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+// rational.h
+
+// 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.
+//
+// Copyright 2005-2010 Google, Inc.
+// Author: riley@google.com (Michael Riley)
+//
+// \file
+// An Fst implementation and base interface for delayed unions,
+// concatenations and closures.
+
+#ifndef FST_LIB_RATIONAL_H__
+#define FST_LIB_RATIONAL_H__
+
+#include <algorithm>
+#include <string>
+#include <vector>
+using std::vector;
+
+#include <fst/mutable-fst.h>
+#include <fst/replace.h>
+#include <fst/test-properties.h>
+
+
+namespace fst {
+
+typedef CacheOptions RationalFstOptions;
+
+// This specifies whether to add the empty string.
+enum ClosureType { CLOSURE_STAR = 0,    // T* -> add the empty string
+                   CLOSURE_PLUS = 1 };  // T+ -> don't add the empty string
+
+template <class A> class RationalFst;
+template <class A> void Union(RationalFst<A> *fst1, const Fst<A> &fst2);
+template <class A> void Concat(RationalFst<A> *fst1, const Fst<A> &fst2);
+template <class A> void Concat(const Fst<A> &fst1, RationalFst<A> *fst2);
+template <class A> void Closure(RationalFst<A> *fst, ClosureType closure_type);
+
+
+// Implementation class for delayed unions, concatenations and closures.
+template<class A>
+class RationalFstImpl : public FstImpl<A> {
+ public:
+  using FstImpl<A>::SetType;
+  using FstImpl<A>::SetProperties;
+  using FstImpl<A>::WriteHeader;
+  using FstImpl<A>::SetInputSymbols;
+  using FstImpl<A>::SetOutputSymbols;
+
+  typedef A Arc;
+  typedef typename A::Weight Weight;
+  typedef typename A::StateId StateId;
+  typedef typename A::Label Label;
+
+  explicit RationalFstImpl(const RationalFstOptions &opts)
+      : nonterminals_(0),
+        replace_(0),
+        replace_options_(opts, 0) {
+    SetType("rational");
+    fst_tuples_.push_back(pair<Label, const Fst<A>*>(0, 0));
+  }
+
+  RationalFstImpl(const RationalFstImpl<A> &impl)
+      : rfst_(impl.rfst_),
+        nonterminals_(impl.nonterminals_),
+
+        replace_(impl.replace_ ? impl.replace_->Copy(true) : 0),
+        replace_options_(impl.replace_options_) {
+    SetType("rational");
+    fst_tuples_.reserve(impl.fst_tuples_.size());
+    for (size_t i = 0; i < impl.fst_tuples_.size(); ++i)
+      fst_tuples_.push_back(make_pair(impl.fst_tuples_[i].first,
+                                      impl.fst_tuples_[i].second
+                                      ? impl.fst_tuples_[i].second->Copy(true)
+                                      : 0));
+  }
+
+  virtual ~RationalFstImpl() {
+    for (size_t i = 0; i < fst_tuples_.size(); ++i)
+      if (fst_tuples_[i].second)
+        delete fst_tuples_[i].second;
+    if (replace_)
+      delete replace_;
+  }
+
+  StateId Start() { return Replace()->Start(); }
+
+  Weight Final(StateId s) { return Replace()->Final(s); }
+
+  size_t NumArcs(StateId s) { return Replace()->NumArcs(s); }
+
+  size_t NumInputEpsilons(StateId s) {
+    return Replace()->NumInputEpsilons(s);
+  }
+
+  size_t NumOutputEpsilons(StateId s) {
+    return Replace()->NumOutputEpsilons(s);
+  }
+
+  uint64 Properties() const { return Properties(kFstProperties); }
+
+  // Set error if found; return FST impl properties.
+  uint64 Properties(uint64 mask) const {
+    if ((mask & kError) && Replace()->Properties(kError, false))
+      SetProperties(kError, kError);
+    return FstImpl<Arc>::Properties(mask);
+  }
+
+  // Implementation of UnionFst(fst1,fst2)
+  void InitUnion(const Fst<A> &fst1, const Fst<A> &fst2) {
+    if (replace_)
+      delete replace_;
+    uint64 props1 = fst1.Properties(kFstProperties, false);
+    uint64 props2 = fst2.Properties(kFstProperties, false);
+    SetInputSymbols(fst1.InputSymbols());
+    SetOutputSymbols(fst1.OutputSymbols());
+    rfst_.AddState();
+    rfst_.AddState();
+    rfst_.SetStart(0);
+    rfst_.SetFinal(1, Weight::One());
+    rfst_.SetInputSymbols(fst1.InputSymbols());
+    rfst_.SetOutputSymbols(fst1.OutputSymbols());
+    nonterminals_ = 2;
+    rfst_.AddArc(0, A(0, -1, Weight::One(), 1));
+    rfst_.AddArc(0, A(0, -2, Weight::One(), 1));
+    fst_tuples_.push_back(make_pair(-1, fst1.Copy()));
+    fst_tuples_.push_back(make_pair(-2, fst2.Copy()));
+    SetProperties(UnionProperties(props1, props2, true), kCopyProperties);
+  }
+
+  // Implementation of ConcatFst(fst1,fst2)
+  void InitConcat(const Fst<A> &fst1, const Fst<A> &fst2) {
+    if (replace_)
+      delete replace_;
+    uint64 props1 = fst1.Properties(kFstProperties, false);
+    uint64 props2 = fst2.Properties(kFstProperties, false);
+    SetInputSymbols(fst1.InputSymbols());
+    SetOutputSymbols(fst1.OutputSymbols());
+    rfst_.AddState();
+    rfst_.AddState();
+    rfst_.AddState();
+    rfst_.SetStart(0);
+    rfst_.SetFinal(2, Weight::One());
+    rfst_.SetInputSymbols(fst1.InputSymbols());
+    rfst_.SetOutputSymbols(fst1.OutputSymbols());
+    nonterminals_ = 2;
+    rfst_.AddArc(0, A(0, -1, Weight::One(), 1));
+    rfst_.AddArc(1, A(0, -2, Weight::One(), 2));
+    fst_tuples_.push_back(make_pair(-1, fst1.Copy()));
+    fst_tuples_.push_back(make_pair(-2, fst2.Copy()));
+    SetProperties(ConcatProperties(props1, props2, true), kCopyProperties);
+  }
+
+  // Implementation of ClosureFst(fst, closure_type)
+  void InitClosure(const Fst<A> &fst, ClosureType closure_type) {
+    if (replace_)
+      delete replace_;
+    uint64 props = fst.Properties(kFstProperties, false);
+    SetInputSymbols(fst.InputSymbols());
+    SetOutputSymbols(fst.OutputSymbols());
+    if (closure_type == CLOSURE_STAR) {
+      rfst_.AddState();
+      rfst_.SetStart(0);
+      rfst_.SetFinal(0, Weight::One());
+      rfst_.AddArc(0, A(0, -1, Weight::One(), 0));
+    } else {
+      rfst_.AddState();
+      rfst_.AddState();
+      rfst_.SetStart(0);
+      rfst_.SetFinal(1, Weight::One());
+      rfst_.AddArc(0, A(0, -1, Weight::One(), 1));
+      rfst_.AddArc(1, A(0, 0, Weight::One(), 0));
+    }
+    rfst_.SetInputSymbols(fst.InputSymbols());
+    rfst_.SetOutputSymbols(fst.OutputSymbols());
+    fst_tuples_.push_back(make_pair(-1, fst.Copy()));
+    nonterminals_ = 1;
+    SetProperties(ClosureProperties(props, closure_type == CLOSURE_STAR, true),
+                  kCopyProperties);
+  }
+
+  // Implementation of Union(Fst &, RationalFst *)
+  void AddUnion(const Fst<A> &fst) {
+    if (replace_)
+      delete replace_;
+    uint64 props1 = FstImpl<A>::Properties();
+    uint64 props2 = fst.Properties(kFstProperties, false);
+    VectorFst<A> afst;
+    afst.AddState();
+    afst.AddState();
+    afst.SetStart(0);
+    afst.SetFinal(1, Weight::One());
+    ++nonterminals_;
+    afst.AddArc(0, A(0, -nonterminals_, Weight::One(), 1));
+    Union(&rfst_, afst);
+    fst_tuples_.push_back(make_pair(-nonterminals_, fst.Copy()));
+    SetProperties(UnionProperties(props1, props2, true), kCopyProperties);
+  }
+
+  // Implementation of Concat(Fst &, RationalFst *)
+  void AddConcat(const Fst<A> &fst, bool append) {
+    if (replace_)
+      delete replace_;
+    uint64 props1 = FstImpl<A>::Properties();
+    uint64 props2 = fst.Properties(kFstProperties, false);
+    VectorFst<A> afst;
+    afst.AddState();
+    afst.AddState();
+    afst.SetStart(0);
+    afst.SetFinal(1, Weight::One());
+    ++nonterminals_;
+    afst.AddArc(0, A(0, -nonterminals_, Weight::One(), 1));
+    if (append)
+      Concat(&rfst_, afst);
+    else
+      Concat(afst, &rfst_);
+    fst_tuples_.push_back(make_pair(-nonterminals_, fst.Copy()));
+    SetProperties(ConcatProperties(props1, props2, true), kCopyProperties);
+  }
+
+  // Implementation of Closure(RationalFst *, closure_type)
+  void AddClosure(ClosureType closure_type) {
+    if (replace_)
+      delete replace_;
+    uint64 props = FstImpl<A>::Properties();
+    Closure(&rfst_, closure_type);
+    SetProperties(ClosureProperties(props, closure_type == CLOSURE_STAR, true),
+                  kCopyProperties);
+  }
+
+  // Returns the underlying ReplaceFst.
+  ReplaceFst<A> *Replace() const {
+    if (!replace_) {
+      fst_tuples_[0].second = rfst_.Copy();
+      replace_ = new ReplaceFst<A>(fst_tuples_, replace_options_);
+    }
+    return replace_;
+  }
+
+ private:
+  VectorFst<A> rfst_;   // rational topology machine; uses neg. nonterminals
+  Label nonterminals_;  // # of nonterminals used
+  // Contains the nonterminals and their corresponding FSTs.
+  mutable vector<pair<Label, const Fst<A>*> > fst_tuples_;
+  mutable ReplaceFst<A> *replace_;        // Underlying ReplaceFst
+  ReplaceFstOptions<A> replace_options_;  // Options for creating 'replace_'
+
+  void operator=(const RationalFstImpl<A> &impl);    // disallow
+};
+
+// Parent class for the delayed rational operations - delayed union,
+// concatenation, and closure.
+//
+// This class attaches interface to implementation and handles
+// reference counting, delegating most methods to ImplToFst.
+template <class A>
+class RationalFst : public ImplToFst< RationalFstImpl<A> > {
+ public:
+  friend class StateIterator< RationalFst<A> >;
+  friend class ArcIterator< RationalFst<A> >;
+  friend void Union<>(RationalFst<A> *fst1, const Fst<A> &fst2);
+  friend void Concat<>(RationalFst<A> *fst1, const Fst<A> &fst2);
+  friend void Concat<>(const Fst<A> &fst1, RationalFst<A> *fst2);
+  friend void Closure<>(RationalFst<A> *fst, ClosureType closure_type);
+
+  typedef A Arc;
+  typedef typename A::StateId StateId;
+  typedef RationalFstImpl<A> Impl;
+
+  virtual void InitStateIterator(StateIteratorData<A> *data) const {
+    GetImpl()->Replace()->InitStateIterator(data);
+  }
+
+  virtual void InitArcIterator(StateId s, ArcIteratorData<A> *data) const {
+    GetImpl()->Replace()->InitArcIterator(s, data);
+  }
+
+ protected:
+  RationalFst()
+      : ImplToFst<Impl>(new Impl(RationalFstOptions())) {}
+
+  explicit RationalFst(const RationalFstOptions &opts)
+      : ImplToFst<Impl>(new Impl(opts)) {}
+
+  // See Fst<>::Copy() for doc.
+  RationalFst(const RationalFst<A> &fst , bool safe = false)
+      : ImplToFst<Impl>(fst, safe) {}
+
+ private:
+  // Makes visible to friends.
+  Impl *GetImpl() const { return ImplToFst<Impl>::GetImpl(); }
+
+  void operator=(const RationalFst<A> &fst);  // disallow
+};
+
+
+// Specialization for RationalFst.
+template <class A>
+class StateIterator< RationalFst<A> >
+    : public StateIterator< ReplaceFst<A> > {
+ public:
+  explicit StateIterator(const RationalFst<A> &fst)
+      : StateIterator< ReplaceFst<A> >(*(fst.GetImpl()->Replace())) {}
+};
+
+
+// Specialization for RationalFst.
+template <class A>
+class ArcIterator< RationalFst<A> >
+    : public CacheArcIterator< ReplaceFst<A> > {
+ public:
+  typedef typename A::StateId StateId;
+
+  ArcIterator(const RationalFst<A> &fst, StateId s)
+      : ArcIterator< ReplaceFst<A> >(*(fst.GetImpl()->Replace()), s) {}
+};
+
+}  // namespace fst
+
+#endif  // FST_LIB_RATIONAL_H__