is-functional.hh

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#pragma once

#include <vcsn/algos/compose.hh>
#include <vcsn/algos/is-partial-identity.hh>
#include <vcsn/dyn/automaton.hh>
#include <vcsn/dyn/fwd.hh>

namespace vcsn
{
  /*---------------.
  | is-functional. |
  `---------------*/

  template <typename Aut>
  bool is_functional(const Aut& aut)
  {
    // Compose aut and its invert.
    auto l = focus<0>(aut);
    auto r = insplit(l);
    auto compose = detail::make_composer(l, r);
    auto c = compose();
    return is_partial_identity(c);
  }

  namespace dyn
  {
    namespace detail
    {
      template <typename Aut>
      bool is_functional(const automaton& aut)
      {
        return is_functional(aut->as<Aut>());
      }
    }
  }
}