public static boolean isomorphic(DefaultRule a, DefaultRule b) {
   a = preprocess(a);
   b = preprocess(b);
   Matching m = new Matching();
   Clause ca = new Clause(Sugar.iterable(a.antecedent().literals(), a.consequent().literals()));
   Clause cb = new Clause(Sugar.iterable(b.antecedent().literals(), b.consequent().literals()));
   return ca.variables().size() == cb.variables().size()
       && ca.literals().size() == cb.literals().size()
       && m.isomorphism(ca, cb);
 }
 public static void main(String[] args) {
   DefaultRule a = new DefaultRule(Clause.parse("a(X)"), Clause.parse("a(Y)"));
   DefaultRule b = new DefaultRule(Clause.parse("a(A)"), Clause.parse("a(B)"));
   DefaultRule c = new DefaultRule(Clause.parse("a(A)"), Clause.parse("a(A)"));
   DefaultRule d = new DefaultRule(Clause.parse("a(A,a)"), Clause.parse("b(B,b)"));
   DefaultRule e = new DefaultRule(Clause.parse("a(A,b)"), Clause.parse("b(B,a)"));
   DefaultRule f = new DefaultRule(Clause.parse("a(A,c)"), Clause.parse("b(B,d)"));
   for (DefaultRule r : selectNonisomorphicDefaultRules(Sugar.list(a, b, c, d))) {
     System.out.println(r);
   }
   System.out.println(
       partitionInterchangeableConstants(Sugar.list(a, b, c, d, e, f), Sugar.<Clause>set()));
 }
 public static Set<DefaultRule> selectNonisomorphicDefaultRules(
     Iterable<DefaultRule> defaultRules) {
   List<Clause> candidates = new ArrayList<Clause>();
   for (DefaultRule rule : defaultRules) {
     DefaultRule preprocessed = preprocess(rule);
     candidates.add(
         new Clause(
             Sugar.<Literal>iterable(
                 preprocessed.antecedent().literals(), preprocessed.consequent().literals())));
   }
   Matching m = new Matching();
   Set<DefaultRule> retVal = new HashSet<DefaultRule>();
   for (Clause c : m.nonisomorphic(candidates)) {
     List<Literal> head = new ArrayList<Literal>();
     List<Literal> body = new ArrayList<Literal>();
     for (Literal l : c.literals()) {
       Literal newLiteral =
           new Literal(
               l.predicate().substring(l.predicate().indexOf(":") + 1), l.isNegated(), l.arity());
       for (int i = 0; i < l.arity(); i++) {
         newLiteral.set(l.get(i), i);
       }
       if (l.predicate().startsWith("antecedent:")
           || l.predicate().startsWith(SymmetricPredicates.PREFIX + "antecedent:")) {
         body.add(newLiteral);
       } else {
         head.add(newLiteral);
       }
     }
     retVal.add(new DefaultRule(new Clause(body), new Clause(head)));
   }
   return retVal;
 }
 private static MultiMap<Variable, Variable> surelyDifferent(DefaultRule rule) {
   Clause body = rule.antecedent();
   Clause head = rule.consequent();
   final MultiMap<Variable, Variable> different = new MultiMap<Variable, Variable>();
   for (Literal literal :
       Sugar.union(
           body.getLiteralsByPredicate(SpecialBinaryPredicates.NEQ),
           body.getLiteralsByPredicate(SpecialBinaryPredicates.GT),
           body.getLiteralsByPredicate(SpecialBinaryPredicates.LT),
           body.getLiteralsByPredicate(SpecialVarargPredicates.ALLDIFF),
           head.getLiteralsByPredicate(SpecialBinaryPredicates.NEQ),
           head.getLiteralsByPredicate(SpecialBinaryPredicates.GT),
           head.getLiteralsByPredicate(SpecialBinaryPredicates.LT),
           head.getLiteralsByPredicate(SpecialVarargPredicates.ALLDIFF))) {
     for (Term a : literal.terms()) {
       if (a instanceof Variable) {
         Variable v1 = (Variable) a;
         for (Term b : literal.terms()) {
           if (b instanceof Variable) {
             Variable v2 = (Variable) b;
             if (v1 != v2) {
               different.put(v1, v2);
             }
           }
         }
       }
     }
   }
   return different;
 }
 public static List<Set<Constant>> partitionInterchangeableConstants(
     Collection<DefaultRule> rules, Collection<Clause> hardRules) {
   List<Set<Constant>> retVal = new ArrayList<Set<Constant>>();
   Collection<DefaultRule> dummyRules =
       Sugar.<Clause, DefaultRule>funcall(
           hardRules,
           new Sugar.Fun<Clause, DefaultRule>() {
             @Override
             public DefaultRule apply(Clause clause) {
               return new DefaultRule(new Clause(Sugar.<Literal>list()), clause);
             }
           });
   for (List<Set<Constant>> list :
       partitionExchangeable_impl(Sugar.union(rules, dummyRules)).values()) {
     retVal.addAll(list);
   }
   return retVal;
 }
 private static Set<Term> constants(Iterable<DefaultRule> rules) {
   Set<Term> retVal = new HashSet<Term>();
   for (DefaultRule rule : rules) {
     for (Term t : Sugar.<Term>iterable(rule.antecedent().terms(), rule.consequent().terms())) {
       if (t instanceof Constant) {
         retVal.add(t);
       }
     }
   }
   return retVal;
 }
  private static MultiList<Object, Set<Constant>> partitionExchangeable_impl(
      Iterable<DefaultRule> rules) {
    MultiMap<Term, Term> partitioning = new MultiMap<Term, Term>();

    List<Term> constants = Sugar.arrayListFromCollections(constants(rules));
    Set<Term> closed = new HashSet<Term>();

    // checking interchangeability pairwise
    for (int i = 0; i < constants.size(); i++) {
      if (!closed.contains(constants.get(i))) {
        partitioning.put(constants.get(i), constants.get(i));
        for (int j = i + 1; j < constants.size(); j++) {
          if (areExchangeable(constants.get(i), constants.get(j), rules)) {
            partitioning.put(constants.get(i), constants.get(j));
            closed.add(constants.get(j));
          }
        }
      }
    }
    Map<Constant, Constant> map = new HashMap<Constant, Constant>();
    for (Map.Entry<Term, Set<Term>> entry : partitioning.entrySet()) {
      Constant lexmin = null;
      for (Term t : entry.getValue()) {
        if (t instanceof Constant) {
          if (lexmin == null || t.toString().compareTo(lexmin.toString()) < 0) {
            lexmin = (Constant) t;
          }
        }
      }
      for (Term t : entry.getValue()) {
        if (t instanceof Constant) {
          map.put((Constant) t, lexmin);
        }
      }
    }

    MultiMap<Pair<Object, Constant>, Constant> mm =
        new MultiMap<Pair<Object, Constant>, Constant>();
    for (Map.Entry<Constant, Constant> entry : map.entrySet()) {
      mm.put(
          new Pair<Object, Constant>(
              entry.getValue().type() == null ? Sugar.NIL : entry.getValue().type(),
              entry.getValue()),
          entry.getKey());
    }

    MultiList<Object, Set<Constant>> retVal = new MultiList<Object, Set<Constant>>();
    for (Map.Entry<Pair<Object, Constant>, Set<Constant>> entry : mm.entrySet()) {
      retVal.put(entry.getKey().r, entry.getValue());
    }
    return retVal;
  }
 public static Triple<Set<DefaultRule>, Set<Clause>, List<Set<Constant>>> preprocessConstants(
     Collection<DefaultRule> rules,
     Collection<Clause> hardRules,
     List<Set<Constant>> interchangeable) {
   final Map<Term, Term> typedConstants = new HashMap<Term, Term>();
   List<Set<Constant>> retInterchangeable = new ArrayList<Set<Constant>>();
   for (Set<Constant> set : interchangeable) {
     String type = min(set).name();
     Set<Constant> newSet = new HashSet<Constant>();
     for (Constant c : set) {
       Constant typedConstant = Constant.construct(c.name(), type);
       typedConstants.put(c, typedConstant);
       newSet.add(typedConstant);
     }
     retInterchangeable.add(newSet);
   }
   Collection<DefaultRule> retDefaultRules =
       Sugar.funcall(
           rules,
           new Sugar.Fun<DefaultRule, DefaultRule>() {
             @Override
             public DefaultRule apply(DefaultRule defaultRule) {
               return DefaultTransformationUtils.substitute(defaultRule, typedConstants);
             }
           });
   Collection<Clause> retHardRules =
       Sugar.funcall(
           hardRules,
           new Sugar.Fun<Clause, Clause>() {
             @Override
             public Clause apply(Clause hardRule) {
               return LogicUtils.substitute(hardRule, typedConstants);
             }
           });
   return new Triple<Set<DefaultRule>, Set<Clause>, List<Set<Constant>>>(
       Sugar.setFromCollections(retDefaultRules),
       Sugar.setFromCollections(retHardRules),
       Sugar.listFromCollections(retInterchangeable));
 }
 public static Clause clauseFromDefault(DefaultRule rule) {
   return new Clause(
       Sugar.iterable(
           Utils.flipSigns(rule.antecedent().literals()), rule.consequent().literals()));
 }
  public static MultiMap<DefaultRule, DefaultRule> representativeBodySpecializations(
      DefaultRule rule, List<Set<Constant>> interchangeableConstants) {
    Clause body = rule.antecedent();
    Clause head = rule.consequent();
    final MultiMap<Variable, Variable> different = surelyDifferent(rule);

    final List<Variable> variables = Sugar.<Variable>listFromCollections(body.variables());
    List<Integer> indices = VectorUtils.toList(VectorUtils.sequence(0, variables.size() - 1));
    List<Tuple<Integer>> unifications =
        Combinatorics.<Integer>cartesianPower(
            indices,
            indices.size(),
            new Sugar.Fun<Tuple<Integer>, Boolean>() {
              @Override
              public Boolean apply(Tuple<Integer> integerTuple) {
                for (int i = 0; i < integerTuple.size(); i++) {
                  if (integerTuple.get(i) > i
                      || !integerTuple.get(i).equals(integerTuple.get(integerTuple.get(i)))
                      || different
                          .get(variables.get(integerTuple.get(i)))
                          .contains(variables.get(i))
                      || !sameType(variables.get(integerTuple.get(i)), variables.get(i))) {
                    return Boolean.FALSE;
                  }
                }
                return Boolean.TRUE;
              }
            });

    Set<DefaultRule> nonIsomorphicUnifications = new HashSet<DefaultRule>();
    for (Tuple<Integer> unification : unifications) {
      Map<Term, Term> substitution = new HashMap<Term, Term>();
      for (int i = 0; i < unification.size(); i++) {
        substitution.put(variables.get(i), variables.get(unification.get(i)));
      }
      Clause newBody = LogicUtils.substitute(rule.antecedent(), substitution);
      Clause newHead = LogicUtils.substitute(rule.consequent(), substitution);
      nonIsomorphicUnifications.add(
          new DefaultRule(
              newBody.variables().size() > 1
                  ? new Clause(Sugar.union(newBody.literals(), allDiffLiteral(newBody)))
                  : newBody,
              newHead));
    }

    nonIsomorphicUnifications =
        DefaultTransformationUtils.selectNonisomorphicDefaultRules(nonIsomorphicUnifications);

    MultiMap<DefaultRule, DefaultRule> retVal = new MultiMap<DefaultRule, DefaultRule>();

    // this needs to be improved... e.g. using typing information...
    MultiList<Integer, Constant> consts = new MultiList<Integer, Constant>();
    int index = 0;
    for (Set<Constant> interch : interchangeableConstants) {
      consts.putAll(index++, interch);
    }
    for (DefaultRule unifiedRule : nonIsomorphicUnifications) {
      List<Variable> unifsVariables = Sugar.listFromCollections(unifiedRule.variables());
      if (unifsVariables.isEmpty()) {
        retVal.put(unifiedRule, unifiedRule);
      } else {
        Set<DefaultRule> substituted = new HashSet<DefaultRule>();
        middleLoop:
        for (Tuple<Integer> tuple :
            Combinatorics.cartesianPower(
                new NaturalNumbersList(0, interchangeableConstants.size()),
                unifsVariables.size())) {
          Counters<Integer> used = new Counters<Integer>();
          Map<Term, Term> substitution = new HashMap<Term, Term>();
          for (int i = 0; i < unifsVariables.size(); i++) {
            int j = used.incrementPost(tuple.get(i));
            if (j >= consts.get(tuple.get(i)).size()) {
              continue middleLoop;
            } else {
              if (unifsVariables.get(i).type() == null) {
                substitution.put(
                    unifsVariables.get(i),
                    Variable.construct(
                        unifsVariables.get(i).name(), consts.get(tuple.get(i)).get(j).type()));
              } else {
                if (unifsVariables.get(i).type().equals(consts.get(tuple.get(i)).get(j).type())) {
                  substitution.put(
                      unifsVariables.get(i),
                      Variable.construct(
                          unifsVariables.get(i).name(), consts.get(tuple.get(i)).get(j).type()));
                } else {
                  continue middleLoop;
                }
              }
            }
          }
          substituted.add(DefaultTransformationUtils.substitute(unifiedRule, substitution));
        }
        retVal.putAll(
            unifiedRule, DefaultTransformationUtils.selectNonisomorphicDefaultRules(substituted));
      }
    }
    return retVal;
  }