projections_fmp.hxx

// projections_fmp.hxx: this file is part of the Vaucanson project.
//
// Vaucanson, a generic library for finite state machines.
//
// Copyright (C) 2005 The Vaucanson Group.
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 2
// of the License, or (at your option) any later version.
//
// The complete GNU General Public Licence Notice can be found as the
// `COPYING' file in the root directory.
//
// The Vaucanson Group consists of people listed in the `AUTHORS' file.
//
#ifndef VCSN_ALGORITHMS_PROJECTIONS_FMP_HXX
# define VCSN_ALGORITHMS_PROJECTIONS_FMP_HXX

# include <vaucanson/algorithms/projections_fmp.hh>

namespace vcsn
{
  template <typename auto_t, typename trans_t>
  static void
  set_states(const trans_t& fmp_trans, auto_t& res,
             std::map<hstate_t, hstate_t>& stmap)
  {
    AUTOMATON_TYPES_(trans_t, trans_);
    AUTOMATON_TYPES(auto_t);

    typedef typename trans_series_set_elt_t::support_t  trans_support_t;

    const series_set_t&         series = res.structure().series();
    const monoid_t&             monoid = res.structure().series().monoid();

    for_each_state(fmp_s, fmp_trans)
    {
      hstate_t s = res.add_state();
      stmap[*fmp_s] = s;

      if (fmp_trans.is_initial(*fmp_s))
      {
        trans_series_set_elt_t  in = fmp_trans.get_initial(*fmp_s);
        trans_support_t         supp = in.supp();

        semiring_elt_t          in_semi_elt = in.get(*(supp.begin()));
        series_set_elt_t                series_elt(series);

        series_elt.assoc(monoid_elt_t(monoid,
                                      algebra::identity_as<
                                      monoid_elt_value_t>::
                                      of(monoid).value()),
                         in_semi_elt);
        res.set_initial(s, series_elt);
      }

      if (fmp_trans.is_final(*fmp_s))
      {
        trans_series_set_elt_t  out = fmp_trans.get_final(*fmp_s);
        trans_support_t         supp = out.supp();

        semiring_elt_t          out_semi_elt =
          out.get(*(supp.begin()));
        series_set_elt_t                series_elt(series);

        series_elt.assoc(monoid_elt_t(monoid,
                                      algebra::identity_as<
                                      monoid_elt_value_t>::
                                      of(monoid).value()),
                         out_semi_elt);
        res.set_final(s, series_elt);
      }
    }
  }

  template <typename S1, typename S2, typename M1, typename M2, typename M3,
            typename auto_t, typename trans_t>
  void
  do_domain(const AutomataBase<S1>&, const algebra::FreeMonoidProduct<M1, M2>&,
            const AutomataBase<S2>&, const algebra::FreeMonoid<M3>&,
            const trans_t& fmp_trans, auto_t& res)
  {
    AUTOMATON_TYPES_(trans_t, trans_);
    AUTOMATON_TYPES(auto_t);

    typedef typename trans_series_set_elt_t::support_t  trans_support_t;
    std::map<hstate_t, hstate_t>        stmap;

    const series_set_t&         series = res.structure().series();
    const monoid_t&             monoid = res.structure().series().monoid();
    const trans_monoid_t&       trans_monoid =
      fmp_trans.structure().series().monoid();

    set_states(fmp_trans, res, stmap);

    for_each_transition(fmp_e, fmp_trans)
    {
      const trans_series_set_elt_t      trans_series_elt =
        fmp_trans.series_of(*fmp_e);
      trans_support_t                   trans_supp = trans_series_elt.supp();
      const trans_monoid_elt_t  trans_monoid_elt
        (trans_monoid, *(trans_supp.begin()));
      const monoid_elt_value_t  word(trans_monoid_elt.value().first);

      series_set_elt_t          series_elt(series);

      series_elt.assoc(monoid_elt_t(monoid, word),
                       trans_series_elt.get(trans_monoid_elt));

      res.add_series_transition(stmap[fmp_trans.src_of(*fmp_e)],
                                stmap[fmp_trans.dst_of(*fmp_e)], series_elt);
    }
  }

  template <typename S1, typename S2, typename M1, typename M2,
            typename auto_t, typename trans_t>
  void
  do_image(const AutomataBase<S1>&, const algebra::FreeMonoidProduct<M1, M2>&,
           const AutomataBase<S2>&, const algebra::FreeMonoidBase<M2>&,
           const trans_t& fmp_trans, auto_t& res)
  {
    AUTOMATON_TYPES_(trans_t, trans_);
    AUTOMATON_TYPES(auto_t);

    typedef typename trans_series_set_elt_t::support_t  trans_support_t;
    std::map<hstate_t, hstate_t>        stmap;

    const series_set_t&         series = res.structure().series();
    const monoid_t&             monoid = res.structure().series().monoid();
    const trans_monoid_t&       trans_monoid =
      fmp_trans.structure().series().monoid();

    set_states(fmp_trans, res, stmap);

    for_each_transition(fmp_e, fmp_trans)
    {
      const trans_series_set_elt_t      trans_series_elt =
        fmp_trans.series_of(*fmp_e);
      trans_support_t                   trans_supp = trans_series_elt.supp();
      const trans_monoid_elt_t  trans_monoid_elt
        (trans_monoid, *(trans_supp.begin()));

      const monoid_elt_value_t  word(trans_monoid_elt.value().second);

      series_set_elt_t          series_elt(series);

      series_elt.assoc(monoid_elt_t(monoid, word),
                       trans_series_elt.get(trans_monoid_elt));

      res.add_series_transition(stmap[fmp_trans.src_of(*fmp_e)],
                                stmap[fmp_trans.dst_of(*fmp_e)], series_elt);
    }
  }

  template <typename S1, typename S2, typename M1, typename M2,
            typename auto_t, typename trans_t>
  void
  do_identity(const AutomataBase<S1>&,
              const algebra::FreeMonoidBase<M1>&,
              const AutomataBase<S2>&,
              const algebra::FreeMonoidProduct<M1,M2>&,
              const auto_t& aut, trans_t& res)
  {
    AUTOMATON_TYPES_(auto_t, aut_);
    AUTOMATON_TYPES(trans_t);

    std::map<hstate_t, hstate_t>        stmap;
    typedef typename aut_series_set_elt_t::support_t    aut_support_t;

    const series_set_t&         series = res.structure().series();
    const monoid_t&             monoid = res.structure().series().monoid();
    const aut_monoid_t&         aut_monoid = aut.structure().series().monoid();

    set_states(aut, res, stmap);

    for_each_transition(aut_e, aut)
    {
      const aut_series_set_elt_t        aut_series_elt =
        aut.series_of(*aut_e);
      aut_support_t                     aut_supp = aut_series_elt.supp();
      const aut_monoid_elt_t    aut_monoid_elt
        (aut_monoid, *(aut_supp.begin()));
      const monoid_elt_value_t  word(aut_monoid_elt.value(),
                                     aut_monoid_elt.value());

      series_set_elt_t          series_elt(series);

      series_elt.assoc(monoid_elt_t(monoid, word),
                       aut_series_elt.get(aut_monoid_elt));

      res.add_series_transition(stmap[aut.src_of(*aut_e)],
                                stmap[aut.dst_of(*aut_e)], series_elt);
    }
  }


  /*-------.
  | Domain |
  `-------*/

  template <typename S, typename S2, typename T, typename T2>
  void
  domain(const Element<S,T>& trans, Element<S2, T2>& res)
  {
    do_domain(trans.structure(), trans.structure().series().monoid(),
              res.structure(), res.structure().series().monoid(), trans, res);
  }


  template <typename S, typename S2, typename T, typename T2>
  Element<S2, T2>
  domain(const Element<S,T>& trans)
  {
    typedef Element<S, T> trans_t;

    typedef algebra::FreeMonoid<
      typename trans_t::series_set_t::monoid_t::first_monoid_t> monoid_t;

    typedef algebra::Series<typename trans_t::series_set_t::semiring_t,
      monoid_t>
      series_set_t;

    monoid_t                            monoid
      (trans.structure().series().monoid().first_monoid());
    series_set_t                        series
      (trans.structure().series().semiring(), monoid);
    Automata<series_set_t>              aut_set(series);
    Element< Automata<series_set_t>, T> res(aut_set);

    do_domain(trans.structure(), trans.structure().series().monoid(),
              res.structure(), res.structure().series().monoid(), trans, res);
    return res;
  }


  /*------.
  | Image |
  `------*/

  template <typename S, typename S2, typename T, typename T2>
  void
  image(const Element<S,T>& trans, Element<S2, T2>& res)
  {
    do_image(trans.structure(), trans.structure().series().monoid(),
             res.structure(), res.structure().series().monoid(), trans, res);
  }


  template <typename S, typename S2, typename T, typename T2>
  Element<S2, T2>
  image(const Element<S,T>& trans)
  {
    typedef Element<S, T> trans_t;

    typedef algebra::FreeMonoid<
      typename trans_t::series_set_t::monoid_t::second_monoid_t> monoid_t;

    typedef algebra::Series<typename trans_t::series_set_t::semiring_t,
      monoid_t>
      series_set_t;

    monoid_t                            monoid
      (trans.structure().series().monoid().second_monoid());
    series_set_t                        series
      (trans.structure().series().semiring(), monoid);
    Automata<series_set_t>              aut_set(series);
    Element< Automata<series_set_t>, T> res(aut_set);

    do_image(trans.structure(), trans.structure().series().monoid(),
             res.structure(), res.structure().series().monoid(), trans, res);
    return res;
  }


  /*---------.
  | Identity |
  `---------*/

  template <typename S, typename S2, typename T, typename T2>
  void
  identity(const Element<S,T>& aut, Element<S2, T2>& res)
  {
    do_identity(aut.structure(), aut.structure().series().monoid(),
                res.structure(), res.structure().series().monoid(), aut, res);
  }

  template <typename S, typename S2, typename T, typename T2>
  Element<S2, T2>
  identity(const Element<S,T>& aut)
  {
    typedef Element<S, T> auto_t;

    typedef algebra::FreeMonoidProduct<
      typename auto_t::series_set_t::monoid_t,
      typename auto_t::series_set_t::monoid_t> monoid_t;

    typedef algebra::Series<typename auto_t::series_set_t::semiring_t,
      monoid_t>
      series_set_t;

    monoid_t            monoid (aut.structure().series().monoid(),
                                aut.structure().series().monoid());

    series_set_t                        series
      (aut.structure().series().semiring(), monoid);
    Automata<series_set_t>              aut_set(series);
    Element< Automata<series_set_t>, T> res(aut_set);

    do_identity(aut.structure(), aut.structure().series().monoid(),
                res.structure(), res.structure().series().monoid(), aut, res);
    return res;
  }


} // End of namespace vcsn.

#endif // ! VCSN_ALGORITHMS_PROJECTIONS_FMP_HXX

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