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.formulas.BinaryOperator;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFactory;
  import org.logicng.formulas.FormulaTransformation;
  import org.logicng.formulas.Literal;
  import org.logicng.formulas.Not;
  import org.logicng.formulas.PBConstraint;
  
  import java.util.ArrayList;
  import java.util.HashMap;
  import java.util.List;
  import java.util.Map;
  
  /**
   * A formula transformation which substitutes literals by other literals.
   * <p>
   * Always the best fit is chosen.  So if there are two mappings for e.g.
   * {@code a -> b} and {@code ~a -> c}.  Then {@code ~a} will be mapped to
   * {@code c} and not to {@code ~b}.  On the other hand if there is only the
   * mapping {@code a -> b}, the literal {@code ~a} will be mapped to {@code ~b}.
   * @version 2.0.0
   * @since 2.0.0
   */
  public final class LiteralSubstitution implements FormulaTransformation {
  
      private final Map<Literal, Literal> substitution;
  
      /**
       * Generate a new formula substitution with a given literal-to-literal
       * mapping.
       * @param substitution a mapping from literals to literals
       */
      public LiteralSubstitution(final Map<Literal, Literal> substitution) {
          this.substitution = substitution;
      }
  
      /**
       * Generates a new formula substitution with an empty literal mapping.
       */
      public LiteralSubstitution() {
          this.substitution = new HashMap<>();
      }
  
      /**
       * Adds a new literal mapping to this substitution.
       * @param from the literal which should be substituted
       * @param to   the literal with which the substituted literal should be replaced
       */
      public void addSubstitution(final Literal from, final Literal to) {
          this.substitution.put(from, to);
      }
  
      @Override
      public Formula apply(final Formula formula, final boolean cache) {
          final FormulaFactory f = formula.factory();
          switch (formula.type()) {
              case TRUE:
              case FALSE:
                  return formula;
              case LITERAL:
                  final Literal literal = (Literal) formula;
                  Literal lit = this.substitution.get(literal);
                  if (lit != null) {
                      return lit;
                  }
                  if (!literal.phase()) {
                      lit = this.substitution.get(literal.variable());
                      return lit != null ? lit.negate() : formula;
                  }
                  return formula;
              case NOT:
                  return f.not(apply(((Not) formula).operand(), cache));
              case EQUIV:
              case IMPL:
                  final BinaryOperator binOp = (BinaryOperator) formula;
                  return f.binaryOperator(formula.type(), apply(binOp.left(), cache), apply(binOp.right(), cache));
              case OR:
              case AND:
                  final List<Formula> operands = new ArrayList<>();
                  for (final Formula op : formula) {
                      operands.add(apply(op, cache));
                  }
                  return f.naryOperator(formula.type(), operands);
              case PBC:
                  final PBConstraint pbc = (PBConstraint) formula;
                  final Literal[] originalOperands = pbc.operands();
                  final Literal[] literals = new Literal[originalOperands.length];
                  for (int i = 0; i < literals.length; i++) {
                      literals[i] = (Literal) apply(originalOperands[i], false);
                  }
                  return f.pbc(pbc.comparator(), pbc.rhs(), literals, pbc.coefficients());
              default:
                  throw new IllegalArgumentException("Unknown formula type: " + formula.type());
          }
      }
  }
  