comparison DEPENDENCIES/generic/include/boost/icl/concept/interval.hpp @ 16:2665513ce2d3

Add boost headers

+/*-----------------------------------------------------------------------------+
+Copyright (c) 2010-2010: Joachim Faulhaber
++------------------------------------------------------------------------------+
+   Distributed under the Boost Software License, Version 1.0.
+      (See accompanying file LICENCE.txt or copy at
+           http://www.boost.org/LICENSE_1_0.txt)
++-----------------------------------------------------------------------------*/
+#ifndef BOOST_ICL_CONCEPT_INTERVAL_HPP_JOFA_100323
+#define BOOST_ICL_CONCEPT_INTERVAL_HPP_JOFA_100323
+
+#include <boost/assert.hpp> 
+#include <boost/utility/enable_if.hpp>
+#include <boost/mpl/and.hpp>
+#include <boost/mpl/or.hpp>
+#include <boost/mpl/not.hpp>
+#include <boost/icl/detail/design_config.hpp>
+#include <boost/icl/type_traits/unit_element.hpp>
+#include <boost/icl/type_traits/identity_element.hpp>
+#include <boost/icl/type_traits/infinity.hpp>
+#include <boost/icl/type_traits/succ_pred.hpp>
+#include <boost/icl/type_traits/is_numeric.hpp>
+#include <boost/icl/type_traits/is_discrete.hpp>
+#include <boost/icl/type_traits/is_continuous.hpp>
+#include <boost/icl/type_traits/is_asymmetric_interval.hpp>
+#include <boost/icl/type_traits/is_discrete_interval.hpp>
+#include <boost/icl/type_traits/is_continuous_interval.hpp>
+
+#include <boost/icl/concept/interval_bounds.hpp>
+#include <boost/icl/interval_traits.hpp>
+#include <boost/icl/dynamic_interval_traits.hpp>
+
+
+namespace boost{namespace icl
+{
+
+//==============================================================================
+//= Ordering
+//==============================================================================
+template<class Type>
+inline typename enable_if<is_interval<Type>, bool>::type
+domain_less(const typename interval_traits<Type>::domain_type& left, 
+            const typename interval_traits<Type>::domain_type& right)
+{
+    return typename interval_traits<Type>::domain_compare()(left, right);
+}
+
+template<class Type>
+inline typename enable_if<is_interval<Type>, bool>::type
+domain_less_equal(const typename interval_traits<Type>::domain_type& left, 
+                  const typename interval_traits<Type>::domain_type& right)
+{
+    return !(typename interval_traits<Type>::domain_compare()(right, left));
+}
+
+template<class Type>
+inline typename enable_if<is_interval<Type>, bool>::type
+domain_equal(const typename interval_traits<Type>::domain_type& left, 
+             const typename interval_traits<Type>::domain_type& right)
+{
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    return !(domain_compare()(left, right)) && !(domain_compare()(right, left));
+}
+
+template<class Type>
+inline typename enable_if< is_interval<Type>
+                         , typename interval_traits<Type>::domain_type>::type
+domain_next(const typename interval_traits<Type>::domain_type value) 
+{
+    typedef typename interval_traits<Type>::domain_type domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    return icl::successor<domain_type,domain_compare>::apply(value);
+}
+
+template<class Type>
+inline typename enable_if< is_interval<Type>
+                         , typename interval_traits<Type>::domain_type>::type
+domain_prior(const typename interval_traits<Type>::domain_type value) 
+{
+    typedef typename interval_traits<Type>::domain_type domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    return icl::predecessor<domain_type,domain_compare>::apply(value);
+}
+
+//==============================================================================
+//= Construct<Interval> singleton
+//==============================================================================
+template<class Type>
+typename enable_if
+<
+    mpl::and_< is_static_right_open<Type>
+             , is_discrete<typename interval_traits<Type>::domain_type> >
+  , Type
+>::type
+singleton(const typename interval_traits<Type>::domain_type& value)
+{
+    //ASSERT: This always creates an interval with exactly one element
+    return interval_traits<Type>::construct(value, domain_next<Type>(value));
+}
+
+template<class Type>
+typename enable_if
+<
+    mpl::and_< is_static_left_open<Type>
+             , is_discrete<typename interval_traits<Type>::domain_type> >
+  , Type
+>::type
+singleton(const typename interval_traits<Type>::domain_type& value)
+{
+    //ASSERT: This always creates an interval with exactly one element
+    typedef typename interval_traits<Type>::domain_type    domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                 ::is_less_than(value) )); 
+
+    return interval_traits<Type>::construct(domain_prior<Type>(value), value);
+}
+
+template<class Type>
+typename enable_if<is_discrete_static_open<Type>, Type>::type
+singleton(const typename interval_traits<Type>::domain_type& value)
+{
+    //ASSERT: This always creates an interval with exactly one element
+    typedef typename interval_traits<Type>::domain_type    domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                 ::is_less_than(value))); 
+
+    return interval_traits<Type>::construct( domain_prior<Type>(value)
+                                           , domain_next<Type>(value));
+}
+
+template<class Type>
+typename enable_if<is_discrete_static_closed<Type>, Type>::type
+singleton(const typename interval_traits<Type>::domain_type& value)
+{
+    //ASSERT: This always creates an interval with exactly one element
+    return interval_traits<Type>::construct(value, value);
+}
+
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, Type>::type
+singleton(const typename interval_traits<Type>::domain_type& value)
+{
+    return dynamic_interval_traits<Type>::construct(value, value, interval_bounds::closed());
+}
+
+namespace detail
+{
+
+//==============================================================================
+//= Construct<Interval> unit_trail == generalized singleton
+// The smallest interval on an incrementable (and decrementable) type that can 
+// be constructed using ++ and -- and such that it contains a given value.
+// If 'Type' is discrete, 'unit_trail' and 'singleton' are identical. So we 
+// can view 'unit_trail' as a generalized singleton for static intervals of 
+// continuous types.
+//==============================================================================
+template<class Type>
+typename enable_if
+<
+    mpl::and_< is_static_right_open<Type>
+             , boost::detail::is_incrementable<typename interval_traits<Type>::domain_type> >
+  , Type
+>::type
+unit_trail(const typename interval_traits<Type>::domain_type& value)
+{
+    return interval_traits<Type>::construct(value, domain_next<Type>(value));
+}
+
+template<class Type>
+typename enable_if
+<
+    mpl::and_< is_static_left_open<Type>
+             , boost::detail::is_incrementable<typename interval_traits<Type>::domain_type> >
+  , Type
+>::type
+unit_trail(const typename interval_traits<Type>::domain_type& value)
+{
+    typedef typename interval_traits<Type>::domain_type    domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                 ::is_less_than(value) )); 
+
+    return interval_traits<Type>::construct(domain_prior<Type>(value), value);
+}
+
+template<class Type>
+typename enable_if
+<
+    mpl::and_< is_static_open<Type>
+             , is_discrete<typename interval_traits<Type>::domain_type> >
+  , Type
+>::type
+unit_trail(const typename interval_traits<Type>::domain_type& value)
+{
+    typedef typename interval_traits<Type>::domain_type    domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                 ::is_less_than(value))); 
+
+    return interval_traits<Type>::construct( domain_prior<Type>(value)
+                                           ,  domain_next<Type>(value));
+}
+
+template<class Type>
+typename enable_if
+<
+    mpl::and_< is_static_closed<Type>
+             , is_discrete<typename interval_traits<Type>::domain_type> >
+  , Type
+>::type
+unit_trail(const typename interval_traits<Type>::domain_type& value)
+{
+    return interval_traits<Type>::construct(value, value);
+}
+
+//NOTE: statically bounded closed or open intervals of continuous domain types
+// are NOT supported by ICL. They can not be used with interval containers
+// consistently.
+
+
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, Type>::type
+unit_trail(const typename interval_traits<Type>::domain_type& value)
+{
+    return dynamic_interval_traits<Type>::construct(value, value, interval_bounds::closed());
+}
+
+} //namespace detail
+
+//==============================================================================
+//= Construct<Interval> multon
+//==============================================================================
+template<class Type>
+typename enable_if<has_static_bounds<Type>, Type>::type
+construct(const typename interval_traits<Type>::domain_type& low,
+          const typename interval_traits<Type>::domain_type& up  )
+{
+    return interval_traits<Type>::construct(low, up);
+}
+
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, Type>::type
+construct(const typename interval_traits<Type>::domain_type& low,
+          const typename interval_traits<Type>::domain_type& up,
+          interval_bounds bounds = interval_bounds::right_open())
+{
+    return dynamic_interval_traits<Type>::construct(low, up, bounds);
+}
+
+
+//- construct form bounded values ----------------------------------------------
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, Type>::type
+construct(const typename Type::bounded_domain_type& low,
+          const typename Type::bounded_domain_type& up)
+{
+    return dynamic_interval_traits<Type>::construct_bounded(low, up);
+}
+
+template<class Type>
+typename enable_if<is_interval<Type>, Type>::type
+span(const typename interval_traits<Type>::domain_type& left,
+     const typename interval_traits<Type>::domain_type& right)
+{
+    if(interval_traits<Type>::domain_compare()(left,right))
+        return construct<Type>(left, right);
+    else
+        return construct<Type>(right, left);
+}
+
+
+//==============================================================================
+template<class Type>
+typename enable_if<is_static_right_open<Type>, Type>::type
+hull(const typename interval_traits<Type>::domain_type& left,
+     const typename interval_traits<Type>::domain_type& right)
+{
+    if(interval_traits<Type>::domain_compare()(left,right))
+        return construct<Type>(left, domain_next<Type>(right));
+    else
+        return construct<Type>(right, domain_next<Type>(left));
+}
+
+template<class Type>
+typename enable_if<is_static_left_open<Type>, Type>::type
+hull(const typename interval_traits<Type>::domain_type& left,
+     const typename interval_traits<Type>::domain_type& right)
+{
+    typedef typename interval_traits<Type>::domain_type    domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    if(interval_traits<Type>::domain_compare()(left,right))
+    {
+        BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                     ::is_less_than(left) )); 
+        return construct<Type>(domain_prior<Type>(left), right);
+    }
+    else
+    {
+        BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                     ::is_less_than(right) )); 
+        return construct<Type>(domain_prior<Type>(right), left);
+    }
+}
+
+template<class Type>
+typename enable_if<is_static_closed<Type>, Type>::type
+hull(const typename interval_traits<Type>::domain_type& left,
+     const typename interval_traits<Type>::domain_type& right)
+{
+    if(interval_traits<Type>::domain_compare()(left,right))
+        return construct<Type>(left, right);
+    else
+        return construct<Type>(right, left);
+}
+
+template<class Type>
+typename enable_if<is_static_open<Type>, Type>::type
+hull(const typename interval_traits<Type>::domain_type& left,
+     const typename interval_traits<Type>::domain_type& right)
+{
+    typedef typename interval_traits<Type>::domain_type    domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    if(interval_traits<Type>::domain_compare()(left,right))
+    {
+        BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                     ::is_less_than(left) )); 
+        return construct<Type>( domain_prior<Type>(left)
+                              ,  domain_next<Type>(right));
+    }
+    else
+    {
+        BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                     ::is_less_than(right) )); 
+        return construct<Type>( domain_prior<Type>(right)
+                              ,  domain_next<Type>(left));
+    }
+}
+
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, Type>::type
+hull(const typename interval_traits<Type>::domain_type& left,
+     const typename interval_traits<Type>::domain_type& right)
+{
+    if(interval_traits<Type>::domain_compare()(left,right))
+        return construct<Type>(left, right, interval_bounds::closed());
+    else
+        return construct<Type>(right, left, interval_bounds::closed());
+}
+
+//==============================================================================
+//= Selection
+//==============================================================================
+
+template<class Type>
+inline typename enable_if<is_interval<Type>, 
+                          typename interval_traits<Type>::domain_type>::type
+lower(const Type& object)
+{ 
+    return interval_traits<Type>::lower(object);
+}
+
+template<class Type>
+inline typename enable_if<is_interval<Type>, 
+                          typename interval_traits<Type>::domain_type>::type
+upper(const Type& object)
+{ 
+    return interval_traits<Type>::upper(object);
+}
+
+
+//- first ----------------------------------------------------------------------
+template<class Type>
+inline typename 
+enable_if< mpl::or_<is_static_right_open<Type>, is_static_closed<Type> >
+         , typename interval_traits<Type>::domain_type>::type
+first(const Type& object)
+{ 
+    return lower(object);
+}
+
+template<class Type>
+inline typename 
+enable_if< mpl::and_< mpl::or_<is_static_left_open<Type>, is_static_open<Type> >
+                    , is_discrete<typename interval_traits<Type>::domain_type> >
+         , typename interval_traits<Type>::domain_type>::type
+first(const Type& object)
+{ 
+    return domain_next<Type>(lower(object));
+}
+
+template<class Type>
+inline typename enable_if<is_discrete_interval<Type>, 
+                          typename interval_traits<Type>::domain_type>::type
+first(const Type& object)
+{ 
+    return is_left_closed(object.bounds()) ? 
+                                 lower(object) : 
+               domain_next<Type>(lower(object));
+}
+
+//- last -----------------------------------------------------------------------
+template<class Type>
+inline typename 
+enable_if< mpl::or_<is_static_left_open<Type>, is_static_closed<Type> >
+         , typename interval_traits<Type>::domain_type>::type
+last(const Type& object)
+{ 
+    return upper(object);
+}
+
+template<class Type>
+inline typename 
+enable_if< mpl::and_< mpl::or_<is_static_right_open<Type>, is_static_open<Type> >
+                    , is_discrete<typename interval_traits<Type>::domain_type>  >
+         , typename interval_traits<Type>::domain_type>::type
+last(const Type& object)
+{ 
+    typedef typename interval_traits<Type>::domain_type    domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                 ::is_less_than(upper(object)) )); 
+    return domain_prior<Type>(upper(object));
+}
+
+template<class Type>
+inline typename enable_if<is_discrete_interval<Type>, 
+                          typename interval_traits<Type>::domain_type>::type
+last(const Type& object)
+{ 
+    typedef typename interval_traits<Type>::domain_type    domain_type;
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+    BOOST_ASSERT((numeric_minimum<domain_type, domain_compare, is_numeric<domain_type>::value>
+                                 ::is_less_than_or(upper(object), is_right_closed(object.bounds())) )); 
+    return is_right_closed(object.bounds()) ? 
+                                  upper(object) : 
+               domain_prior<Type>(upper(object));
+}
+
+//- last_next ------------------------------------------------------------------
+template<class Type>
+inline typename 
+enable_if< mpl::and_< mpl::or_<is_static_left_open<Type>, is_static_closed<Type> >
+                    , is_discrete<typename interval_traits<Type>::domain_type>  >
+         , typename interval_traits<Type>::domain_type>::type
+last_next(const Type& object)
+{ 
+    return domain_next<Type>(upper(object));
+}
+
+template<class Type>
+inline typename 
+enable_if< mpl::and_< mpl::or_<is_static_right_open<Type>, is_static_open<Type> >
+                    , is_discrete<typename interval_traits<Type>::domain_type>  >
+         , typename interval_traits<Type>::domain_type>::type
+last_next(const Type& object)
+{ 
+    typedef typename interval_traits<Type>::domain_type domain_type;
+    return upper(object); // NOTE: last_next is implemented to avoid calling pred(object)
+}                         // For unsigned integral types this may cause underflow.
+
+template<class Type>
+inline typename enable_if<is_discrete_interval<Type>, 
+                          typename interval_traits<Type>::domain_type>::type
+last_next(const Type& object)
+{ 
+    return is_right_closed(object.bounds()) ? 
+               domain_next<Type>(upper(object)): 
+                                 upper(object) ;
+}
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, 
+                   typename Type::bounded_domain_type>::type
+bounded_lower(const Type& object)
+{ 
+    return typename 
+        Type::bounded_domain_type(lower(object), object.bounds().left()); 
+}
+
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, 
+                   typename Type::bounded_domain_type>::type
+reverse_bounded_lower(const Type& object)
+{ 
+    return typename 
+        Type::bounded_domain_type(lower(object), 
+                                  object.bounds().reverse_left()); 
+}
+
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, 
+                   typename Type::bounded_domain_type>::type
+bounded_upper(const Type& object)
+{ 
+    return typename 
+        Type::bounded_domain_type(upper(object), 
+                                  object.bounds().right()); 
+}
+
+template<class Type>
+typename enable_if<has_dynamic_bounds<Type>, 
+                   typename Type::bounded_domain_type>::type
+reverse_bounded_upper(const Type& object)
+{ 
+    return typename 
+        Type::bounded_domain_type(upper(object), 
+                                  object.bounds().reverse_right()); 
+}
+
+//- bounds ---------------------------------------------------------------------
+template<class Type>
+inline typename enable_if<has_dynamic_bounds<Type>, interval_bounds>::type
+bounds(const Type& object)
+{
+    return object.bounds();
+}
+
+template<class Type>
+inline typename enable_if<has_static_bounds<Type>, interval_bounds>::type
+bounds(const Type&)
+{
+    return interval_bounds(interval_bound_type<Type>::value);
+}
+
+
+//==============================================================================
+//= Emptieness
+//==============================================================================
+/** Is the interval empty? */
+template<class Type>
+typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
+is_empty(const Type& object)
+{ 
+    return domain_less_equal<Type>(upper(object), lower(object)); 
+}
+
+template<class Type>
+typename boost::enable_if<is_static_closed<Type>, bool>::type
+is_empty(const Type& object)
+{ 
+    return domain_less<Type>(upper(object), lower(object)); 
+}
+
+template<class Type>
+typename boost::enable_if<is_static_open<Type>, bool>::type
+is_empty(const Type& object)
+{ 
+    return domain_less_equal<Type>(upper(object),                   lower(object) ) 
+        || domain_less_equal<Type>(upper(object), domain_next<Type>(lower(object)));
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_interval<Type>, bool>::type
+is_empty(const Type& object)
+{ 
+    if(object.bounds() == interval_bounds::closed())
+        return domain_less<Type>(upper(object), lower(object)); 
+    else if(object.bounds() == interval_bounds::open())
+        return domain_less_equal<Type>(upper(object),                   lower(object) )
+            || domain_less_equal<Type>(upper(object), domain_next<Type>(lower(object)));
+    else
+        return domain_less_equal<Type>(upper(object), lower(object)); 
+}
+
+template<class Type>
+typename boost::enable_if<is_continuous_interval<Type>, bool>::type
+is_empty(const Type& object)
+{
+    return     domain_less<Type>(upper(object), lower(object))
+        || (   domain_equal<Type>(upper(object), lower(object))
+            && object.bounds() != interval_bounds::closed()    );
+}
+
+//==============================================================================
+//= Orderings, containedness (non empty)
+//==============================================================================
+namespace non_empty
+{
+
+    template<class Type>
+    inline typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
+    exclusive_less(const Type& left, const Type& right)
+    { 
+        BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right)));
+        return domain_less_equal<Type>(upper(left), lower(right)); 
+    }
+
+    template<class Type>
+    inline typename boost::enable_if<is_discrete_interval<Type>, bool>::type
+    exclusive_less(const Type& left, const Type& right)
+    { 
+        BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right)));
+        return domain_less<Type>(last(left), first(right)); 
+    }
+
+    template<class Type>
+    inline typename boost::
+    enable_if<has_symmetric_bounds<Type>, bool>::type
+    exclusive_less(const Type& left, const Type& right)
+    { 
+        BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right)));
+        return domain_less<Type>(last(left), first(right)); 
+    }
+
+    template<class Type>
+    inline typename boost::enable_if<is_continuous_interval<Type>, bool>::type
+    exclusive_less(const Type& left, const Type& right)
+    { 
+        BOOST_ASSERT(!(icl::is_empty(left) || icl::is_empty(right)));
+        return     domain_less <Type>(upper(left), lower(right))
+            || (   domain_equal<Type>(upper(left), lower(right))
+                && inner_bounds(left,right) != interval_bounds::open() );
+    }
+
+    template<class Type>
+    inline typename boost::enable_if<is_interval<Type>, bool>::type
+    contains(const Type& super, const Type& sub)
+    { 
+        return lower_less_equal(super,sub) && upper_less_equal(sub,super);
+    }
+
+
+} //namespace non_empty
+
+
+//- contains -------------------------------------------------------------------
+template<class Type>
+inline typename boost::enable_if<is_interval<Type>, bool>::type
+contains(const Type& super, const Type& sub)
+{ 
+    return icl::is_empty(sub) || non_empty::contains(super, sub);
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_static<Type>, bool>::type
+contains(const Type& super, const typename interval_traits<Type>::domain_type& element)
+{
+    return domain_less_equal<Type>(icl::first(super), element                  ) 
+        && domain_less_equal<Type>(                   element, icl::last(super));
+}
+
+template<class Type>
+typename boost::enable_if<is_continuous_left_open<Type>, bool>::type
+contains(const Type& super, const typename interval_traits<Type>::domain_type& element)
+{
+    return domain_less      <Type>(icl::lower(super), element                   ) 
+        && domain_less_equal<Type>(                   element, icl::upper(super));
+}
+
+template<class Type>
+typename boost::enable_if<is_continuous_right_open<Type>, bool>::type
+contains(const Type& super, const typename interval_traits<Type>::domain_type& element)
+{
+    return domain_less_equal<Type>(icl::lower(super), element                   ) 
+        && domain_less      <Type>(                   element, icl::upper(super));
+}
+
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, bool>::type
+contains(const Type& super, const typename interval_traits<Type>::domain_type& element)
+{
+    return
+        (is_left_closed(super.bounds())  
+            ? domain_less_equal<Type>(lower(super), element) 
+            :       domain_less<Type>(lower(super), element))
+    &&
+        (is_right_closed(super.bounds()) 
+            ? domain_less_equal<Type>(element, upper(super)) 
+            :       domain_less<Type>(element, upper(super)));
+}
+
+//- within ---------------------------------------------------------------------
+template<class Type>
+inline typename boost::enable_if<is_interval<Type>, bool>::type
+within(const Type& sub, const Type& super)
+{ 
+    return contains(super,sub);
+}
+
+
+//==============================================================================
+//= Equivalences and Orderings
+//==============================================================================
+//- exclusive_less -------------------------------------------------------------
+/** Maximal element of <tt>left</tt> is less than the minimal element of 
+    <tt>right</tt> */
+template<class Type>
+inline typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
+exclusive_less(const Type& left, const Type& right)
+{ 
+    return icl::is_empty(left) || icl::is_empty(right)
+        || domain_less_equal<Type>(upper(left), lower(right)); 
+}
+
+template<class Type>
+inline typename boost::enable_if<is_discrete_interval<Type>, bool>::type
+exclusive_less(const Type& left, const Type& right)
+{ 
+    return icl::is_empty(left) || icl::is_empty(right)
+        || domain_less<Type>(last(left), first(right)); 
+}
+
+template<class Type>
+inline typename boost::
+enable_if<has_symmetric_bounds<Type>, bool>::type
+exclusive_less(const Type& left, const Type& right)
+{ 
+    return icl::is_empty(left) || icl::is_empty(right)
+        || domain_less<Type>(last(left), first(right)); 
+}
+
+template<class Type>
+inline typename boost::enable_if<is_continuous_interval<Type>, bool>::type
+exclusive_less(const Type& left, const Type& right)
+{ 
+    return     icl::is_empty(left) || icl::is_empty(right)
+        ||     domain_less<Type>(upper(left), lower(right))
+        || (   domain_equal<Type>(upper(left), lower(right))
+            && inner_bounds(left,right) != interval_bounds::open() );
+}
+
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<has_static_bounds<Type>, bool>::type
+lower_less(const Type& left, const Type& right)
+{
+    return domain_less<Type>(lower(left), lower(right));
+}
+    
+template<class Type>
+typename boost::enable_if<is_discrete_interval<Type>, bool>::type
+lower_less(const Type& left, const Type& right)
+{
+    return domain_less<Type>(first(left), first(right));
+}
+    
+template<class Type>
+typename boost::enable_if<is_continuous_interval<Type>, bool>::type
+lower_less(const Type& left, const Type& right)
+{
+    if(left_bounds(left,right) == interval_bounds::right_open())  //'[(' == 10
+        return domain_less_equal<Type>(lower(left), lower(right));
+    else 
+        return domain_less<Type>(lower(left), lower(right));
+}
+    
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<has_static_bounds<Type>, bool>::type
+upper_less(const Type& left, const Type& right)
+{
+    return domain_less<Type>(upper(left), upper(right));
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_interval<Type>, bool>::type
+upper_less(const Type& left, const Type& right)
+{
+    return domain_less<Type>(last(left), last(right));
+}
+    
+template<class Type>
+typename boost::enable_if<is_continuous_interval<Type>, bool>::type
+upper_less(const Type& left, const Type& right)
+{
+    if(right_bounds(left,right) == interval_bounds::left_open())
+        return domain_less_equal<Type>(upper(left), upper(right));
+    else
+        return domain_less<Type>(upper(left), upper(right));
+}
+    
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, 
+                          typename Type::bounded_domain_type   >::type
+lower_min(const Type& left, const Type& right)
+{
+    return lower_less(left, right) ? bounded_lower(left) : bounded_lower(right);
+}
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, 
+                          typename Type::bounded_domain_type   >::type
+lower_max(const Type& left, const Type& right)
+{
+    return lower_less(left, right) ? bounded_lower(right) : bounded_lower(left);
+}
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, 
+                          typename Type::bounded_domain_type   >::type
+upper_max(const Type& left, const Type& right)
+{
+    return upper_less(left, right) ? bounded_upper(right) : bounded_upper(left);
+}
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, 
+                          typename Type::bounded_domain_type   >::type
+upper_min(const Type& left, const Type& right)
+{
+    return upper_less(left, right) ? bounded_upper(left) : bounded_upper(right);
+}
+
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
+lower_equal(const Type& left, const Type& right)
+{
+    return domain_equal<Type>(lower(left), lower(right));
+}
+
+template<class Type>
+typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type
+lower_equal(const Type& left, const Type& right)
+{
+    return domain_equal<Type>(first(left), first(right));
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_interval<Type>, bool>::type
+lower_equal(const Type& left, const Type& right)
+{
+    return domain_equal<Type>(first(left), first(right));
+}
+
+template<class Type>
+typename boost::enable_if<is_continuous_interval<Type>, bool>::type
+lower_equal(const Type& left, const Type& right)
+{
+    return (left.bounds().left()==right.bounds().left())
+        && domain_equal<Type>(lower(left), lower(right));
+}
+
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
+upper_equal(const Type& left, const Type& right)
+{
+    return domain_equal<Type>(upper(left), upper(right));
+}
+
+template<class Type>
+typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type
+upper_equal(const Type& left, const Type& right)
+{
+    return domain_equal<Type>(last(left), last(right));
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_interval<Type>, bool>::type
+upper_equal(const Type& left, const Type& right)
+{
+    return domain_equal<Type>(last(left), last(right));
+}
+
+template<class Type>
+typename boost::enable_if<is_continuous_interval<Type>, bool>::type
+upper_equal(const Type& left, const Type& right)
+{
+    return (left.bounds().right()==right.bounds().right())
+        && domain_equal<Type>(upper(left), upper(right));
+}
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<is_interval<Type>, bool>::type
+lower_less_equal(const Type& left, const Type& right)
+{
+    return lower_less(left,right) || lower_equal(left,right);
+}
+
+template<class Type>
+typename boost::enable_if<is_interval<Type>, bool>::type
+upper_less_equal(const Type& left, const Type& right)
+{
+    return upper_less(left,right) || upper_equal(left,right);
+}
+
+
+//- operator == ----------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<is_interval<Type>, bool>::type
+operator == (const Type& left, const Type& right)
+{
+    return (icl::is_empty(left) && icl::is_empty(right)) 
+        || (lower_equal(left,right) && upper_equal(left,right));
+}
+
+template<class Type>
+typename boost::enable_if<is_interval<Type>, bool>::type
+operator != (const Type& left, const Type& right)
+{
+    return !(left == right);
+}
+
+//- operator < -----------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<is_interval<Type>, bool>::type
+operator < (const Type& left, const Type& right)
+{
+    if(icl::is_empty(left)) 
+        return !icl::is_empty(right);
+    else 
+        return lower_less(left,right) 
+            || (lower_equal(left,right) && upper_less(left,right)); 
+}
+
+template<class Type>
+inline typename boost::enable_if<is_interval<Type>, bool>::type
+operator > (const Type& left, const Type& right)
+{
+    return right < left;
+}
+
+
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<is_asymmetric_interval<Type>, bool>::type
+touches(const Type& left, const Type& right)
+{ 
+    return domain_equal<Type>(upper(left), lower(right)); 
+}
+
+template<class Type>
+typename boost::enable_if<has_symmetric_bounds<Type>, bool>::type
+touches(const Type& left, const Type& right)
+{ 
+    return domain_equal<Type>(last_next(left), first(right)); 
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_interval<Type>, bool>::type
+touches(const Type& left, const Type& right)
+{
+    return domain_equal<Type>(domain_next<Type>(last(left)), first(right));
+}
+
+template<class Type>
+typename boost::enable_if<is_continuous_interval<Type>, bool>::type
+touches(const Type& left, const Type& right)
+{
+    return is_complementary(inner_bounds(left,right))
+        && domain_equal<Type>(upper(left), lower(right));
+}
+
+
+//==============================================================================
+//= Size
+//==============================================================================
+//- cardinality ----------------------------------------------------------------
+
+template<class Type>
+typename boost::enable_if<is_continuous_interval<Type>, 
+    typename size_type_of<interval_traits<Type> >::type>::type
+cardinality(const Type& object)
+{
+    typedef typename size_type_of<interval_traits<Type> >::type SizeT;
+    if(icl::is_empty(object))
+        return icl::identity_element<SizeT>::value();
+    else if(   object.bounds() == interval_bounds::closed() 
+            && domain_equal<Type>(lower(object), upper(object)))
+        return icl::unit_element<SizeT>::value();
+    else 
+        return icl::infinity<SizeT>::value();
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_interval<Type>, 
+    typename size_type_of<interval_traits<Type> >::type>::type
+cardinality(const Type& object)
+{
+    typedef typename size_type_of<interval_traits<Type> >::type SizeT;
+    return icl::is_empty(object) ? identity_element<SizeT>::value()
+                                 : static_cast<SizeT>(last_next(object) - first(object));
+}
+
+template<class Type>
+typename boost::enable_if<is_continuous_asymmetric<Type>, 
+    typename size_type_of<interval_traits<Type> >::type>::type
+cardinality(const Type& object)
+{
+    typedef typename size_type_of<interval_traits<Type> >::type SizeT;
+    if(icl::is_empty(object))
+        return icl::identity_element<SizeT>::value();
+    else 
+        return icl::infinity<SizeT>::value();
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_asymmetric<Type>, 
+    typename size_type_of<interval_traits<Type> >::type>::type
+cardinality(const Type& object)
+{
+    typedef typename size_type_of<interval_traits<Type> >::type SizeT;
+    return icl::is_empty(object) ? identity_element<SizeT>::value()
+                                 : static_cast<SizeT>(last_next(object) - first(object));
+}
+
+template<class Type>
+typename boost::enable_if<has_symmetric_bounds<Type>, 
+    typename size_type_of<interval_traits<Type> >::type>::type
+cardinality(const Type& object)
+{
+    typedef typename size_type_of<interval_traits<Type> >::type SizeT;
+    return icl::is_empty(object) ? identity_element<SizeT>::value()
+                                 : static_cast<SizeT>(last_next(object) - first(object));
+}
+
+
+
+//- size -----------------------------------------------------------------------
+template<class Type>
+inline typename enable_if<is_interval<Type>, 
+    typename size_type_of<interval_traits<Type> >::type>::type
+size(const Type& object)
+{
+    return cardinality(object);
+}
+
+//- length ---------------------------------------------------------------------
+template<class Type>
+inline typename boost::enable_if<is_continuous_interval<Type>, 
+    typename difference_type_of<interval_traits<Type> >::type>::type
+length(const Type& object)
+{
+    typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
+    return icl::is_empty(object) ? identity_element<DiffT>::value()
+                                 : upper(object) - lower(object);
+}
+
+template<class Type>
+inline typename boost::enable_if<is_discrete_interval<Type>, 
+    typename difference_type_of<interval_traits<Type> >::type>::type
+length(const Type& object)
+{
+    typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
+    return icl::is_empty(object) ? identity_element<DiffT>::value()
+                                 : last_next(object) - first(object);
+}
+
+template<class Type>
+typename boost::enable_if<is_continuous_asymmetric<Type>, 
+    typename difference_type_of<interval_traits<Type> >::type>::type
+length(const Type& object)
+{
+    typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
+    return icl::is_empty(object) ? identity_element<DiffT>::value()
+                                 : upper(object) - lower(object);
+}
+
+template<class Type>
+inline typename boost::enable_if<is_discrete_static<Type>, 
+    typename difference_type_of<interval_traits<Type> >::type>::type
+length(const Type& object)
+{
+    typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
+    return icl::is_empty(object) ? identity_element<DiffT>::value()
+                                 : last_next(object) - first(object);
+}
+
+//- iterative_size -------------------------------------------------------------
+template<class Type>
+inline typename enable_if<is_interval<Type>, 
+    typename size_type_of<interval_traits<Type> >::type>::type
+iterative_size(const Type&)
+{
+    return 2;
+}
+
+
+//==============================================================================
+//= Addition
+//==============================================================================
+//- hull -----------------------------------------------------------------------
+/** \c hull returns the smallest interval containing \c left and \c right. */
+template<class Type>
+typename boost::enable_if<has_static_bounds<Type>, Type>::type
+hull(Type left, const Type& right)
+{
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+
+    if(icl::is_empty(right))
+        return left;
+    else if(icl::is_empty(left))
+        return right;
+
+    return 
+        construct<Type>
+        (
+            (std::min)(lower(left), lower(right), domain_compare()), 
+            (std::max)(upper(left), upper(right), domain_compare())
+        );
+}
+
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
+hull(Type left, const Type& right)
+{
+    if(icl::is_empty(right))
+        return left;
+    else if(icl::is_empty(left))
+        return right;
+
+    return  dynamic_interval_traits<Type>::construct_bounded
+            (
+                lower_min(left, right), 
+                upper_max(left, right)
+            );
+}
+
+//==============================================================================
+//= Subtraction
+//==============================================================================
+//- left_subtract --------------------------------------------------------------
+/** subtract \c left_minuend from the \c right interval on it's left side. 
+    Return the difference: The part of \c right right of \c left_minuend.
+\code
+right_over = right - left_minuend; //on the left.
+...      d) : right
+... c)      : left_minuend
+     [c  d) : right_over
+\endcode
+*/
+template<class Type>
+typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type
+left_subtract(Type right, const Type& left_minuend)
+{
+    if(exclusive_less(left_minuend, right))
+        return right; 
+
+    return construct<Type>(upper(left_minuend), upper(right));
+}
+
+template<class Type>
+typename boost::enable_if<is_static_closed<Type>, Type>::type
+left_subtract(Type right, const Type& left_minuend)
+{
+    if(exclusive_less(left_minuend, right))
+        return right; 
+
+    return construct<Type>(domain_next<Type>(upper(left_minuend)), upper(right));
+}
+
+template<class Type>
+typename boost::enable_if<is_static_open<Type>, Type>::type
+left_subtract(Type right, const Type& left_minuend)
+{
+    if(exclusive_less(left_minuend, right))
+        return right; 
+
+    return construct<Type>(domain_prior<Type>(upper(left_minuend)), upper(right));
+}
+
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
+left_subtract(Type right, const Type& left_minuend)
+{
+    if(exclusive_less(left_minuend, right))
+        return right; 
+    return  dynamic_interval_traits<Type>::construct_bounded
+            ( reverse_bounded_upper(left_minuend), bounded_upper(right) );
+}
+
+
+//- right_subtract -------------------------------------------------------------
+/** subtract \c right_minuend from the \c left interval on it's right side. 
+    Return the difference: The part of \c left right of \c right_minuend.
+\code
+left_over = left - right_minuend; //on the right side.
+[a      ...  : left
+     [b ...  : right_minuend
+[a  b)       : left_over
+\endcode
+*/
+template<class Type>
+typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type
+right_subtract(Type left, const Type& right_minuend)
+{
+    if(exclusive_less(left, right_minuend))
+        return left; 
+    return construct<Type>(lower(left), lower(right_minuend));
+}
+
+template<class Type>
+typename boost::enable_if<is_static_closed<Type>, Type>::type
+right_subtract(Type left, const Type& right_minuend)
+{
+    if(exclusive_less(left, right_minuend))
+        return left;
+    else if(lower_less_equal(right_minuend, left))
+        return identity_element<Type>::value();
+
+    return construct<Type>(lower(left), domain_prior<Type>(lower(right_minuend)));
+}
+
+template<class Type>
+typename boost::enable_if<is_static_open<Type>, Type>::type
+right_subtract(Type left, const Type& right_minuend)
+{
+    if(exclusive_less(left, right_minuend))
+        return left;
+
+    return construct<Type>(lower(left), domain_next<Type>(lower(right_minuend)));
+}
+
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
+right_subtract(Type left, const Type& right_minuend)
+{
+    if(exclusive_less(left, right_minuend))
+        return left; 
+
+    return  dynamic_interval_traits<Type>::construct_bounded
+            ( bounded_lower(left), reverse_bounded_lower(right_minuend) );
+}
+
+//==============================================================================
+//= Intersection
+//==============================================================================
+//- operator & -----------------------------------------------------------------
+/** Returns the intersection of \c left and \c right interval. */
+template<class Type>
+typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type
+operator & (Type left, const Type& right)
+{
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+
+    if(icl::is_empty(left) || icl::is_empty(right))
+        return identity_element<Type>::value();
+    else
+        return
+        construct<Type>
+        (
+            (std::max)(icl::lower(left), icl::lower(right), domain_compare()),
+            (std::min)(icl::upper(left), icl::upper(right), domain_compare())
+        );
+}
+
+template<class Type>
+typename boost::enable_if<has_symmetric_bounds<Type>, Type>::type
+operator & (Type left, const Type& right)
+{
+    typedef typename interval_traits<Type>::domain_compare domain_compare;
+
+    if(icl::is_empty(left) || icl::is_empty(right))
+        return identity_element<Type>::value();
+    else
+        return
+        construct<Type>
+        (
+            (std::max)(icl::lower(left), icl::lower(right), domain_compare()),
+            (std::min)(icl::upper(left), icl::upper(right), domain_compare())
+        );
+}
+
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
+operator & (Type left, const Type& right)
+{
+    if(icl::is_empty(left) || icl::is_empty(right))
+        return identity_element<Type>::value();
+    else 
+        return  dynamic_interval_traits<Type>::construct_bounded
+                (
+                    lower_max(left, right), 
+                    upper_min(left, right) 
+                );
+}
+
+
+//- intersects -----------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<is_interval<Type>, bool>::type
+intersects(const Type& left, const Type& right)
+{ 
+    return !(   icl::is_empty(left) || icl::is_empty(right) 
+             || exclusive_less(left,right) || exclusive_less(right,left)); 
+}
+
+//- disjoint -------------------------------------------------------------------
+template<class Type>
+typename boost::enable_if<is_interval<Type>, bool>::type
+disjoint(const Type& left, const Type& right)
+{ 
+    return icl::is_empty(left) || icl::is_empty(right) 
+        || exclusive_less(left,right) || exclusive_less(right,left); 
+}
+
+//==============================================================================
+//= Complement
+//==============================================================================
+
+template<class Type>
+typename boost::enable_if<is_asymmetric_interval<Type>, Type>::type
+inner_complement(const Type& left, const Type& right)
+{
+    if(icl::is_empty(left) || icl::is_empty(right))
+        return  identity_element<Type>::value();
+    else if(exclusive_less(left, right))
+        return construct<Type>(upper(left), lower(right));
+    else if(exclusive_less(right, left))
+        return construct<Type>(upper(right), lower(left));
+    else
+        return identity_element<Type>::value();
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_static_closed<Type>, Type>::type
+inner_complement(const Type& left, const Type& right)
+{
+    if(icl::is_empty(left) || icl::is_empty(right))
+        return  identity_element<Type>::value();
+    else if(exclusive_less(left, right))
+        return construct<Type>(domain_next<Type>(upper(left)), domain_prior<Type>(lower(right)));
+    else if(exclusive_less(right, left))
+        return construct<Type>(domain_next<Type>(upper(right)), domain_prior<Type>(lower(left)));
+    else
+        return identity_element<Type>::value();
+}
+
+template<class Type>
+typename boost::enable_if<is_discrete_static_open<Type>, Type>::type
+inner_complement(const Type& left, const Type& right)
+{
+    if(icl::is_empty(left) || icl::is_empty(right))
+        return  identity_element<Type>::value();
+    else if(exclusive_less(left, right))
+        return construct<Type>(last(left), first(right));
+    else if(exclusive_less(right, left))
+        return construct<Type>(last(right), first(left));
+    else
+        return identity_element<Type>::value();
+}
+
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, Type>::type
+inner_complement(const Type& left, const Type& right)
+{
+    if(icl::is_empty(left) || icl::is_empty(right))
+        return  identity_element<Type>::value();
+    else if(exclusive_less(left, right))
+        return right_subtract(left_subtract(hull(left, right), left), right);
+    else if(exclusive_less(right, left))
+        return right_subtract(left_subtract(hull(right, left), right), left);
+    else
+        return identity_element<Type>::value();
+}
+
+template<class Type>
+inline typename boost::enable_if<is_interval<Type>, Type>::type
+between(const Type& left, const Type& right)
+{ 
+    return inner_complement(left, right);
+}
+
+
+
+//==============================================================================
+//= Distance
+//==============================================================================
+template<class Type>
+typename boost::
+enable_if< mpl::and_< is_interval<Type>
+                    , has_difference<typename interval_traits<Type>::domain_type>
+                    , is_discrete<typename interval_traits<Type>::domain_type>        
+                    >
+         , typename difference_type_of<interval_traits<Type> >::type>::type
+distance(const Type& x1, const Type& x2)
+{
+    typedef typename difference_type_of<interval_traits<Type> >::type difference_type;
+
+    if(icl::is_empty(x1) || icl::is_empty(x2))
+        return icl::identity_element<difference_type>::value();
+    else if(domain_less<Type>(last(x1), first(x2)))
+        return static_cast<difference_type>(icl::pred(first(x2) - last(x1)));
+    else if(domain_less<Type>(last(x2), first(x1)))
+        return static_cast<difference_type>(icl::pred(first(x1) - last(x2)));
+    else
+        return icl::identity_element<difference_type>::value();
+}
+
+template<class Type>
+typename boost::
+enable_if< mpl::and_< is_interval<Type>
+                    , has_difference<typename interval_traits<Type>::domain_type>
+                    , is_continuous<typename interval_traits<Type>::domain_type>        
+                    >
+         , typename difference_type_of<interval_traits<Type> >::type>::type
+distance(const Type& x1, const Type& x2)
+{
+    typedef typename difference_type_of<interval_traits<Type> >::type DiffT;
+
+    if(icl::is_empty(x1) || icl::is_empty(x2))
+        return icl::identity_element<DiffT>::value();
+    else if(domain_less<Type>(upper(x1), lower(x2)))
+        return lower(x2) - upper(x1);
+    else if(domain_less<Type>(upper(x2), lower(x1)))
+        return lower(x1) - upper(x2);
+    else
+        return icl::identity_element<DiffT>::value();
+}
+
+//==============================================================================
+//= Streaming, representation
+//==============================================================================
+template<class Type>
+typename boost::
+    enable_if< mpl::or_< is_static_left_open<Type>
+                       , is_static_open<Type>    >, std::string>::type
+left_bracket(const Type&) { return "("; }
+
+template<class Type>
+typename boost::
+    enable_if< mpl::or_< is_static_right_open<Type>
+                       , is_static_closed<Type>   >, std::string>::type
+left_bracket(const Type&) { return "["; }
+
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, std::string>::type
+left_bracket(const Type& object) 
+{ 
+    return left_bracket(object.bounds()); 
+}
+
+//------------------------------------------------------------------------------
+template<class Type>
+typename boost::
+    enable_if< mpl::or_< is_static_right_open<Type>
+                       , is_static_open<Type>     >, std::string>::type
+right_bracket(const Type&) { return ")"; }
+
+template<class Type>
+typename boost::
+    enable_if< mpl::or_< is_static_left_open<Type>
+                       , is_static_closed<Type>    >, std::string>::type
+right_bracket(const Type&) { return "]"; }
+
+template<class Type>
+typename boost::enable_if<has_dynamic_bounds<Type>, std::string>::type
+right_bracket(const Type& object) 
+{ 
+    return right_bracket(object.bounds()); 
+}
+
+//------------------------------------------------------------------------------
+template<class CharType, class CharTraits, class Type>
+typename boost::enable_if<is_interval<Type>, 
+                          std::basic_ostream<CharType, CharTraits> >::type&
+operator << (std::basic_ostream<CharType, CharTraits> &stream, Type const& object)
+{
+    if(boost::icl::is_empty(object))
+        return stream << left_bracket<Type>(object) << right_bracket<Type>(object); 
+    else
+        return stream << left_bracket<Type>(object) 
+                      << interval_traits<Type>::lower(object) 
+                      << "," 
+                      << interval_traits<Type>::upper(object) 
+                      << right_bracket<Type>(object) ;
+}
+
+}} // namespace icl boost
+
+#endif
+