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/********************* */
/*! \file proof_checker.cpp
** \verbatim
** Top contributors (to current version):
** Alex Ozdemir
** This file is part of the CVC4 project.
** Copyright (c) 2009-2019 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.\endverbatim
**
** \brief Implementation of arithmetic proof checker
**/
#include "theory/arith/proof_checker.h"
#include <iostream>
#include <set>
#include "expr/skolem_manager.h"
#include "theory/arith/arith_utilities.h"
#include "theory/arith/constraint.h"
#include "theory/arith/normal_form.h"
#include "theory/arith/operator_elim.h"
namespace CVC4 {
namespace theory {
namespace arith {
void ArithProofRuleChecker::registerTo(ProofChecker* pc)
{
pc->registerChecker(PfRule::ARITH_SCALE_SUM_UPPER_BOUNDS, this);
pc->registerChecker(PfRule::ARITH_TRICHOTOMY, this);
pc->registerChecker(PfRule::INT_TIGHT_UB, this);
pc->registerChecker(PfRule::INT_TIGHT_LB, this);
pc->registerChecker(PfRule::INT_TRUST, this);
pc->registerChecker(PfRule::ARITH_OP_ELIM_AXIOM, this);
}
Node ArithProofRuleChecker::checkInternal(PfRule id,
const std::vector<Node>& children,
const std::vector<Node>& args)
{
if (Debug.isOn("arith::pf::check"))
{
Debug("arith::pf::check") << "Arith PfRule:" << id << std::endl;
Debug("arith::pf::check") << " children: " << std::endl;
for (const auto& c : children)
{
Debug("arith::pf::check") << " * " << c << std::endl;
}
Debug("arith::pf::check") << " args:" << std::endl;
for (const auto& c : args)
{
Debug("arith::pf::check") << " * " << c << std::endl;
}
}
switch (id)
{
case PfRule::ARITH_SCALE_SUM_UPPER_BOUNDS:
{
// Children: (P1:l1, ..., Pn:ln)
// where each li is an ArithLiteral
// not(= ...) is dis-allowed!
//
// Arguments: (k1, ..., kn), non-zero reals
// ---------------------
// Conclusion: (>< (* k t1) (* k t2))
// where >< is the fusion of the combination of the ><i, (flipping each
// it its ki is negative). >< is always one of <, <= NB: this implies
// that lower bounds must have negative ki,
// and upper bounds must have positive ki.
// t1 is the sum of the polynomials.
// t2 is the sum of the constants.
Assert(children.size() == args.size());
if (children.size() < 2)
{
return Node::null();
}
// Whether a strict inequality is in the sum.
auto nm = NodeManager::currentNM();
bool strict = false;
NodeBuilder<> leftSum(Kind::PLUS);
NodeBuilder<> rightSum(Kind::PLUS);
for (size_t i = 0; i < children.size(); ++i)
{
Rational scalar = args[i].getConst<Rational>();
if (scalar == 0)
{
Debug("arith::pf::check") << "Error: zero scalar" << std::endl;
return Node::null();
}
// Adjust strictness
switch (children[i].getKind())
{
case Kind::GT:
case Kind::LT:
{
strict = true;
break;
}
case Kind::GEQ:
case Kind::LEQ:
case Kind::EQUAL:
{
break;
}
default:
{
Debug("arith::pf::check")
<< "Bad kind: " << children[i].getKind() << std::endl;
}
}
// Check sign
switch (children[i].getKind())
{
case Kind::GT:
case Kind::GEQ:
{
if (scalar > 0)
{
Debug("arith::pf::check")
<< "Positive scalar for lower bound: " << scalar << " for "
<< children[i] << std::endl;
return Node::null();
}
break;
}
case Kind::LEQ:
case Kind::LT:
{
if (scalar < 0)
{
Debug("arith::pf::check")
<< "Negative scalar for upper bound: " << scalar << " for "
<< children[i] << std::endl;
return Node::null();
}
break;
}
case Kind::EQUAL:
{
break;
}
default:
{
Debug("arith::pf::check")
<< "Bad kind: " << children[i].getKind() << std::endl;
}
}
leftSum << nm->mkNode(
Kind::MULT, children[i][0], nm->mkConst<Rational>(scalar));
rightSum << nm->mkNode(
Kind::MULT, children[i][1], nm->mkConst<Rational>(scalar));
}
Node r = nm->mkNode(strict ? Kind::LT : Kind::LEQ,
leftSum.constructNode(),
rightSum.constructNode());
return r;
}
case PfRule::INT_TIGHT_LB:
{
// Children: (P:(> i c))
// where i has integer type.
// Arguments: none
// ---------------------
// Conclusion: (>= i leastIntGreaterThan(c)})
if (children.size() != 1
|| (children[0].getKind() != Kind::GT
&& children[0].getKind() != Kind::GEQ)
|| !children[0][0].getType().isInteger()
|| children[0][1].getKind() != Kind::CONST_RATIONAL)
{
Debug("arith::pf::check") << "Illformed input: " << children;
return Node::null();
}
else
{
Rational originalBound = children[0][1].getConst<Rational>();
Rational newBound = leastIntGreaterThan(originalBound);
auto nm = NodeManager::currentNM();
Node rational = nm->mkConst<Rational>(newBound);
return nm->mkNode(kind::GEQ, children[0][0], rational);
}
}
case PfRule::INT_TIGHT_UB:
{
// ======== Tightening Strict Integer Upper Bounds
// Children: (P:(< i c))
// where i has integer type.
// Arguments: none
// ---------------------
// Conclusion: (<= i greatestIntLessThan(c)})
if (children.size() != 1
|| (children[0].getKind() != Kind::LT
&& children[0].getKind() != Kind::LEQ)
|| !children[0][0].getType().isInteger()
|| children[0][1].getKind() != Kind::CONST_RATIONAL)
{
Debug("arith::pf::check") << "Illformed input: " << children;
return Node::null();
}
else
{
Rational originalBound = children[0][1].getConst<Rational>();
Rational newBound = greatestIntLessThan(originalBound);
auto nm = NodeManager::currentNM();
Node rational = nm->mkConst<Rational>(newBound);
return nm->mkNode(kind::LEQ, children[0][0], rational);
}
}
case PfRule::ARITH_TRICHOTOMY:
{
Node a = negateProofLiteral(children[0]);
Node b = negateProofLiteral(children[1]);
Node c = args[0];
if (a[0] == b[0] && b[0] == c[0] && a[1] == b[1] && b[1] == c[1])
{
std::set<Kind> cmps;
cmps.insert(a.getKind());
cmps.insert(b.getKind());
cmps.insert(c.getKind());
if (cmps.count(Kind::EQUAL) == 0)
{
Debug("arith::pf::check") << "Error: No = " << std::endl;
return Node::null();
}
if (cmps.count(Kind::GT) == 0)
{
Debug("arith::pf::check") << "Error: No > " << std::endl;
return Node::null();
}
if (cmps.count(Kind::LT) == 0)
{
Debug("arith::pf::check") << "Error: No < " << std::endl;
return Node::null();
}
return args[0];
}
else
{
Debug("arith::pf::check")
<< "Error: Different polynomials / values" << std::endl;
Debug("arith::pf::check") << " a: " << a << std::endl;
Debug("arith::pf::check") << " b: " << b << std::endl;
Debug("arith::pf::check") << " c: " << c << std::endl;
return Node::null();
}
// Check that all have the same constant:
}
case PfRule::INT_TRUST:
{
Assert(args.size() == 1);
return args[0];
}
case PfRule::ARITH_OP_ELIM_AXIOM:
{
Assert(children.empty());
Assert(args.size() == 1);
return OperatorElim::getAxiomFor(args[0]);
}
default: return Node::null();
}
}
} // namespace arith
} // namespace theory
} // namespace CVC4
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