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/******************************************************************************
* Top contributors (to current version):
* Andrew Reynolds, Makai Mann, Gereon Kremer
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* Implementation of pow2 solver.
*/
#include "theory/arith/nl/pow2_solver.h"
#include "options/arith_options.h"
#include "options/smt_options.h"
#include "preprocessing/passes/bv_to_int.h"
#include "theory/arith/arith_msum.h"
#include "theory/arith/arith_state.h"
#include "theory/arith/arith_utilities.h"
#include "theory/arith/inference_manager.h"
#include "theory/arith/nl/nl_model.h"
#include "theory/rewriter.h"
#include "util/bitvector.h"
using namespace cvc5::kind;
namespace cvc5 {
namespace theory {
namespace arith {
namespace nl {
Pow2Solver::Pow2Solver(Env& env,
InferenceManager& im,
ArithState& state,
NlModel& model)
: EnvObj(env), d_im(im), d_model(model), d_initRefine(userContext())
{
NodeManager* nm = NodeManager::currentNM();
d_false = nm->mkConst(false);
d_true = nm->mkConst(true);
d_zero = nm->mkConst(Rational(0));
d_one = nm->mkConst(Rational(1));
d_two = nm->mkConst(Rational(2));
}
Pow2Solver::~Pow2Solver() {}
void Pow2Solver::initLastCall(const std::vector<Node>& assertions,
const std::vector<Node>& false_asserts,
const std::vector<Node>& xts)
{
d_pow2s.clear();
Trace("pow2-mv") << "POW2 terms : " << std::endl;
for (const Node& a : xts)
{
Kind ak = a.getKind();
if (ak != POW2)
{
// don't care about other terms
continue;
}
d_pow2s.push_back(a);
}
Trace("pow2") << "We have " << d_pow2s.size() << " pow2 terms." << std::endl;
}
void Pow2Solver::checkInitialRefine()
{
Trace("pow2-check") << "Pow2Solver::checkInitialRefine" << std::endl;
NodeManager* nm = NodeManager::currentNM();
for (const Node& i : d_pow2s)
{
if (d_initRefine.find(i) != d_initRefine.end())
{
// already sent initial axioms for i in this user context
continue;
}
d_initRefine.insert(i);
// initial refinement lemmas
std::vector<Node> conj;
// x>=0 -> x < pow2(x)
Node xgeq0 = nm->mkNode(LEQ, d_zero, i[0]);
Node xltpow2x = nm->mkNode(LT, i[0], i);
conj.push_back(nm->mkNode(IMPLIES, xgeq0, xltpow2x));
Node lem = nm->mkAnd(conj);
Trace("pow2-lemma") << "Pow2Solver::Lemma: " << lem << " ; INIT_REFINE"
<< std::endl;
d_im.addPendingLemma(lem, InferenceId::ARITH_NL_POW2_INIT_REFINE);
}
}
void Pow2Solver::sortPow2sBasedOnModel()
{
struct
{
bool operator()(Node a, Node b, NlModel& model) const
{
return model.computeConcreteModelValue(a[0])
< model.computeConcreteModelValue(b[0]);
}
} modelSort;
using namespace std::placeholders;
std::sort(
d_pow2s.begin(), d_pow2s.end(), std::bind(modelSort, _1, _2, d_model));
}
void Pow2Solver::checkFullRefine()
{
Trace("pow2-check") << "Pow2Solver::checkFullRefine" << std::endl;
NodeManager* nm = NodeManager::currentNM();
sortPow2sBasedOnModel();
// add lemmas for each pow2 term
for (uint64_t i = 0, size = d_pow2s.size(); i < size; i++)
{
Node n = d_pow2s[i];
Node valPow2xAbstract = d_model.computeAbstractModelValue(n);
Node valPow2xConcrete = d_model.computeConcreteModelValue(n);
Node valXConcrete = d_model.computeConcreteModelValue(n[0]);
if (Trace.isOn("pow2-check"))
{
Trace("pow2-check") << "* " << i << ", value = " << valPow2xAbstract
<< std::endl;
Trace("pow2-check") << " actual " << valXConcrete << " = "
<< valPow2xConcrete << std::endl;
}
if (valPow2xAbstract == valPow2xConcrete)
{
Trace("pow2-check") << "...already correct" << std::endl;
continue;
}
Integer x = valXConcrete.getConst<Rational>().getNumerator();
Integer pow2x = valPow2xAbstract.getConst<Rational>().getNumerator();
// add monotinicity lemmas
for (uint64_t j = i + 1; j < size; j++)
{
Node m = d_pow2s[j];
Node valPow2yAbstract = d_model.computeAbstractModelValue(m);
Node valYConcrete = d_model.computeConcreteModelValue(m[0]);
Integer y = valYConcrete.getConst<Rational>().getNumerator();
Integer pow2y = valPow2yAbstract.getConst<Rational>().getNumerator();
if (x < y && pow2x >= pow2y)
{
Node assumption = nm->mkNode(LEQ, n[0], m[0]);
Node conclusion = nm->mkNode(LEQ, n, m);
Node lem = nm->mkNode(IMPLIES, assumption, conclusion);
d_im.addPendingLemma(
lem, InferenceId::ARITH_NL_POW2_MONOTONE_REFINE, nullptr, true);
}
}
// triviality lemmas: pow2(x) = 0 whenever x < 0
if (x < 0 && pow2x != 0)
{
Node assumption = nm->mkNode(LT, n[0], d_zero);
Node conclusion = nm->mkNode(EQUAL, n, d_zero);
Node lem = nm->mkNode(IMPLIES, assumption, conclusion);
d_im.addPendingLemma(
lem, InferenceId::ARITH_NL_POW2_TRIVIAL_CASE_REFINE, nullptr, true);
}
// Place holder for additional lemma schemas
// End of additional lemma schemas
// this is the most naive model-based schema based on model values
Node lem = valueBasedLemma(n);
Trace("pow2-lemma") << "Pow2Solver::Lemma: " << lem << " ; VALUE_REFINE"
<< std::endl;
// send the value lemma
d_im.addPendingLemma(
lem, InferenceId::ARITH_NL_POW2_VALUE_REFINE, nullptr, true);
}
}
Node Pow2Solver::valueBasedLemma(Node i)
{
Assert(i.getKind() == POW2);
Node x = i[0];
Node valX = d_model.computeConcreteModelValue(x);
NodeManager* nm = NodeManager::currentNM();
Node valC = nm->mkNode(POW2, valX);
valC = rewrite(valC);
Node lem = nm->mkNode(IMPLIES, x.eqNode(valX), i.eqNode(valC));
return lem;
}
} // namespace nl
} // namespace arith
} // namespace theory
} // namespace cvc5
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