z3-z3-4.13.0.src.ast.proofs.proof_utils.cpp Maven / Gradle / Ivy
The newest version!
/*++
Copyright (c) 2017 Arie Gurfinkel
Module Name:
proof_utils.cpp
Abstract:
Utilities to traverse and manipulate proofs
Author:
Bernhard Gleiss
Arie Gurfinkel
Revision History:
--*/
#include "ast/ast_util.h"
#include "ast/ast_pp.h"
#include "ast/proofs/proof_utils.h"
#include "ast/proofs/proof_checker.h"
#include "ast/rewriter/var_subst.h"
#include "util/container_util.h"
proof_post_order::proof_post_order(proof* root, ast_manager& manager) : m(manager) {
m_todo.push_back(root);
}
bool proof_post_order::hasNext() {
return !m_todo.empty();
}
/*
* iterative post-order depth-first search (DFS) through the proof DAG
*/
proof* proof_post_order::next() {
while (!m_todo.empty()) {
proof* currentNode = m_todo.back();
// if we haven't already visited the current unit
if (!m_visited.is_marked(currentNode)) {
bool existsUnvisitedParent = false;
// add unprocessed premises to stack for DFS.
// If there is at least one unprocessed premise, don't compute the result
// for currentProof now, but wait until those unprocessed premises are processed.
for (unsigned i = 0; i < m.get_num_parents(currentNode); ++i) {
SASSERT(m.is_proof(currentNode->get_arg(i)));
proof* premise = to_app(currentNode->get_arg(i));
// if we haven't visited the current premise yet
if (!m_visited.is_marked(premise)) {
// add it to the stack
m_todo.push_back(premise);
existsUnvisitedParent = true;
}
}
// if we already visited all parent-inferences, we can visit the inference too
if (!existsUnvisitedParent) {
m_visited.mark(currentNode, true);
m_todo.pop_back();
return currentNode;
}
} else {
m_todo.pop_back();
}
}
// we have already iterated through all inferences
return nullptr;
}
class reduce_hypotheses {
ast_manager &m;
// tracking all created expressions
expr_ref_vector m_pinned;
// cache for the transformation
obj_map m_cache;
// map from unit literals to their hypotheses-free derivations
obj_map m_units;
// -- all hypotheses in the proof
obj_hashtable m_hyps;
// marks hypothetical proofs
ast_mark m_hypmark;
// stack
ptr_vector m_todo;
void reset() {
m_cache.reset();
m_units.reset();
m_hyps.reset();
m_hypmark.reset();
m_pinned.reset();
}
bool compute_mark1(proof *pr) {
bool hyp_mark = false;
// lemmas clear all hypotheses
if (!m.is_lemma(pr)) {
for (unsigned i = 0, sz = m.get_num_parents(pr); i < sz; ++i) {
if (m_hypmark.is_marked(m.get_parent(pr, i))) {
hyp_mark = true;
break;
}
}
}
m_hypmark.mark(pr, hyp_mark);
return hyp_mark;
}
void compute_marks(proof* pr) {
proof *p;
proof_post_order pit(pr, m);
while (pit.hasNext()) {
p = pit.next();
if (m.is_hypothesis(p)) {
m_hypmark.mark(p, true);
m_hyps.insert(m.get_fact(p));
}
else {
bool hyp_mark = compute_mark1(p);
// collect units that are hyp-free and are used as hypotheses somewhere
if (!hyp_mark && m.has_fact(p) && m_hyps.contains(m.get_fact(p))) {
m_units.insert(m.get_fact(p), p);
}
}
}
}
void find_units(proof *pr)
{
// optional. not implemented yet.
}
void reduce(proof* pf, proof_ref &out)
{
proof *res = nullptr;
m_todo.reset();
m_todo.push_back(pf);
ptr_buffer args;
bool dirty = false;
while (!m_todo.empty()) {
proof *p, *tmp, *pp;
unsigned todo_sz;
p = m_todo.back();
if (m_cache.find(p, tmp)) {
res = tmp;
m_todo.pop_back();
continue;
}
dirty = false;
args.reset();
todo_sz = m_todo.size();
for (unsigned i = 0, sz = m.get_num_parents(p); i < sz; ++i) {
pp = m.get_parent(p, i);
if (m_cache.find(pp, tmp)) {
args.push_back(tmp);
dirty |= pp != tmp;
} else {
m_todo.push_back(pp);
}
}
if (todo_sz < m_todo.size()) { continue; }
else { m_todo.pop_back(); }
if (m.is_hypothesis(p)) {
// hyp: replace by a corresponding unit
if (m_units.find(m.get_fact(p), tmp)) {
res = tmp;
} else { res = p; }
}
else if (!dirty) { res = p; }
else if (m.is_lemma(p)) {
//lemma: reduce the premise; remove reduced consequences from conclusion
SASSERT(args.size() == 1);
res = mk_lemma_core(args.get(0), m.get_fact(p));
compute_mark1(res);
} else if (m.is_unit_resolution(p)) {
// unit: reduce units; reduce the first premise; rebuild unit resolution
res = mk_unit_resolution_core(args.size(), args.data());
compute_mark1(res);
} else {
// other: reduce all premises; reapply
if (m.has_fact(p)) { args.push_back(to_app(m.get_fact(p))); }
SASSERT(p->get_decl()->get_arity() == args.size());
res = m.mk_app(p->get_decl(), args.size(), (expr * const*)args.data());
compute_mark1(res);
}
SASSERT(res);
m_pinned.push_back(res);
m_cache.insert(p, res);
if (m.has_fact(res) && m.is_false(m.get_fact(res))) { break; }
}
out = res;
}
// returns true if (hypothesis (not a)) would be reduced
bool is_reduced(expr *a)
{
expr_ref e(mk_not(m, a), m);
return m_units.contains(e);
}
proof *mk_lemma_core(proof *pf, expr *fact)
{
ptr_buffer args;
expr_ref lemma(m);
if (m.is_or(fact)) {
for (expr* a : *to_app(fact)) {
if (!is_reduced(a))
args.push_back(a);
}
}
else if (!is_reduced(fact)) {
args.push_back(fact);
}
if (args.empty()) {
return pf;
}
lemma = mk_or(m, args.size(), args.data());
proof* res = m.mk_lemma(pf, lemma);
m_pinned.push_back(res);
if (m_hyps.contains(lemma))
{ m_units.insert(lemma, res); }
return res;
}
proof *mk_unit_resolution_core(unsigned num_args, proof* const *args)
{
ptr_buffer pf_args;
pf_args.push_back(args [0]);
app *cls_fact = to_app(m.get_fact(args[0]));
ptr_buffer cls;
if (m.is_or(cls_fact)) {
for (unsigned i = 0, sz = cls_fact->get_num_args(); i < sz; ++i)
{ cls.push_back(cls_fact->get_arg(i)); }
} else { cls.push_back(cls_fact); }
// construct new resolvent
ptr_buffer new_fact_cls;
bool found;
// XXX quadratic
for (unsigned i = 0, sz = cls.size(); i < sz; ++i) {
found = false;
for (unsigned j = 1; j < num_args; ++j) {
if (m.is_complement(cls.get(i), m.get_fact(args [j]))) {
found = true;
pf_args.push_back(args [j]);
break;
}
}
if (!found) {
new_fact_cls.push_back(cls.get(i));
}
}
SASSERT(new_fact_cls.size() + pf_args.size() - 1 == cls.size());
expr_ref new_fact(m);
new_fact = mk_or(m, new_fact_cls.size(), new_fact_cls.data());
// create new proof step
proof *res = m.mk_unit_resolution(pf_args.size(), pf_args.data(), new_fact);
m_pinned.push_back(res);
return res;
}
// reduce all units, if any unit reduces to false return true and put its proof into out
bool reduce_units(proof_ref &out)
{
proof_ref res(m);
for (auto entry : m_units) {
reduce(entry.get_value(), res);
if (m.is_false(m.get_fact(res))) {
out = res;
return true;
}
res.reset();
}
return false;
}
public:
reduce_hypotheses(ast_manager &m) : m(m), m_pinned(m) {}
void operator()(proof_ref &pr)
{
compute_marks(pr);
if (!reduce_units(pr)) {
reduce(pr.get(), pr);
}
reset();
}
};
void reduce_hypotheses(proof_ref &pr) {
ast_manager &m = pr.get_manager();
class reduce_hypotheses hypred(m);
hypred(pr);
DEBUG_CODE(proof_checker pc(m);
expr_ref_vector side(m);
SASSERT(pc.check(pr, side));
);
}
#include "ast/ast_smt2_pp.h"
class reduce_hypotheses0 {
typedef obj_hashtable expr_set;
ast_manager& m;
// reference for any expression created by the transformation
expr_ref_vector m_refs;
// currently computed result
obj_map m_cache;
// map conclusions to closed proofs that derive them
obj_map m_units;
// currently active units
ptr_vector m_units_trail;
// size of m_units_trail at the last push
unsigned_vector m_limits;
// map from proofs to active hypotheses
obj_map m_hypmap;
// reference train for hypotheses sets
ptr_vector m_hyprefs;
ptr_vector m_literals;
void reset() {
m_refs.reset();
m_cache.reset();
m_units.reset();
m_units_trail.reset();
m_limits.reset();
std::for_each(m_hyprefs.begin(), m_hyprefs.end(), delete_proc());
m_hypmap.reset();
m_hyprefs.reset();
m_literals.reset();
}
void push() {
m_limits.push_back(m_units_trail.size());
}
void pop() {
unsigned sz = m_limits.back();
while (m_units_trail.size() > sz) {
m_units.remove(m_units_trail.back());
m_units_trail.pop_back();
}
m_limits.pop_back();
}
void get_literals(expr* clause) {
m_literals.reset();
if (m.is_or(clause)) {
m_literals.append(to_app(clause)->get_num_args(), to_app(clause)->get_args());
}
else {
m_literals.push_back(clause);
}
}
void add_hypotheses(proof* p) {
expr_set* hyps = nullptr;
bool inherited = false;
if (p->get_decl_kind() == PR_HYPOTHESIS) {
hyps = alloc(expr_set);
hyps->insert(m.get_fact(p));
m_hyprefs.push_back(hyps);
}
else {
for (unsigned i = 0; i < m.get_num_parents(p); ++i) {
expr_set* hyps1 = m_hypmap.find(m.get_parent(p, i));
if (hyps1) {
if (!hyps) {
hyps = hyps1;
inherited = true;
continue;
}
if (inherited) {
hyps = alloc(expr_set,*hyps);
m_hyprefs.push_back(hyps);
inherited = false;
}
set_union(*hyps, *hyps1);
}
}
}
m_hypmap.insert(p, hyps);
}
expr_ref complement_lit(expr* e) {
expr* e1;
if (m.is_not(e, e1)) {
return expr_ref(e1, m);
}
else {
return expr_ref(m.mk_not(e), m);
}
}
bool in_hypotheses(expr* e, expr_set* hyps) {
if (!hyps) {
return false;
}
expr_ref not_e = complement_lit(e);
return hyps->contains(not_e);
}
bool contains_hypothesis(proof* p) {
ptr_vector todo;
ast_mark visit;
todo.push_back(p);
while (!todo.empty()) {
p = todo.back();
todo.pop_back();
if (visit.is_marked(p)) {
continue;
}
visit.mark(p, true);
if (PR_HYPOTHESIS == p->get_decl_kind()) {
return true;
}
for (unsigned i = 0; i < m.get_num_parents(p); ++i) {
todo.push_back(m.get_parent(p, i));
}
}
return false;
}
bool is_closed(proof* p) {
expr_set* hyps = m_hypmap.find(p);
return !hyps || hyps->empty();
}
public:
reduce_hypotheses0(ast_manager& m): m(m), m_refs(m) {}
void operator()(proof_ref& pr) {
if (!pr)
throw default_exception("proof reduction requires well defined proofs");
proof_ref tmp(m);
tmp = pr;
elim(pr);
reset();
CTRACE("proof_utils", contains_hypothesis(pr),
tout << "Contains hypothesis:\n";
tout << mk_ismt2_pp(tmp, m) << "\n====>\n";
tout << mk_ismt2_pp(pr, m) << "\n";);
}
void elim(proof_ref& p) {
proof_ref tmp(m);
proof* result = p.get();
if (m_cache.find(p, result)) {
p = result;
return;
}
//SASSERT (p.get () == result);
switch(p->get_decl_kind()) {
case PR_HYPOTHESIS:
// replace result by m_units[m.get_fact (p)] if defined
// AG: This is the main step. Replace a hypothesis by a derivation of its consequence
if (!m_units.find(m.get_fact(p), result)) {
// restore the result back to p
result = p.get();
}
// compute hypothesis of the result
// not clear what 'result' is at this point.
// probably the proof at the top of the call
// XXX not clear why this is re-computed each time
// XXX moreover, m_units are guaranteed to be closed!
// XXX so no hypotheses are needed for them
add_hypotheses(result);
break;
case PR_LEMMA: {
SASSERT(m.get_num_parents(p) == 1);
tmp = m.get_parent(p, 0);
// eliminate hypothesis recursively in the proof of the lemma
elim(tmp);
expr_set* hyps = m_hypmap.find(tmp);
expr_set* new_hyps = nullptr;
// XXX if the proof is correct, the hypotheses of the tmp
// XXX should be exactly those of the consequence of the lemma
// XXX but if this code actually eliminates hypotheses, the set might be a subset
if (hyps) {
new_hyps = alloc(expr_set, *hyps);
}
expr* fact = m.get_fact(p);
// when hypothesis is a single literal of the form
// (or A B), and the fact of p is (or A B).
if (hyps && hyps->size() == 1 && in_hypotheses(fact, hyps)) {
m_literals.reset();
m_literals.push_back(fact);
}
else {
get_literals(fact);
}
// go over all the literals in the consequence of the lemma
for (unsigned i = 0; i < m_literals.size(); ++i) {
expr* e = m_literals[i];
// if the literal is not in hypothesis, skip it
if (!in_hypotheses(e, hyps)) {
m_literals[i] = m_literals.back();
m_literals.pop_back();
--i;
}
// if the literal is in hypothesis remove it because
// it is not in hypothesis set of the lemma
// XXX but we assume that lemmas have empty hypothesis set.
// XXX eventually every element of new_hyps must be removed!
else {
SASSERT(new_hyps);
expr_ref not_e = complement_lit(e);
SASSERT(new_hyps->contains(not_e));
new_hyps->remove(not_e);
}
}
// killed all hypotheses, so can stop at the lemma since
// we have a closed pf of false
if (m_literals.empty()) {
result = tmp;
}
else {
// create a new lemma, but might be re-creating existing one
expr_ref clause(m);
if (m_literals.size() == 1) {
clause = m_literals[0];
}
else {
clause = m.mk_or(m_literals.size(), m_literals.data());
}
tmp = m.mk_lemma(tmp, clause);
m_refs.push_back(tmp);
result = tmp;
}
if (new_hyps && new_hyps->empty()) {
dealloc(new_hyps);
new_hyps = nullptr;
}
m_hypmap.insert(result, new_hyps);
// might push 0 into m_hyprefs. No reason for that
m_hyprefs.push_back(new_hyps);
TRACE("proof_utils",
tout << "New lemma: " << mk_pp(m.get_fact(p), m)
<< "\n==>\n"
<< mk_pp(m.get_fact(result), m) << "\n";
if (hyps) {
expr_set::iterator it = hyps->begin();
expr_set::iterator end = hyps->end();
for (; it != end; ++it) {
tout << "Hypothesis: " << mk_pp(*it, m) << "\n";
}
});
break;
}
case PR_UNIT_RESOLUTION: {
proof_ref_vector parents(m);
// get the clause being resolved with
parents.push_back(m.get_parent(p, 0));
// save state
push();
bool found_false = false;
// for every derivation of a unit literal
for (unsigned i = 1; i < m.get_num_parents(p); ++i) {
// see if it derives false
tmp = m.get_parent(p, i);
elim(tmp);
if (m.is_false(m.get_fact(tmp))) {
// if derived false, the whole pf is false and we can bail out
result = tmp;
found_false = true;
break;
}
// -- otherwise, the fact has not changed. nothing to simplify
SASSERT(m.get_fact(tmp) == m.get_fact(m.get_parent(p, i)));
parents.push_back(tmp);
// remember that we have this derivation while we have not popped the trail
// but only if the proof is closed (i.e., a real unit)
if (is_closed(tmp) && !m_units.contains(m.get_fact(tmp))) {
m_units.insert(m.get_fact(tmp), tmp);
m_units_trail.push_back(m.get_fact(tmp));
}
}
if (found_false) {
pop();
break;
}
// look at the clause being resolved with
tmp = m.get_parent(p, 0);
// remember its fact
expr* old_clause = m.get_fact(tmp);
// attempt to reduce its fact
elim(tmp);
// update parents
parents[0] = tmp;
// if the new fact is false, bail out
expr* clause = m.get_fact(tmp);
if (m.is_false(clause)) {
m_refs.push_back(tmp);
result = tmp;
pop();
break;
}
//
// case where clause is a literal in the old clause.
// i.e., reduce multi-literal clause to a unit
//
if (is_literal_in_clause(clause, old_clause)) {
// if the resulting literal was resolved, get a pf of false and bail out
bool found = false;
for (unsigned i = 1; !found && i < parents.size(); ++i) {
if (m.is_complement(clause, m.get_fact(parents[i].get()))) {
parents[1] = parents[i].get();
parents.resize(2);
result = m.mk_unit_resolution(parents.size(), parents.data());
m_refs.push_back(result);
add_hypotheses(result);
found = true;
}
}
// else if the resulting literal is not resolved, it is the new consequence
if (!found) {
result = parents[0].get();
}
pop();
break;
}
//
// case where new clause is a subset of old clause.
// the literals in clause should be a subset of literals in old_clause.
//
get_literals(clause);
for (unsigned i = 1; i < parents.size(); ++i) {
bool found = false;
for (unsigned j = 0; j < m_literals.size(); ++j) {
if (m.is_complement(m_literals[j], m.get_fact(parents[i].get()))) {
found = true;
break;
}
}
if (!found) {
// literal was removed as hypothesis.
parents[i] = parents.back();
parents.pop_back();
--i;
}
}
if (parents.size() == 1) {
result = parents[0].get();
}
else {
result = m.mk_unit_resolution(parents.size(), parents.data());
m_refs.push_back(result);
add_hypotheses(result);
}
pop();
break;
}
default: {
ptr_buffer args;
bool change = false;
bool found_false = false;
for (unsigned i = 0; i < m.get_num_parents(p); ++i) {
tmp = m.get_parent(p, i);
elim(tmp);
if (m.is_false(m.get_fact(tmp))) {
result = tmp;
found_false = true;
break;
}
// SASSERT(m.get_fact(tmp) == m.get_fact(m.get_parent(p, i)));
change = change || (tmp != m.get_parent(p, i));
args.push_back(tmp);
}
if (found_false) {
break;
}
if (m.has_fact(p)) {
args.push_back(m.get_fact(p));
}
if (change) {
tmp = m.mk_app(p->get_decl(), args.size(), args.data());
m_refs.push_back(tmp);
}
else {
tmp = p;
}
result = tmp;
add_hypotheses(result);
break;
}
}
SASSERT(m_hypmap.contains(result));
m_cache.insert(p, result);
p = result;
}
bool is_literal_in_clause(expr* fml, expr* clause) {
if (!m.is_or(clause)) {
return false;
}
app* cl = to_app(clause);
for (unsigned i = 0; i < cl->get_num_args(); ++i) {
if (cl->get_arg(i) == fml) {
return true;
}
}
return false;
}
};
void proof_utils::reduce_hypotheses(proof_ref& pr) {
ast_manager& m = pr.get_manager();
class reduce_hypotheses0 reduce(m);
reduce(pr);
CTRACE("proof_utils", !is_closed(m, pr), tout << mk_pp(pr, m) << "\n";);
}
class proof_is_closed {
ast_manager& m;
ptr_vector m_literals;
ast_mark m_visit;
void reset() {
m_literals.reset();
m_visit.reset();
}
bool check(proof* p) {
// really just a partial check because nodes may be visited
// already under a different lemma scope.
if (m_visit.is_marked(p)) {
return true;
}
bool result = false;
m_visit.mark(p, true);
switch(p->get_decl_kind()) {
case PR_LEMMA: {
unsigned sz = m_literals.size();
expr* cls = m.get_fact(p);
m_literals.push_back(cls);
if (m.is_or(cls)) {
m_literals.append(to_app(cls)->get_num_args(), to_app(cls)->get_args());
}
SASSERT(m.get_num_parents(p) == 1);
result = check(m.get_parent(p, 0));
m_literals.resize(sz);
break;
}
case PR_HYPOTHESIS: {
expr* fact = m.get_fact(p);
for (unsigned i = 0; i < m_literals.size(); ++i) {
if (m.is_complement(m_literals[i], fact)) {
result = true;
break;
}
}
break;
}
default:
result = true;
for (unsigned i = 0; i < m.get_num_parents(p); ++i) {
if (!check(m.get_parent(p, i))) {
result = false;
break;
}
}
break;
}
return result;
}
public:
proof_is_closed(ast_manager& m): m(m) {}
bool operator()(proof *p) {
bool ok = check(p);
reset();
return ok;
}
};
bool proof_utils::is_closed(ast_manager& m, proof* p) {
proof_is_closed checker(m);
return checker(p);
}
static void permute_unit_resolution(expr_ref_vector& refs, obj_map& cache, proof_ref& pr) {
ast_manager& m = pr.get_manager();
proof* pr2 = nullptr;
proof_ref_vector parents(m);
proof_ref prNew(pr);
if (cache.find(pr, pr2)) {
pr = pr2;
return;
}
for (unsigned i = 0; i < m.get_num_parents(pr); ++i) {
prNew = m.get_parent(pr, i);
permute_unit_resolution(refs, cache, prNew);
parents.push_back(prNew);
}
prNew = pr;
if (pr->get_decl_kind() == PR_UNIT_RESOLUTION &&
parents[0]->get_decl_kind() == PR_TH_LEMMA) {
/*
Unit resolution:
T1: (or l_1 ... l_n l_1' ... l_m')
T2: (not l_1)
...
T(n+1): (not l_n)
[unit-resolution T1 ... T(n+1)]: (or l_1' ... l_m')
Th lemma:
T1: (not l_1)
...
Tn: (not l_n)
[th-lemma T1 ... Tn]: (or l_{n+1} ... l_m)
Such that (or l_1 .. l_n l_{n+1} .. l_m) is a theory axiom.
Implement conversion:
T1 |- not l_1 ... Tn |- not l_n
------------------------------- TH_LEMMA
(or k_1 .. k_m j_1 ... j_m) S1 |- not k_1 ... Sm |- not k_m
-------------------------------------------------------------- UNIT_RESOLUTION
(or j_1 .. j_m)
|->
T1 |- not l_1 ... Tn |- not l_n S1 |- not k_1 ... Sm |- not k_m
---------------------------------------------------------------- TH_LEMMA
(or j_1 .. j_m)
*/
proof_ref_vector premises(m);
proof* thLemma = parents[0].get();
for (unsigned i = 0; i < m.get_num_parents(thLemma); ++i) {
premises.push_back(m.get_parent(thLemma, i));
}
for (unsigned i = 1; i < parents.size(); ++i) {
premises.push_back(parents[i].get());
}
parameter const* params = thLemma->get_decl()->get_parameters();
unsigned num_params = thLemma->get_decl()->get_num_parameters();
SASSERT(params[0].is_symbol());
family_id tid = m.mk_family_id(params[0].get_symbol());
SASSERT(tid != null_family_id);
// AG: This can break a theory lemma. In particular, for Farkas lemmas the coefficients
// AG: for the literals propagated from the unit resolution are missing.
// AG: Why is this a good thing to do?
// AG: This can lead to merging of the units with other terms in interpolation,
// AG: but without farkas coefficients this does not make sense
prNew = m.mk_th_lemma(tid, m.get_fact(pr),
premises.size(), premises.data(), num_params-1, params+1);
}
else {
ptr_vector args;
for (unsigned i = 0; i < parents.size(); ++i) {
args.push_back(parents[i].get());
}
if (m.has_fact(pr)) {
args.push_back(m.get_fact(pr));
}
prNew = m.mk_app(pr->get_decl(), args.size(), args.data());
}
cache.insert(pr, prNew);
refs.push_back(prNew);
pr = prNew;
}
// permute unit resolution over Theory lemmas to track premises.
void proof_utils::permute_unit_resolution(proof_ref& pr) {
expr_ref_vector refs(pr.get_manager());
obj_map cache;
::permute_unit_resolution(refs, cache, pr);
}
class push_instantiations_up_cl {
ast_manager& m;
public:
push_instantiations_up_cl(ast_manager& m): m(m) {}
void operator()(proof_ref& p) {
expr_ref_vector s0(m);
p = push(p, s0);
}
private:
proof* push(proof* p, expr_ref_vector const& sub) {
proof_ref_vector premises(m);
expr_ref conclusion(m);
svector > positions;
vector substs;
if (m.is_hyper_resolve(p, premises, conclusion, positions, substs)) {
for (unsigned i = 0; i < premises.size(); ++i) {
compose(substs[i], sub);
premises[i] = push(premises[i].get(), substs[i]);
substs[i].reset();
}
instantiate(sub, conclusion);
return
m.mk_hyper_resolve(premises.size(), premises.data(), conclusion,
positions,
substs);
}
if (sub.empty()) {
return p;
}
if (m.is_modus_ponens(p)) {
SASSERT(m.get_num_parents(p) == 2);
proof* p0 = m.get_parent(p, 0);
proof* p1 = m.get_parent(p, 1);
if (m.get_fact(p0) == m.get_fact(p)) {
return push(p0, sub);
}
expr* e1, *e2;
if (m.is_rewrite(p1, e1, e2) &&
is_quantifier(e1) && is_quantifier(e2) &&
to_quantifier(e1)->get_num_decls() == to_quantifier(e2)->get_num_decls()) {
expr_ref r1(e1,m), r2(e2,m);
instantiate(sub, r1);
instantiate(sub, r2);
p1 = m.mk_rewrite(r1, r2);
return m.mk_modus_ponens(push(p0, sub), p1);
}
}
premises.push_back(p);
substs.push_back(sub);
conclusion = m.get_fact(p);
instantiate(sub, conclusion);
return m.mk_hyper_resolve(premises.size(), premises.data(), conclusion, positions, substs);
}
void compose(expr_ref_vector& sub, expr_ref_vector const& s0) {
for (unsigned i = 0; i < sub.size(); ++i) {
sub[i] = var_subst(m, false)(sub[i].get(), s0.size(), s0.data());
}
}
void instantiate(expr_ref_vector const& sub, expr_ref& fml) {
if (sub.empty()) {
return;
}
if (!is_forall(fml)) {
return;
}
quantifier* q = to_quantifier(fml);
if (q->get_num_decls() != sub.size()) {
TRACE("proof_utils", tout << "quantifier has different number of variables than substitution";
tout << mk_pp(q, m) << "\n";
tout << sub.size() << "\n";);
return;
}
fml = var_subst(m, false)(q->get_expr(), sub.size(), sub.data());
}
};
void proof_utils::push_instantiations_up(proof_ref& pr) {
push_instantiations_up_cl push(pr.get_manager());
push(pr);
}