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/****************************************************************************** |
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* Top contributors (to current version): |
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* Alex Ozdemir, Gereon Kremer, Andres Noetzli |
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* |
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* This file is part of the cvc5 project. |
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* |
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* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS |
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* in the top-level source directory and their institutional affiliations. |
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* All rights reserved. See the file COPYING in the top-level source |
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* directory for licensing information. |
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* **************************************************************************** |
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* |
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* Implementation of arithmetic proof checker. |
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*/ |
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#include "theory/arith/proof_checker.h" |
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#include <iostream> |
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#include <set> |
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#include "expr/skolem_manager.h" |
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#include "theory/arith/arith_utilities.h" |
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#include "theory/arith/constraint.h" |
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#include "theory/arith/normal_form.h" |
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#include "theory/arith/operator_elim.h" |
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namespace cvc5 { |
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namespace theory { |
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namespace arith { |
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3796 |
void ArithProofRuleChecker::registerTo(ProofChecker* pc) |
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{ |
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3796 |
pc->registerChecker(PfRule::MACRO_ARITH_SCALE_SUM_UB, this); |
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3796 |
pc->registerChecker(PfRule::ARITH_SUM_UB, this); |
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3796 |
pc->registerChecker(PfRule::ARITH_TRICHOTOMY, this); |
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3796 |
pc->registerChecker(PfRule::INT_TIGHT_UB, this); |
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3796 |
pc->registerChecker(PfRule::INT_TIGHT_LB, this); |
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3796 |
pc->registerChecker(PfRule::ARITH_OP_ELIM_AXIOM, this); |
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3796 |
pc->registerChecker(PfRule::ARITH_MULT_POS, this); |
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3796 |
pc->registerChecker(PfRule::ARITH_MULT_NEG, this); |
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3796 |
} |
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192754 |
Node ArithProofRuleChecker::checkInternal(PfRule id, |
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const std::vector<Node>& children, |
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const std::vector<Node>& args) |
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{ |
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192754 |
NodeManager* nm = NodeManager::currentNM(); |
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385508 |
auto zero = nm->mkConst<Rational>(0); |
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192754 |
if (Debug.isOn("arith::pf::check")) |
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{ |
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Debug("arith::pf::check") << "Arith PfRule:" << id << std::endl; |
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Debug("arith::pf::check") << " children: " << std::endl; |
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for (const auto& c : children) |
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{ |
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Debug("arith::pf::check") << " * " << c << std::endl; |
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} |
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Debug("arith::pf::check") << " args:" << std::endl; |
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for (const auto& c : args) |
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{ |
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Debug("arith::pf::check") << " * " << c << std::endl; |
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} |
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} |
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192754 |
switch (id) |
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{ |
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23994 |
case PfRule::ARITH_MULT_POS: |
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{ |
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23994 |
Assert(children.empty()); |
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23994 |
Assert(args.size() == 2); |
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47988 |
Node mult = args[0]; |
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23994 |
Kind rel = args[1].getKind(); |
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23994 |
Assert(rel == Kind::EQUAL || rel == Kind::DISTINCT || rel == Kind::LT |
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|| rel == Kind::LEQ || rel == Kind::GT || rel == Kind::GEQ); |
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47988 |
Node lhs = args[1][0]; |
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47988 |
Node rhs = args[1][1]; |
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return nm->mkNode(Kind::IMPLIES, |
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119970 |
nm->mkAnd(std::vector<Node>{ |
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71982 |
nm->mkNode(Kind::GT, mult, zero), args[1]}), |
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95976 |
nm->mkNode(rel, |
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47988 |
nm->mkNode(Kind::MULT, mult, lhs), |
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119970 |
nm->mkNode(Kind::MULT, mult, rhs))); |
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} |
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27147 |
case PfRule::ARITH_MULT_NEG: |
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{ |
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27147 |
Assert(children.empty()); |
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27147 |
Assert(args.size() == 2); |
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54294 |
Node mult = args[0]; |
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27147 |
Kind rel = args[1].getKind(); |
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27147 |
Assert(rel == Kind::EQUAL || rel == Kind::DISTINCT || rel == Kind::LT |
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|| rel == Kind::LEQ || rel == Kind::GT || rel == Kind::GEQ); |
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27147 |
Kind rel_inv = (rel == Kind::DISTINCT ? rel : reverseRelationKind(rel)); |
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54294 |
Node lhs = args[1][0]; |
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54294 |
Node rhs = args[1][1]; |
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return nm->mkNode(Kind::IMPLIES, |
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135735 |
nm->mkAnd(std::vector<Node>{ |
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nm->mkNode(Kind::LT, mult, zero), args[1]}), |
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108588 |
nm->mkNode(rel_inv, |
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nm->mkNode(Kind::MULT, mult, lhs), |
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nm->mkNode(Kind::MULT, mult, rhs))); |
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} |
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9722 |
case PfRule::ARITH_SUM_UB: |
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{ |
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if (children.size() < 2) |
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{ |
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return Node::null(); |
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} |
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// Whether a strict inequality is in the sum. |
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9722 |
bool strict = false; |
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19444 |
NodeBuilder leftSum(Kind::PLUS); |
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19444 |
NodeBuilder rightSum(Kind::PLUS); |
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62144 |
for (size_t i = 0; i < children.size(); ++i) |
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{ |
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// Adjust strictness |
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52422 |
switch (children[i].getKind()) |
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{ |
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9024 |
case Kind::LT: |
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{ |
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9024 |
strict = true; |
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9024 |
break; |
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} |
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43398 |
case Kind::LEQ: |
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case Kind::EQUAL: |
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{ |
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43398 |
break; |
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} |
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default: |
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{ |
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Debug("arith::pf::check") |
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<< "Bad kind: " << children[i].getKind() << std::endl; |
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return Node::null(); |
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} |
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} |
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52422 |
leftSum << children[i][0]; |
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rightSum << children[i][1]; |
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} |
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Node r = nm->mkNode(strict ? Kind::LT : Kind::LEQ, |
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19444 |
leftSum.constructNode(), |
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38888 |
rightSum.constructNode()); |
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return r; |
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} |
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85144 |
case PfRule::MACRO_ARITH_SCALE_SUM_UB: |
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{ |
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//================================================= Arithmetic rules |
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// ======== Adding Inequalities |
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// Note: an ArithLiteral is a term of the form (>< poly const) |
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// where |
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// >< is >=, >, ==, <, <=, or not(== ...). |
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// poly is a polynomial |
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// const is a rational constant |
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// Children: (P1:l1, ..., Pn:ln) |
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// where each li is an ArithLiteral |
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// not(= ...) is dis-allowed! |
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// |
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// Arguments: (k1, ..., kn), non-zero reals |
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// --------------------- |
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// Conclusion: (>< t1 t2) |
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// where >< is the fusion of the combination of the ><i, (flipping each |
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// it its ki is negative). >< is always one of <, <= NB: this implies |
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// that lower bounds must have negative ki, |
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// and upper bounds must have positive ki. |
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// t1 is the sum of the scaled polynomials (k_1 * poly_1 + ... + k_n * |
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// poly_n) t2 is the sum of the scaled constants (k_1 * const_1 + ... + |
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// k_n * const_n) |
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85144 |
Assert(children.size() == args.size()); |
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85144 |
if (children.size() < 2) |
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{ |
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return Node::null(); |
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} |
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// Whether a strict inequality is in the sum. |
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85144 |
bool strict = false; |
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170288 |
NodeBuilder leftSum(Kind::PLUS); |
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170288 |
NodeBuilder rightSum(Kind::PLUS); |
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365956 |
for (size_t i = 0; i < children.size(); ++i) |
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{ |
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561624 |
Rational scalar = args[i].getConst<Rational>(); |
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280812 |
if (scalar == 0) |
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{ |
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Debug("arith::pf::check") << "Error: zero scalar" << std::endl; |
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return Node::null(); |
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} |
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// Adjust strictness |
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280812 |
switch (children[i].getKind()) |
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{ |
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case Kind::GT: |
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case Kind::LT: |
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{ |
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strict = true; |
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break; |
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} |
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case Kind::GEQ: |
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case Kind::LEQ: |
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case Kind::EQUAL: |
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{ |
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227534 |
break; |
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} |
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default: |
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{ |
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Debug("arith::pf::check") |
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<< "Bad kind: " << children[i].getKind() << std::endl; |
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} |
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} |
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// Check sign |
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280812 |
switch (children[i].getKind()) |
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{ |
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76840 |
case Kind::GT: |
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case Kind::GEQ: |
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{ |
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76840 |
if (scalar > 0) |
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Debug("arith::pf::check") |
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<< "Positive scalar for lower bound: " << scalar << " for " |
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<< children[i] << std::endl; |
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return Node::null(); |
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} |
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76840 |
break; |
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} |
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84724 |
case Kind::LEQ: |
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case Kind::LT: |
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{ |
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84724 |
if (scalar < 0) |
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{ |
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Debug("arith::pf::check") |
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<< "Negative scalar for upper bound: " << scalar << " for " |
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<< children[i] << std::endl; |
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return Node::null(); |
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} |
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84724 |
break; |
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} |
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119248 |
case Kind::EQUAL: |
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{ |
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119248 |
break; |
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} |
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default: |
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{ |
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Debug("arith::pf::check") |
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<< "Bad kind: " << children[i].getKind() << std::endl; |
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} |
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} |
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1404060 |
leftSum << nm->mkNode( |
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1404060 |
Kind::MULT, nm->mkConst<Rational>(scalar), children[i][0]); |
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1404060 |
rightSum << nm->mkNode( |
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1404060 |
Kind::MULT, nm->mkConst<Rational>(scalar), children[i][1]); |
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} |
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Node r = nm->mkNode(strict ? Kind::LT : Kind::LEQ, |
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170288 |
leftSum.constructNode(), |
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340576 |
rightSum.constructNode()); |
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85144 |
return r; |
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} |
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case PfRule::INT_TIGHT_LB: |
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{ |
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// Children: (P:(> i c)) |
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// where i has integer type. |
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// Arguments: none |
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// --------------------- |
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// Conclusion: (>= i leastIntGreaterThan(c)}) |
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if (children.size() != 1 |
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|| (children[0].getKind() != Kind::GT |
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&& children[0].getKind() != Kind::GEQ) |
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|| !children[0][0].getType().isInteger() |
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|| children[0][1].getKind() != Kind::CONST_RATIONAL) |
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{ |
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Debug("arith::pf::check") << "Illformed input: " << children; |
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return Node::null(); |
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} |
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else |
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{ |
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Rational originalBound = children[0][1].getConst<Rational>(); |
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Rational newBound = leastIntGreaterThan(originalBound); |
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Node rational = nm->mkConst<Rational>(newBound); |
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return nm->mkNode(kind::GEQ, children[0][0], rational); |
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} |
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} |
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4135 |
case PfRule::INT_TIGHT_UB: |
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{ |
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// ======== Tightening Strict Integer Upper Bounds |
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// Children: (P:(< i c)) |
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// where i has integer type. |
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// Arguments: none |
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// --------------------- |
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// Conclusion: (<= i greatestIntLessThan(c)}) |
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8270 |
if (children.size() != 1 |
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4135 |
|| (children[0].getKind() != Kind::LT |
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&& children[0].getKind() != Kind::LEQ) |
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8270 |
|| !children[0][0].getType().isInteger() |
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12405 |
|| children[0][1].getKind() != Kind::CONST_RATIONAL) |
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{ |
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Debug("arith::pf::check") << "Illformed input: " << children; |
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return Node::null(); |
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} |
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else |
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{ |
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8270 |
Rational originalBound = children[0][1].getConst<Rational>(); |
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8270 |
Rational newBound = greatestIntLessThan(originalBound); |
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8270 |
Node rational = nm->mkConst<Rational>(newBound); |
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4135 |
return nm->mkNode(kind::LEQ, children[0][0], rational); |
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} |
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} |
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42342 |
case PfRule::ARITH_TRICHOTOMY: |
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{ |
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84684 |
Node a = negateProofLiteral(children[0]); |
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84684 |
Node b = negateProofLiteral(children[1]); |
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84684 |
Node c = args[0]; |
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42342 |
if (a[0] == b[0] && b[0] == c[0] && a[1] == b[1] && b[1] == c[1]) |
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{ |
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84684 |
std::set<Kind> cmps; |
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42342 |
cmps.insert(a.getKind()); |
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42342 |
cmps.insert(b.getKind()); |
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42342 |
cmps.insert(c.getKind()); |
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42342 |
if (cmps.count(Kind::EQUAL) == 0) |
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{ |
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Debug("arith::pf::check") << "Error: No = " << std::endl; |
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return Node::null(); |
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} |
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42342 |
if (cmps.count(Kind::GT) == 0) |
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{ |
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Debug("arith::pf::check") << "Error: No > " << std::endl; |
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return Node::null(); |
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} |
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42342 |
if (cmps.count(Kind::LT) == 0) |
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{ |
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Debug("arith::pf::check") << "Error: No < " << std::endl; |
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return Node::null(); |
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} |
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42342 |
return args[0]; |
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} |
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else |
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{ |
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Debug("arith::pf::check") |
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<< "Error: Different polynomials / values" << std::endl; |
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Debug("arith::pf::check") << " a: " << a << std::endl; |
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Debug("arith::pf::check") << " b: " << b << std::endl; |
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Debug("arith::pf::check") << " c: " << c << std::endl; |
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return Node::null(); |
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} |
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// Check that all have the same constant: |
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} |
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case PfRule::ARITH_OP_ELIM_AXIOM: |
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{ |
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Assert(children.empty()); |
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Assert(args.size() == 1); |
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return OperatorElim::getAxiomFor(args[0]); |
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} |
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default: return Node::null(); |
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} |
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} |
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} // namespace arith |
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} // namespace theory |
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29577 |
} // namespace cvc5 |