i) do not contain f or variables not in {x_1, ..., x_n}
The idea is to use r.get_defs(i) as the interpretation for f in a model M whenever r.get_cond(i)
Given a model M and values { v_1, ..., v_n }
Let M' be M{x_1 -> v_1, ..., v_n -> v_n}
Note that M'(f(x_1, ..., x_n)) = M(f)(v_1, ..., v_n)
Then, IF we have that M(f)(v_1, ..., v_n) = M'(r.get_def(i)) AND
M'(r.get_cond(i)) = true
THEN M'(atom) = true
That is, if the conditional macro is used then the atom is satisfied when M'(r.get_cond(i)) = true
IF r.is_ineq(i) = false, then
M(f)(v_1, ..., v_n) ***MUST BE*** M'(r.get_def(i)) whenever M'(r.get_cond(i)) = true
IF r.satisfy_atom(i) = true, then we have the stronger property:
Then, IF we have that (M'(r.get_cond(i)) = true IMPLIES M(f)(v_1, ..., v_n) = M'(r.get_def(i)))
THEN M'(atom) = true
*/
void macro_util::collect_macro_candidates_core(expr * atom, unsigned num_decls, macro_candidates & r) {
expr* lhs, *rhs;
TRACE("macro_util", tout << "Candidate check for: " << mk_ismt2_pp(atom, m_manager) << std::endl;);
if (m_manager.is_eq(atom, lhs, rhs) || m_manager.is_iff(atom, lhs, rhs)) {
if (is_quasi_macro_head(lhs, num_decls) &&
!is_forbidden(to_app(lhs)->get_decl()) &&
!occurs(to_app(lhs)->get_decl(), rhs) &&
!rest_contains_decl(to_app(lhs)->get_decl(), atom)) {
expr_ref cond(m_manager);
get_rest_clause_as_cond(atom, cond);
insert_quasi_macro(to_app(lhs), num_decls, rhs, cond, false, true, false, r);
}
else if (is_hint_atom(lhs, rhs)) {
insert_quasi_macro(to_app(lhs), num_decls, rhs, nullptr, false, true, true, r);
}
if (is_quasi_macro_head(rhs, num_decls) &&
!is_forbidden(to_app(rhs)->get_decl()) &&
!occurs(to_app(rhs)->get_decl(), lhs) &&
!rest_contains_decl(to_app(rhs)->get_decl(), atom)) {
expr_ref cond(m_manager);
get_rest_clause_as_cond(atom, cond);
insert_quasi_macro(to_app(rhs), num_decls, lhs, cond, false, true, false, r);
}
else if (is_hint_atom(rhs, lhs)) {
insert_quasi_macro(to_app(rhs), num_decls, lhs, nullptr, false, true, true, r);
}
}
collect_arith_macro_candidates(atom, num_decls, r);
}
void macro_util::collect_macro_candidates(expr * atom, unsigned num_decls, macro_candidates & r) {
m_curr_clause = nullptr;
r.reset();
collect_macro_candidates_core(atom, num_decls, r);
}
void macro_util::collect_macro_candidates(quantifier * q, macro_candidates & r) {
r.reset();
expr * n = q->get_expr();
if (has_quantifiers(n))
return;
unsigned num_decls = q->get_num_decls();
SASSERT(m_curr_clause == 0);
if (is_clause(m_manager, n)) {
m_curr_clause = n;
unsigned num_lits = get_clause_num_literals(m_manager, n);
for (unsigned i = 0; i < num_lits; i++)
collect_macro_candidates_core(get_clause_literal(m_manager, n, i), num_decls, r);
m_curr_clause = nullptr;
}
else {
collect_macro_candidates_core(n, num_decls, r);
}
}
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