code: ///////////////////////////////////////////////////////////////////////////
  //                   __                _      _   ________               //
  //                  / /   ____  ____ _(_)____/ | / / ____/               //
  //                 / /   / __ \/ __ `/ / ___/  |/ / / __                 //
  //                / /___/ /_/ / /_/ / / /__/ /|  / /_/ /                 //
  //               /_____/\____/\__, /_/\___/_/ |_/\____/                  //
  //                           /____/                                      //
  //                                                                       //
  //               The Next Generation Logic Library                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  //                                                                       //
  //  Copyright 2015-20xx Christoph Zengler                                //
  //                                                                       //
  //  Licensed under the Apache License, Version 2.0 (the "License");      //
  //  you may not use this file except in compliance with the License.     //
  //  You may obtain a copy of the License at                              //
  //                                                                       //
  //  http://www.apache.org/licenses/LICENSE-2.0                           //
  //                                                                       //
  //  Unless required by applicable law or agreed to in writing, software  //
  //  distributed under the License is distributed on an "AS IS" BASIS,    //
  //  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or      //
  //  implied.  See the License for the specific language governing        //
  //  permissions and limitations under the License.                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  
  package org.logicng.transformations;
  
  import org.logicng.collections.LNGIntVector;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFactory;
  import org.logicng.formulas.FormulaTransformation;
  import org.logicng.formulas.Literal;
  import org.logicng.formulas.cache.TransformationCacheEntry;
  import org.logicng.solvers.datastructures.MSClause;
  import org.logicng.solvers.sat.MiniSat2Solver;
  import org.logicng.solvers.sat.MiniSatConfig;
  
  import java.util.ArrayList;
  import java.util.List;
  
  /**
   * A formula transformation which performs unit propagation.
   * @version 2.3.0
   * @since 1.2
   */
  public final class UnitPropagation implements FormulaTransformation {
  
      private static final UnitPropagation INSTANCE = new UnitPropagation();
  
      /**
       * @deprecated In the next version, the standard constructor will be replaced by a private constructor.
       * In order to instantiate an object of this class, use the {@link #get()} method.
       */
      @Deprecated
      public UnitPropagation() {
          // Intentionally left empty
      }
  
      /**
       * Returns the singleton instance of this function.
       * @return an instance of this function
       */
      public static UnitPropagation get() {
          return INSTANCE;
      }
  
      @Override
      public Formula apply(final Formula formula, final boolean cache) {
          final Formula cached = formula.transformationCacheEntry(TransformationCacheEntry.UNIT_PROPAGATION);
          if (cached != null) {
              return cached;
          }
          final MiniSatPropagator miniSatPropagator = new MiniSatPropagator();
          miniSatPropagator.add(formula);
          final Formula result = miniSatPropagator.propagatedFormula(formula.factory());
          if (cache) {
              formula.setTransformationCacheEntry(TransformationCacheEntry.UNIT_PROPAGATION, result);
          }
          return result;
      }
  
      /**
       * An extension of Minisat to propagate units on formulas.
       */
      private static class MiniSatPropagator extends MiniSat2Solver {
  
          /**
           * Constructs a new MiniSatPropagator.
           */
          public MiniSatPropagator() {
              super(MiniSatConfig.builder().incremental(false).build());
          }
  
          /**
           * Adds an arbitrary formula to the propagator.
           * @param formula the formula
           */
          public void add(final Formula formula) {
              final Formula cnf = formula.cnf();
              switch (cnf.type()) {
                  case TRUE:
                      break;
                  case FALSE:
                  case LITERAL:
                  case OR:
                      this.addClause(generateClauseVector(cnf), null);
                      break;
                  case AND:
                      for (final Formula op : cnf) {
                          this.addClause(generateClauseVector(op), null);
                      }
                      break;
                  default:
                      throw new IllegalStateException("Unexpected formula type in CNF: " + cnf.type());
              }
          }
  
          /**
           * Performs unit propagation on level 0 and returns the propagated formula.
           * @param f the formula factory
           * @return the propagated formula
           */
          public Formula propagatedFormula(final FormulaFactory f) {
              assert decisionLevel() == 0;
              if (!this.ok || this.propagate() != null) {
                  return f.falsum();
              }
              final List<Formula> clauses = new ArrayList<>();
              for (final MSClause clause : this.clauses) {
                  clauses.add(clauseToFormula(clause, f));
              }
              for (int i = 0; i < this.trail.size(); i++) {
                  clauses.add(solverLiteralToFormula(this.trail.get(i), f));
              }
              return f.and(clauses);
          }
  
          /**
           * Transforms a solver literal into the corresponding formula literal.
           * @param lit the solver literal
           * @param f   the formula factory
           * @return the formula literal
           */
          private Literal solverLiteralToFormula(final int lit, final FormulaFactory f) {
              return f.literal(this.nameForIdx(var(lit)), !sign(lit));
          }
  
          /**
           * Transforms a solver clause into a formula, respecting the current solver state.
           * I.e. all falsified literals are removed from the resulting clause and
           * if any literal of the clause is satisfied, the result is {@link org.logicng.formulas.CTrue}.
           * @param clause the solver clause to transform
           * @param f      the formula factory
           * @return the transformed clause
           */
          private Formula clauseToFormula(final MSClause clause, final FormulaFactory f) {
              final List<Literal> literals = new ArrayList<>(clause.size());
              for (int i = 0; i < clause.size(); i++) {
                  final int lit = clause.get(i);
                  switch (value(lit)) {
                      case TRUE:
                          return f.verum();
                      case UNDEF:
                          literals.add(solverLiteralToFormula(lit, f));
                          break;
                      case FALSE:
                          // ignore this literal
                  }
              }
              return f.or(literals);
          }
  
          /**
           * Generates a solver vector of a clause.
           * @param clause the clause
           * @return the solver vector
           */
          private LNGIntVector generateClauseVector(final Formula clause) {
              final LNGIntVector clauseVec = new LNGIntVector(clause.numberOfOperands());
              for (final Literal lit : clause.literals()) {
                  int index = this.idxForName(lit.name());
                  if (index == -1) {
                      index = this.newVar(false, false);
                      this.addName(lit.name(), index);
                  }
                  final int litNum = lit.phase() ? index * 2 : (index * 2) ^ 1;
                  clauseVec.push(litNum);
              }
              return clauseVec;
          }
      }
  }
  