z3-z3-4.13.0.src.ast.proofs.proof_utils.h Maven / Gradle / Ivy
The newest version!
/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
proof_utils.h
Abstract:
Utilities to traverse and manipulate proofs
Author:
Bernhard Gleiss
Arie Gurfinkel
Nikolaj Bjorner
Revision History:
--*/
#pragma once
#include "ast/ast.h"
#include "ast/ast_pp.h"
#include "ast/rewriter/bool_rewriter.h"
#include "ast/proofs/proof_checker.h"
/*
* iterator, which traverses the proof in depth-first post-order.
*/
class proof_post_order {
public:
proof_post_order(proof* refutation, ast_manager& manager);
bool hasNext();
proof* next();
private:
ptr_vector m_todo;
ast_mark m_visited; // the proof nodes we have already visited
ast_manager& m;
};
void reduce_hypotheses(proof_ref &pr);
class proof_utils {
public:
/**
\brief reduce the set of hypotheses used in the proof.
*/
static void reduce_hypotheses(proof_ref& pr);
/**
\brief Check that a proof does not contain open hypotheses.
*/
static bool is_closed(ast_manager& m, proof* p);
/**
\brief Permute unit resolution rule with th-lemma
*/
static void permute_unit_resolution(proof_ref& pr);
/**
\brief Push instantiations created in hyper-resolutions up to leaves.
This produces a "ground" proof where leaves are annotated by instantiations.
*/
static void push_instantiations_up(proof_ref& pr);
};
class elim_aux_assertions {
static bool matches_fact(expr_ref_vector &args, expr* &match) {
ast_manager &m = args.get_manager();
expr *fact = args.back();
for (unsigned i = 0, sz = args.size() - 1; i < sz; ++i) {
expr *arg = args.get(i);
if (m.is_proof(arg) &&
m.has_fact(to_app(arg)) &&
m.get_fact(to_app(arg)) == fact) {
match = arg;
return true;
}
}
return false;
}
app_ref m_aux;
public:
elim_aux_assertions(app_ref const& aux) : m_aux(aux) {}
void mk_or_core(expr_ref_vector &args, expr_ref &res)
{
ast_manager &m = args.get_manager();
unsigned j = 0;
for (unsigned i = 0, sz = args.size(); i < sz; ++i) {
if (m.is_false(args.get(i))) { continue; }
if (i != j) { args [j] = args.get(i); }
++j;
}
SASSERT(j >= 1);
res = j > 1 ? m.mk_or(j, args.data()) : args.get(0);
}
void mk_app(func_decl *decl, expr_ref_vector &args, expr_ref &res)
{
ast_manager &m = args.get_manager();
bool_rewriter brwr(m);
brwr.set_flat_and_or(false);
if (m.is_or(decl))
{ mk_or_core(args, res); }
else if (m.is_eq(decl) && args.size() == 2)
// avoiding simplifying equalities. In particular,
// we don't want (= (not a) (not b)) to be reduced to (= a b)
{ res = m.mk_eq(args.get(0), args.get(1)); }
else
{ brwr.mk_app(decl, args.size(), args.data(), res); }
}
void operator()(ast_manager &m, proof *pr, proof_ref &res)
{
DEBUG_CODE(proof_checker pc(m);
expr_ref_vector side(m);
if (!pc.check(pr, side)) IF_VERBOSE(1, verbose_stream() << "check failed: " << mk_pp(pr, m) << "\n");
);
obj_map cache;
bool_rewriter brwr(m);
// for reference counting of new proofs
app_ref_vector pinned(m);
ptr_vector todo;
todo.push_back(pr);
expr_ref not_aux(m);
not_aux = m.mk_not(m_aux);
expr_ref_vector args(m);
while (!todo.empty()) {
app *p, *r;
expr *a;
p = todo.back();
if (cache.find(pr, r)) {
todo.pop_back();
continue;
}
SASSERT(!todo.empty() || pr == p);
bool dirty = false;
unsigned todo_sz = todo.size();
args.reset();
for (unsigned i = 0, sz = p->get_num_args(); i < sz; ++i) {
expr* arg = p->get_arg(i);
if (arg == m_aux.get()) {
dirty = true;
args.push_back(m.mk_true());
} else if (arg == not_aux.get()) {
dirty = true;
args.push_back(m.mk_false());
}
// skip (asserted m_aux)
else if (m.is_asserted(arg, a) && a == m_aux.get()) {
dirty = true;
args.push_back(m.mk_true_proof());
}
// skip (hypothesis m_aux)
else if (m.is_hypothesis(arg, a) && a == m_aux.get()) {
dirty = true;
args.push_back(m.mk_true_proof());
} else if (is_app(arg) && cache.find(to_app(arg), r)) {
dirty |= (arg != r);
args.push_back(r);
} else if (is_app(arg))
{ todo.push_back(to_app(arg)); }
else
// -- not an app
{ args.push_back(arg); }
}
if (todo_sz < todo.size()) {
// -- process parents
args.reset();
continue;
}
// ready to re-create
app_ref newp(m);
if (!dirty) { newp = p; }
else if (m.is_unit_resolution(p)) {
ptr_buffer parents;
for (unsigned i = 0, sz = args.size() - 1; i < sz; ++i) {
app *arg = to_app(args.get(i));
if (!m.is_true(m.get_fact(arg)))
parents.push_back(arg);
}
// unit resolution that collapsed to nothing
if (parents.size() == 1) {
newp = parents.get(0);
}
else {
// rebuild unit resolution
newp = m.mk_unit_resolution(parents.size(), parents.data());
// XXX the old and new facts should be
// equivalent. The test here is much
// stronger. It might need to be relaxed.
SASSERT(m.get_fact(newp) == args.back());
pinned.push_back(newp);
}
}
else if (matches_fact(args, a)) {
newp = to_app(a);
}
else {
expr_ref papp(m);
mk_app(p->get_decl(), args, papp);
newp = to_app(papp.get());
pinned.push_back(newp);
}
cache.insert(p, newp);
todo.pop_back();
CTRACE("virtual",
p->get_decl_kind() == PR_TH_LEMMA &&
p->get_decl()->get_parameter(0).get_symbol() == "arith" &&
p->get_decl()->get_num_parameters() > 1 &&
p->get_decl()->get_parameter(1).get_symbol() == "farkas",
tout << "Old pf: " << mk_pp(p, m) << "\n"
<< "New pf: " << mk_pp(newp, m) << "\n";);
}
proof *r;
VERIFY(cache.find(pr, r));
DEBUG_CODE(
proof_checker pc(m);
expr_ref_vector side(m);
if (!pc.check(r, side)) IF_VERBOSE(1, verbose_stream() << mk_pp(r, m) << "check failed\n");
);
res = r ;
}
};