diff DEPENDENCIES/generic/include/boost/icl/interval_base_map.hpp @ 16:2665513ce2d3

Add boost headers

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/DEPENDENCIES/generic/include/boost/icl/interval_base_map.hpp	Tue Aug 05 11:11:38 2014 +0100
@@ -0,0 +1,1390 @@
+/*-----------------------------------------------------------------------------+
+Copyright (c) 2007-2012: Joachim Faulhaber
+Copyright (c) 1999-2006: Cortex Software GmbH, Kantstrasse 57, Berlin
++------------------------------------------------------------------------------+
+   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_INTERVAL_BASE_MAP_HPP_JOFA_990223
+#define BOOST_ICL_INTERVAL_BASE_MAP_HPP_JOFA_990223
+
+#include <limits>
+#include <boost/type_traits/ice.hpp>
+#include <boost/mpl/and.hpp>
+#include <boost/mpl/or.hpp>
+#include <boost/mpl/not.hpp>
+
+#include <boost/icl/detail/notate.hpp>
+#include <boost/icl/detail/design_config.hpp>
+#include <boost/icl/detail/on_absorbtion.hpp>
+#include <boost/icl/detail/interval_map_algo.hpp>
+
+#include <boost/icl/associative_interval_container.hpp>
+
+#include <boost/icl/type_traits/is_interval_splitter.hpp>
+#include <boost/icl/map.hpp>
+
+namespace boost{namespace icl
+{
+
+template<class DomainT, class CodomainT>
+struct mapping_pair
+{
+    DomainT   key;
+    CodomainT data;
+
+    mapping_pair():key(), data(){}
+
+    mapping_pair(const DomainT& key_value, const CodomainT& data_value)
+        :key(key_value), data(data_value){}
+
+    mapping_pair(const std::pair<DomainT,CodomainT>& std_pair)
+        :key(std_pair.first), data(std_pair.second){}
+};
+
+/** \brief Implements a map as a map of intervals (base class) */
+template
+<
+    class SubType,
+    typename DomainT,
+    typename CodomainT,
+    class Traits = icl::partial_absorber,
+    ICL_COMPARE Compare  = ICL_COMPARE_INSTANCE(ICL_COMPARE_DEFAULT, DomainT),
+    ICL_COMBINE Combine  = ICL_COMBINE_INSTANCE(icl::inplace_plus, CodomainT),
+    ICL_SECTION Section  = ICL_SECTION_INSTANCE(icl::inter_section, CodomainT), 
+    ICL_INTERVAL(ICL_COMPARE) Interval = ICL_INTERVAL_INSTANCE(ICL_INTERVAL_DEFAULT, DomainT, Compare),
+    ICL_ALLOC   Alloc    = std::allocator
+>
+class interval_base_map
+{
+public:
+    //==========================================================================
+    //= Associated types
+    //==========================================================================
+    typedef interval_base_map<SubType,DomainT,CodomainT,
+                              Traits,Compare,Combine,Section,Interval,Alloc>
+                              type;
+
+    /// The designated \e derived or \e sub_type of this base class
+    typedef SubType sub_type;
+
+    /// Auxilliary type for overloadresolution
+    typedef type overloadable_type;
+
+    /// Traits of an itl map
+    typedef Traits traits;
+
+    //--------------------------------------------------------------------------
+    //- Associated types: Related types
+    //--------------------------------------------------------------------------
+    /// The atomized type representing the corresponding container of elements
+    typedef typename icl::map<DomainT,CodomainT,
+                              Traits,Compare,Combine,Section,Alloc> atomized_type;
+
+    //--------------------------------------------------------------------------
+    //- Associated types: Data
+    //--------------------------------------------------------------------------
+    /// Domain type (type of the keys) of the map
+    typedef DomainT   domain_type;
+    typedef typename boost::call_traits<DomainT>::param_type domain_param;
+    /// Domain type (type of the keys) of the map
+    typedef CodomainT codomain_type;
+    /// Auxiliary type to help the compiler resolve ambiguities when using std::make_pair
+    typedef mapping_pair<domain_type,codomain_type> domain_mapping_type;
+    /// Conceptual is a map a set of elements of type \c element_type
+    typedef domain_mapping_type element_type;
+    /// The interval type of the map
+    typedef ICL_INTERVAL_TYPE(Interval,DomainT,Compare) interval_type;
+    /// Auxiliary type for overload resolution
+    typedef std::pair<interval_type,CodomainT> interval_mapping_type;
+    /// Type of an interval containers segment, that is spanned by an interval
+    typedef std::pair<interval_type,CodomainT> segment_type;
+
+    //--------------------------------------------------------------------------
+    //- Associated types: Size
+    //--------------------------------------------------------------------------
+    /// The difference type of an interval which is sometimes different form the domain_type
+    typedef typename difference_type_of<domain_type>::type difference_type;
+    /// The size type of an interval which is mostly std::size_t
+    typedef typename size_type_of<domain_type>::type size_type;
+
+    //--------------------------------------------------------------------------
+    //- Associated types: Functors
+    //--------------------------------------------------------------------------
+    /// Comparison functor for domain values
+    typedef ICL_COMPARE_DOMAIN(Compare,DomainT)      domain_compare;
+    typedef ICL_COMPARE_DOMAIN(Compare,segment_type) segment_compare;
+    /// Combine functor for codomain value aggregation
+    typedef ICL_COMBINE_CODOMAIN(Combine,CodomainT)  codomain_combine;
+    /// Inverse Combine functor for codomain value aggregation
+    typedef typename inverse<codomain_combine>::type inverse_codomain_combine;
+    /// Intersection functor for codomain values
+
+    typedef typename mpl::if_
+    <has_set_semantics<codomain_type>
+    , ICL_SECTION_CODOMAIN(Section,CodomainT)     
+    , codomain_combine
+    >::type                                            codomain_intersect;
+
+
+    /// Inverse Combine functor for codomain value intersection
+    typedef typename inverse<codomain_intersect>::type inverse_codomain_intersect;
+
+    /// Comparison functor for intervals which are keys as well
+    typedef exclusive_less_than<interval_type> interval_compare;
+
+    /// Comparison functor for keys
+    typedef exclusive_less_than<interval_type> key_compare;
+
+    //--------------------------------------------------------------------------
+    //- Associated types: Implementation and stl related
+    //--------------------------------------------------------------------------
+    /// The allocator type of the set
+    typedef Alloc<std::pair<const interval_type, codomain_type> > 
+        allocator_type;
+
+    /// Container type for the implementation 
+    typedef ICL_IMPL_SPACE::map<interval_type,codomain_type,
+                                key_compare,allocator_type> ImplMapT;
+
+    /// key type of the implementing container
+    typedef typename ImplMapT::key_type   key_type;
+    /// value type of the implementing container
+    typedef typename ImplMapT::value_type value_type;
+    /// data type of the implementing container
+    typedef typename ImplMapT::value_type::second_type data_type;
+
+    /// pointer type
+    typedef typename ImplMapT::pointer         pointer;
+    /// const pointer type
+    typedef typename ImplMapT::const_pointer   const_pointer;
+    /// reference type
+    typedef typename ImplMapT::reference       reference;
+    /// const reference type
+    typedef typename ImplMapT::const_reference const_reference;
+
+    /// iterator for iteration over intervals
+    typedef typename ImplMapT::iterator iterator;
+    /// const_iterator for iteration over intervals
+    typedef typename ImplMapT::const_iterator const_iterator;
+    /// iterator for reverse iteration over intervals
+    typedef typename ImplMapT::reverse_iterator reverse_iterator;
+    /// const_iterator for iteration over intervals
+    typedef typename ImplMapT::const_reverse_iterator const_reverse_iterator;
+
+    /// element iterator: Depreciated, see documentation.
+    typedef boost::icl::element_iterator<iterator> element_iterator; 
+    /// const element iterator: Depreciated, see documentation.
+    typedef boost::icl::element_iterator<const_iterator> element_const_iterator; 
+    /// element reverse iterator: Depreciated, see documentation.
+    typedef boost::icl::element_iterator<reverse_iterator> element_reverse_iterator; 
+    /// element const reverse iterator: Depreciated, see documentation.
+    typedef boost::icl::element_iterator<const_reverse_iterator> element_const_reverse_iterator; 
+    
+    typedef typename on_absorbtion<type, codomain_combine, 
+                                Traits::absorbs_identities>::type on_codomain_absorbtion;
+
+public:
+    BOOST_STATIC_CONSTANT(bool, 
+        is_total_invertible = (   Traits::is_total 
+                               && has_inverse<codomain_type>::value));
+
+    BOOST_STATIC_CONSTANT(int, fineness = 0); 
+
+public:
+
+    //==========================================================================
+    //= Construct, copy, destruct
+    //==========================================================================
+    /** Default constructor for the empty object */
+    interval_base_map()
+    {
+        BOOST_CONCEPT_ASSERT((DefaultConstructibleConcept<DomainT>));
+        BOOST_CONCEPT_ASSERT((LessThanComparableConcept<DomainT>));
+        BOOST_CONCEPT_ASSERT((DefaultConstructibleConcept<CodomainT>));
+        BOOST_CONCEPT_ASSERT((EqualComparableConcept<CodomainT>));
+    }
+
+    /** Copy constructor */
+    interval_base_map(const interval_base_map& src): _map(src._map)
+    {
+        BOOST_CONCEPT_ASSERT((DefaultConstructibleConcept<DomainT>));
+        BOOST_CONCEPT_ASSERT((LessThanComparableConcept<DomainT>));
+        BOOST_CONCEPT_ASSERT((DefaultConstructibleConcept<CodomainT>));
+        BOOST_CONCEPT_ASSERT((EqualComparableConcept<CodomainT>));
+    }
+
+    /** Copy assignment operator */
+    interval_base_map& operator = (const interval_base_map& src) 
+    { 
+        this->_map = src._map;
+        return *this; 
+    }
+
+#   ifndef BOOST_ICL_NO_CXX11_RVALUE_REFERENCES
+    //==========================================================================
+    //= Move semantics
+    //==========================================================================
+
+    /** Move constructor */
+    interval_base_map(interval_base_map&& src): _map(boost::move(src._map))
+    {
+        BOOST_CONCEPT_ASSERT((DefaultConstructibleConcept<DomainT>));
+        BOOST_CONCEPT_ASSERT((LessThanComparableConcept<DomainT>));
+        BOOST_CONCEPT_ASSERT((DefaultConstructibleConcept<CodomainT>));
+        BOOST_CONCEPT_ASSERT((EqualComparableConcept<CodomainT>));
+    }
+
+    /** Move assignment operator */
+    interval_base_map& operator = (interval_base_map&& src) 
+    { 
+        this->_map = boost::move(src._map);
+        return *this; 
+    }
+
+    //==========================================================================
+#   endif // BOOST_ICL_NO_CXX11_RVALUE_REFERENCES
+
+    /** swap the content of containers */
+    void swap(interval_base_map& object) { _map.swap(object._map); }
+
+    //==========================================================================
+    //= Containedness
+    //==========================================================================
+    /** clear the map */
+    void clear() { icl::clear(*that()); }
+
+    /** is the map empty? */
+    bool empty()const { return icl::is_empty(*that()); }
+
+    //==========================================================================
+    //= Size
+    //==========================================================================
+    /** An interval map's size is it's cardinality */
+    size_type size()const
+    {
+        return icl::cardinality(*that());
+    }
+
+    /** Size of the iteration over this container */
+    std::size_t iterative_size()const 
+    { 
+        return _map.size(); 
+    }
+
+    //==========================================================================
+    //= Selection
+    //==========================================================================
+
+    /** Find the interval value pair, that contains \c key */
+    const_iterator find(const domain_type& key_value)const
+    { 
+        return icl::find(*this, key_value);
+    }
+
+    /** Find the first interval value pair, that collides with interval 
+        \c key_interval */
+    const_iterator find(const interval_type& key_interval)const
+    { 
+        return _map.find(key_interval); 
+    }
+
+    /** Total select function. */
+    codomain_type operator()(const domain_type& key_value)const
+    {
+        const_iterator it_ = icl::find(*this, key_value);
+        return it_==end() ? identity_element<codomain_type>::value()
+                          : (*it_).second;
+    }
+
+    //==========================================================================
+    //= Addition
+    //==========================================================================
+
+    /** Addition of a key value pair to the map */
+    SubType& add(const element_type& key_value_pair) 
+    {
+        return icl::add(*that(), key_value_pair);
+    }
+
+    /** Addition of an interval value pair to the map. */
+    SubType& add(const segment_type& interval_value_pair) 
+    {
+        this->template _add<codomain_combine>(interval_value_pair);
+        return *that();
+    }
+
+    /** Addition of an interval value pair \c interval_value_pair to the map. 
+        Iterator \c prior_ is a hint to the position \c interval_value_pair can be 
+        inserted after. */
+    iterator add(iterator prior_, const segment_type& interval_value_pair) 
+    {
+        return this->template _add<codomain_combine>(prior_, interval_value_pair);
+    }
+
+    //==========================================================================
+    //= Subtraction
+    //==========================================================================
+    /** Subtraction of a key value pair from the map */
+    SubType& subtract(const element_type& key_value_pair)
+    { 
+        return icl::subtract(*that(), key_value_pair);
+    }
+
+    /** Subtraction of an interval value pair from the map. */
+    SubType& subtract(const segment_type& interval_value_pair)
+    {
+        on_invertible<type, is_total_invertible>
+            ::subtract(*that(), interval_value_pair);
+        return *that();
+    }
+
+    //==========================================================================
+    //= Insertion
+    //==========================================================================
+    /** Insertion of a \c key_value_pair into the map. */
+    SubType& insert(const element_type& key_value_pair) 
+    {
+        return icl::insert(*that(), key_value_pair);
+    }
+
+    /** Insertion of an \c interval_value_pair into the map. */
+    SubType& insert(const segment_type& interval_value_pair)
+    { 
+        _insert(interval_value_pair); 
+        return *that();
+    }
+
+    /** Insertion of an \c interval_value_pair into the map. Iterator \c prior_. 
+        serves as a hint to insert after the element \c prior point to. */
+    iterator insert(iterator prior, const segment_type& interval_value_pair)
+    { 
+        return _insert(prior, interval_value_pair);
+    }
+
+    /** With <tt>key_value_pair = (k,v)</tt> set value \c v for key \c k */
+    SubType& set(const element_type& key_value_pair) 
+    { 
+        return icl::set_at(*that(), key_value_pair);
+    }
+
+    /** With <tt>interval_value_pair = (I,v)</tt> set value \c v 
+        for all keys in interval \c I in the map. */
+    SubType& set(const segment_type& interval_value_pair)
+    { 
+        return icl::set_at(*that(), interval_value_pair);
+    }
+
+    //==========================================================================
+    //= Erasure
+    //==========================================================================
+    /** Erase a \c key_value_pair from the map. */
+    SubType& erase(const element_type& key_value_pair) 
+    { 
+        icl::erase(*that(), key_value_pair);
+        return *that();
+    }
+
+    /** Erase an \c interval_value_pair from the map. */
+    SubType& erase(const segment_type& interval_value_pair);
+
+    /** Erase a key value pair for \c key. */
+    SubType& erase(const domain_type& key) 
+    { 
+        return icl::erase(*that(), key); 
+    }
+
+    /** Erase all value pairs within the range of the 
+        interval <tt>inter_val</tt> from the map.   */
+    SubType& erase(const interval_type& inter_val);
+
+
+    /** Erase all value pairs within the range of the interval that iterator 
+        \c position points to. */
+    void erase(iterator position){ this->_map.erase(position); }
+
+    /** Erase all value pairs for a range of iterators <tt>[first,past)</tt>. */
+    void erase(iterator first, iterator past){ this->_map.erase(first, past); }
+
+    //==========================================================================
+    //= Intersection
+    //==========================================================================
+    /** The intersection of \c interval_value_pair and \c *this map is added to \c section. */
+    void add_intersection(SubType& section, const segment_type& interval_value_pair)const
+    {
+        on_definedness<SubType, Traits::is_total>
+            ::add_intersection(section, *that(), interval_value_pair);
+    }
+
+    //==========================================================================
+    //= Symmetric difference
+    //==========================================================================
+    /** If \c *this map contains \c key_value_pair it is erased, otherwise it is added. */
+    SubType& flip(const element_type& key_value_pair)
+    { 
+        return icl::flip(*that(), key_value_pair); 
+    }
+
+    /** If \c *this map contains \c interval_value_pair it is erased, otherwise it is added. */
+    SubType& flip(const segment_type& interval_value_pair)
+    {
+        on_total_absorbable<SubType, Traits::is_total, Traits::absorbs_identities>
+            ::flip(*that(), interval_value_pair);
+        return *that();
+    }
+
+    //==========================================================================
+    //= Iterator related
+    //==========================================================================
+
+    iterator lower_bound(const key_type& interval)
+    { return _map.lower_bound(interval); }
+
+    iterator upper_bound(const key_type& interval)
+    { return _map.upper_bound(interval); }
+
+    const_iterator lower_bound(const key_type& interval)const
+    { return _map.lower_bound(interval); }
+
+    const_iterator upper_bound(const key_type& interval)const
+    { return _map.upper_bound(interval); }
+
+    std::pair<iterator,iterator> equal_range(const key_type& interval)
+    { 
+        return std::pair<iterator,iterator>
+               (lower_bound(interval), upper_bound(interval)); 
+    }
+
+    std::pair<const_iterator,const_iterator> 
+        equal_range(const key_type& interval)const
+    { 
+        return std::pair<const_iterator,const_iterator>
+               (lower_bound(interval), upper_bound(interval)); 
+    }
+
+    iterator begin() { return _map.begin(); }
+    iterator end()   { return _map.end(); }
+    const_iterator begin()const { return _map.begin(); }
+    const_iterator end()const   { return _map.end(); }
+    reverse_iterator rbegin() { return _map.rbegin(); }
+    reverse_iterator rend()   { return _map.rend(); }
+    const_reverse_iterator rbegin()const { return _map.rbegin(); }
+    const_reverse_iterator rend()const   { return _map.rend(); }
+
+private:
+    template<class Combiner>
+    iterator _add(const segment_type& interval_value_pair);
+
+    template<class Combiner>
+    iterator _add(iterator prior_, const segment_type& interval_value_pair);
+
+    template<class Combiner>
+    void _subtract(const segment_type& interval_value_pair);
+
+    iterator _insert(const segment_type& interval_value_pair);
+    iterator _insert(iterator prior_, const segment_type& interval_value_pair);
+
+private:
+    template<class Combiner>
+    void add_segment(const interval_type& inter_val, const CodomainT& co_val, iterator& it_);
+
+    template<class Combiner>
+    void add_main(interval_type& inter_val, const CodomainT& co_val, 
+                  iterator& it_, const iterator& last_);
+
+    template<class Combiner>
+    void add_rear(const interval_type& inter_val, const CodomainT& co_val, iterator& it_);
+
+    void add_front(const interval_type& inter_val, iterator& first_);
+
+private:
+    void subtract_front(const interval_type& inter_val, iterator& first_);
+
+    template<class Combiner>
+    void subtract_main(const CodomainT& co_val, iterator& it_, const iterator& last_);
+
+    template<class Combiner>
+    void subtract_rear(interval_type& inter_val, const CodomainT& co_val, iterator& it_);
+
+private:
+    void insert_main(const interval_type&, const CodomainT&, iterator&, const iterator&);
+    void erase_rest (      interval_type&, const CodomainT&, iterator&, const iterator&);
+
+    template<class FragmentT>
+    void total_add_intersection(SubType& section, const FragmentT& fragment)const
+    {
+        section += *that();
+        section.add(fragment);
+    }
+
+    void partial_add_intersection(SubType& section, const segment_type& operand)const
+    {
+        interval_type inter_val = operand.first;
+        if(icl::is_empty(inter_val)) 
+            return;
+
+        std::pair<const_iterator, const_iterator> exterior = equal_range(inter_val);
+        if(exterior.first == exterior.second)
+            return;
+
+        for(const_iterator it_=exterior.first; it_ != exterior.second; it_++) 
+        {
+            interval_type common_interval = (*it_).first & inter_val; 
+            if(!icl::is_empty(common_interval))
+            {
+                section.template _add<codomain_combine>  (value_type(common_interval, (*it_).second) );
+                section.template _add<codomain_intersect>(value_type(common_interval, operand.second));
+            }
+        }
+    }
+
+    void partial_add_intersection(SubType& section, const element_type& operand)const
+    {
+        partial_add_intersection(section, make_segment<type>(operand));
+    }
+
+
+protected:
+
+    template <class Combiner>
+    iterator gap_insert(iterator prior_, const interval_type& inter_val, 
+                                         const codomain_type& co_val   )
+    {
+        // inter_val is not conained in this map. Insertion will be successful
+        BOOST_ASSERT(this->_map.find(inter_val) == this->_map.end());
+        BOOST_ASSERT((!on_absorbtion<type,Combiner,Traits::absorbs_identities>::is_absorbable(co_val)));
+        return this->_map.insert(prior_, value_type(inter_val, version<Combiner>()(co_val)));
+    }
+
+    template <class Combiner>
+    std::pair<iterator, bool>
+    add_at(const iterator& prior_, const interval_type& inter_val, 
+                                   const codomain_type& co_val   )
+    {
+        // Never try to insert an identity element into an identity element absorber here:
+        BOOST_ASSERT((!(on_absorbtion<type,Combiner,Traits::absorbs_identities>::is_absorbable(co_val))));
+
+        iterator inserted_ 
+            = this->_map.insert(prior_, value_type(inter_val, Combiner::identity_element()));
+
+        if((*inserted_).first == inter_val && (*inserted_).second == Combiner::identity_element())
+        {
+            Combiner()((*inserted_).second, co_val);
+            return std::pair<iterator,bool>(inserted_, true);
+        }
+        else
+            return std::pair<iterator,bool>(inserted_, false);
+    }
+
+    std::pair<iterator, bool>
+    insert_at(const iterator& prior_, const interval_type& inter_val, 
+                                      const codomain_type& co_val   )
+    {
+        iterator inserted_
+            = this->_map.insert(prior_, value_type(inter_val, co_val));
+
+        if(inserted_ == prior_)
+            return std::pair<iterator,bool>(inserted_, false);
+        else if((*inserted_).first == inter_val)
+            return std::pair<iterator,bool>(inserted_, true);
+        else
+            return std::pair<iterator,bool>(inserted_, false);
+    }
+
+
+protected:
+    sub_type* that() { return static_cast<sub_type*>(this); }
+    const sub_type* that()const { return static_cast<const sub_type*>(this); }
+
+protected:
+    ImplMapT _map;
+
+
+private:
+    //--------------------------------------------------------------------------
+    template<class Type, bool is_total_invertible>
+    struct on_invertible;
+
+    template<class Type>
+    struct on_invertible<Type, true>
+    {
+        typedef typename Type::segment_type segment_type;
+        typedef typename Type::inverse_codomain_combine inverse_codomain_combine;
+
+        static void subtract(Type& object, const segment_type& operand)
+        { object.template _add<inverse_codomain_combine>(operand); }
+    };
+
+    template<class Type>
+    struct on_invertible<Type, false>
+    {
+        typedef typename Type::segment_type segment_type;
+        typedef typename Type::inverse_codomain_combine inverse_codomain_combine;
+
+        static void subtract(Type& object, const segment_type& operand)
+        { object.template _subtract<inverse_codomain_combine>(operand); }
+    };
+
+    friend struct on_invertible<type, true>;
+    friend struct on_invertible<type, false>;
+    //--------------------------------------------------------------------------
+
+    //--------------------------------------------------------------------------
+    template<class Type, bool is_total>
+    struct on_definedness;
+
+    template<class Type>
+    struct on_definedness<Type, true>
+    {
+        static void add_intersection(Type& section, const Type& object, 
+                                     const segment_type& operand)
+        { object.total_add_intersection(section, operand); }
+    };
+
+    template<class Type>
+    struct on_definedness<Type, false>
+    {
+        static void add_intersection(Type& section, const Type& object, 
+                                     const segment_type& operand)
+        { object.partial_add_intersection(section, operand); }
+    };
+
+    friend struct on_definedness<type, true>;
+    friend struct on_definedness<type, false>;
+    //--------------------------------------------------------------------------
+
+    //--------------------------------------------------------------------------
+    template<class Type, bool has_set_semantics> 
+    struct on_codomain_model;
+
+    template<class Type>
+    struct on_codomain_model<Type, true>
+    {
+        typedef typename Type::interval_type interval_type;
+        typedef typename Type::codomain_type codomain_type;
+        typedef typename Type::segment_type  segment_type;
+        typedef typename Type::codomain_combine codomain_combine;
+        typedef typename Type::inverse_codomain_intersect inverse_codomain_intersect;
+
+        static void add(Type& intersection, interval_type& common_interval, 
+                        const codomain_type& flip_value, const codomain_type& co_value)
+        {
+            codomain_type common_value = flip_value;
+            inverse_codomain_intersect()(common_value, co_value);
+            intersection.template 
+                _add<codomain_combine>(segment_type(common_interval, common_value));
+        }
+    };
+
+    template<class Type>
+    struct on_codomain_model<Type, false>
+    {
+        typedef typename Type::interval_type interval_type;
+        typedef typename Type::codomain_type codomain_type;
+        typedef typename Type::segment_type  segment_type;
+        typedef typename Type::codomain_combine codomain_combine;
+
+        static void add(Type& intersection, interval_type& common_interval, 
+                        const codomain_type&, const codomain_type&)
+        {
+            intersection.template 
+              _add<codomain_combine>(segment_type(common_interval, 
+                                                  identity_element<codomain_type>::value()));
+        }
+    };
+
+    friend struct on_codomain_model<type, true>;
+    friend struct on_codomain_model<type, false>;
+    //--------------------------------------------------------------------------
+
+
+    //--------------------------------------------------------------------------
+    template<class Type, bool is_total, bool absorbs_identities>
+    struct on_total_absorbable;
+
+    template<class Type>
+    struct on_total_absorbable<Type, true, true>
+    {
+        static void flip(Type& object, const typename Type::segment_type&)
+        { icl::clear(object); }
+    };
+
+#ifdef BOOST_MSVC 
+#pragma warning(push)
+#pragma warning(disable:4127) // conditional expression is constant
+#endif                        
+
+    template<class Type>
+    struct on_total_absorbable<Type, true, false>
+    {
+        typedef typename Type::segment_type  segment_type;
+        typedef typename Type::codomain_type codomain_type;
+
+        static void flip(Type& object, const segment_type& operand)
+        { 
+            object += operand;
+            ICL_FORALL(typename Type, it_, object)
+                (*it_).second = identity_element<codomain_type>::value();
+
+            if(mpl::not_<is_interval_splitter<Type> >::value)
+                icl::join(object);
+        }
+    };
+
+#ifdef BOOST_MSVC
+#pragma warning(pop)
+#endif
+
+    template<class Type, bool absorbs_identities>
+    struct on_total_absorbable<Type, false, absorbs_identities>
+    {
+        typedef typename Type::segment_type   segment_type;
+        typedef typename Type::codomain_type  codomain_type;
+        typedef typename Type::interval_type  interval_type;
+        typedef typename Type::value_type     value_type;
+        typedef typename Type::const_iterator const_iterator;
+        typedef typename Type::set_type       set_type;
+        typedef typename Type::inverse_codomain_intersect inverse_codomain_intersect;
+
+        static void flip(Type& object, const segment_type& interval_value_pair)
+        {
+            // That which is common shall be subtracted
+            // That which is not shall be added
+            // So interval_value_pair has to be 'complementary added' or flipped
+            interval_type span = interval_value_pair.first;
+            std::pair<const_iterator, const_iterator> exterior 
+                = object.equal_range(span);
+
+            const_iterator first_ = exterior.first;
+            const_iterator end_   = exterior.second;
+
+            interval_type covered, left_over, common_interval;
+            const codomain_type& x_value = interval_value_pair.second;
+            const_iterator it_ = first_;
+
+            set_type eraser;
+            Type     intersection;
+
+            while(it_ != end_  ) 
+            {
+                const codomain_type& co_value = (*it_).second;
+                covered = (*it_++).first;
+                //[a      ...  : span
+                //     [b ...  : covered
+                //[a  b)       : left_over
+                left_over = right_subtract(span, covered);
+
+                //That which is common ...
+                common_interval = span & covered;
+                if(!icl::is_empty(common_interval))
+                {
+                    // ... shall be subtracted
+                    icl::add(eraser, common_interval);
+
+                    on_codomain_model<Type, has_set_semantics<codomain_type>::value>
+                        ::add(intersection, common_interval, x_value, co_value);
+                }
+
+                icl::add(object, value_type(left_over, x_value)); //That which is not shall be added
+                // Because this is a collision free addition I don't have to distinguish codomain_types.
+
+                //...      d) : span
+                //... c)      : covered
+                //     [c  d) : span'
+                span = left_subtract(span, covered);
+            }
+
+            //If span is not empty here, it is not in the set so it shall be added
+            icl::add(object, value_type(span, x_value));
+
+            //finally rewrite the common segments
+            icl::erase(object, eraser);
+            object += intersection;
+        }
+    };
+    //--------------------------------------------------------------------------
+} ;
+
+
+//==============================================================================
+//= Addition detail
+//==============================================================================
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::add_front(const interval_type& inter_val, iterator& first_)
+{
+    // If the collision sequence has a left residual 'left_resid' it will
+    // be split, to provide a standardized start of algorithms:
+    // The addend interval 'inter_val' covers the beginning of the collision sequence.
+
+    // only for the first there can be a left_resid: a part of *first_ left of inter_val
+    interval_type left_resid = right_subtract((*first_).first, inter_val);
+
+    if(!icl::is_empty(left_resid))
+    {   //            [------------ . . .
+        // [left_resid---first_ --- . . .
+        iterator prior_ = cyclic_prior(*this, first_);
+        const_cast<interval_type&>((*first_).first) 
+            = left_subtract((*first_).first, left_resid);
+        //NOTE: Only splitting
+        this->_map.insert(prior_, segment_type(left_resid, (*first_).second));
+    }
+    //POST:
+    // [----- inter_val ---- . . .
+    // ...[-- first_ --...
+}
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+    template<class Combiner>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::add_segment(const interval_type& inter_val, const CodomainT& co_val, iterator& it_)
+{
+    interval_type lead_gap = right_subtract(inter_val, (*it_).first);
+    if(!icl::is_empty(lead_gap))
+    {
+        // [lead_gap--- . . .
+        //          [-- it_ ...
+        iterator prior_ = prior(it_); 
+        iterator inserted_ = this->template gap_insert<Combiner>(prior_, lead_gap, co_val);
+        that()->handle_inserted(prior_, inserted_);
+    }
+
+    // . . . --------- . . . addend interval
+    //      [-- it_ --)      has a common part with the first overval
+    Combiner()((*it_).second, co_val);
+    that()->template handle_left_combined<Combiner>(it_++);
+}
+
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+    template<class Combiner>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::add_main(interval_type& inter_val, const CodomainT& co_val, 
+               iterator& it_, const iterator& last_)
+{
+    interval_type cur_interval;
+    while(it_!=last_)
+    {
+        cur_interval = (*it_).first ;
+        add_segment<Combiner>(inter_val, co_val, it_);
+        // shrink interval
+        inter_val = left_subtract(inter_val, cur_interval);
+    }
+}
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+    template<class Combiner>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::add_rear(const interval_type& inter_val, const CodomainT& co_val, iterator& it_)
+{
+    iterator prior_ = cyclic_prior(*that(), it_);
+    interval_type cur_itv = (*it_).first ;
+
+    interval_type lead_gap = right_subtract(inter_val, cur_itv);
+    if(!icl::is_empty(lead_gap))
+    {   //         [lead_gap--- . . .
+        // [prior)          [-- it_ ...
+        iterator inserted_ = this->template gap_insert<Combiner>(prior_, lead_gap, co_val);
+        that()->handle_inserted(prior_, inserted_);
+    }
+
+    interval_type end_gap = left_subtract(inter_val, cur_itv);
+    if(!icl::is_empty(end_gap))
+    {
+        // [----------------end_gap)
+        //  . . . -- it_ --)
+        Combiner()((*it_).second, co_val);
+        that()->template gap_insert_at<Combiner>(it_, prior_, end_gap, co_val);
+    }
+    else
+    {
+        // only for the last there can be a right_resid: a part of *it_ right of x
+        interval_type right_resid = left_subtract(cur_itv, inter_val);
+
+        if(icl::is_empty(right_resid))
+        {
+            // [---------------)
+            //      [-- it_ ---)
+            Combiner()((*it_).second, co_val);
+            that()->template handle_preceeded_combined<Combiner>(prior_, it_);
+        }
+        else
+        {
+            // [--------------)
+            //      [-- it_ --right_resid)
+            const_cast<interval_type&>((*it_).first) = right_subtract((*it_).first, right_resid);
+
+            //NOTE: This is NOT an insertion that has to take care for correct application of
+            // the Combiner functor. It only reestablished that state after splitting the
+            // 'it_' interval value pair. Using _map_insert<Combiner> does not work here.
+            iterator insertion_ = this->_map.insert(it_, value_type(right_resid, (*it_).second));
+            that()->handle_reinserted(insertion_);
+
+            Combiner()((*it_).second, co_val);
+            that()->template handle_preceeded_combined<Combiner>(insertion_, it_);
+        }
+    }
+}
+
+
+//==============================================================================
+//= Addition
+//==============================================================================
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+    template<class Combiner>
+inline typename interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>::iterator
+    interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::_add(const segment_type& addend)
+{
+    typedef typename on_absorbtion<type,Combiner,
+                                absorbs_identities<type>::value>::type on_absorbtion_;
+
+    const interval_type& inter_val = addend.first;
+    if(icl::is_empty(inter_val)) 
+        return this->_map.end();
+
+    const codomain_type& co_val = addend.second;
+    if(on_absorbtion_::is_absorbable(co_val))
+        return this->_map.end();
+
+    std::pair<iterator,bool> insertion 
+        = this->_map.insert(value_type(inter_val, version<Combiner>()(co_val)));
+
+    if(insertion.second)
+        return that()->handle_inserted(insertion.first);
+    else
+    {
+        // Detect the first and the end iterator of the collision sequence
+        iterator first_ = this->_map.lower_bound(inter_val),
+                 last_  = insertion.first;
+        //assert(end_ == this->_map.upper_bound(inter_val));
+        iterator it_ = first_;
+        interval_type rest_interval = inter_val;
+
+        add_front         (rest_interval,         it_       );
+        add_main<Combiner>(rest_interval, co_val, it_, last_);
+        add_rear<Combiner>(rest_interval, co_val, it_       );
+        return it_;
+    }
+}
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+    template<class Combiner>
+inline typename interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>::iterator
+    interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::_add(iterator prior_, const segment_type& addend)
+{
+    typedef typename on_absorbtion<type,Combiner,
+                                absorbs_identities<type>::value>::type on_absorbtion_;
+
+    const interval_type& inter_val = addend.first;
+    if(icl::is_empty(inter_val)) 
+        return prior_;
+
+    const codomain_type& co_val = addend.second;
+    if(on_absorbtion_::is_absorbable(co_val))
+        return prior_;
+
+    std::pair<iterator,bool> insertion 
+        = add_at<Combiner>(prior_, inter_val, co_val);
+
+    if(insertion.second)
+        return that()->handle_inserted(insertion.first);
+    else
+    {
+        // Detect the first and the end iterator of the collision sequence
+        std::pair<iterator,iterator> overlap = equal_range(inter_val);
+        iterator it_   = overlap.first,
+                 last_ = prior(overlap.second);
+        interval_type rest_interval = inter_val;
+
+        add_front         (rest_interval,         it_       );
+        add_main<Combiner>(rest_interval, co_val, it_, last_);
+        add_rear<Combiner>(rest_interval, co_val, it_       );
+        return it_;
+    }
+}
+
+//==============================================================================
+//= Subtraction detail
+//==============================================================================
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::subtract_front(const interval_type& inter_val, iterator& it_)
+{
+    interval_type left_resid = right_subtract((*it_).first, inter_val);
+
+    if(!icl::is_empty(left_resid)) //                     [--- inter_val ---)
+    {                              //[prior_) [left_resid)[--- it_ . . .
+        iterator prior_ = cyclic_prior(*this, it_); 
+        const_cast<interval_type&>((*it_).first) = left_subtract((*it_).first, left_resid);
+        this->_map.insert(prior_, value_type(left_resid, (*it_).second));
+        // The segemnt *it_ is split at inter_val.first(), so as an invariant
+        // segment *it_ is always "under" inter_val and a left_resid is empty.
+    }
+}
+
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+    template<class Combiner>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::subtract_main(const CodomainT& co_val, iterator& it_, const iterator& last_)
+{
+    while(it_ != last_)
+    {
+        Combiner()((*it_).second, co_val);
+        that()->template handle_left_combined<Combiner>(it_++);
+    }
+}
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+    template<class Combiner>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::subtract_rear(interval_type& inter_val, const CodomainT& co_val, iterator& it_)
+{
+    interval_type right_resid = left_subtract((*it_).first, inter_val);
+
+    if(icl::is_empty(right_resid))
+    {
+        Combiner()((*it_).second, co_val);
+        that()->template handle_combined<Combiner>(it_);
+    }
+    else
+    {
+        const_cast<interval_type&>((*it_).first) = right_subtract((*it_).first, right_resid);
+        iterator next_ = this->_map.insert(it_, value_type(right_resid, (*it_).second));
+        Combiner()((*it_).second, co_val);
+        that()->template handle_succeeded_combined<Combiner>(it_, next_);
+    }
+}
+
+//==============================================================================
+//= Subtraction
+//==============================================================================
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+    template<class Combiner>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::_subtract(const segment_type& minuend)
+{
+    interval_type inter_val = minuend.first;
+    if(icl::is_empty(inter_val)) 
+        return;
+
+    const codomain_type& co_val = minuend.second;
+    if(on_absorbtion<type,Combiner,Traits::absorbs_identities>::is_absorbable(co_val)) 
+        return;
+
+    std::pair<iterator, iterator> exterior = equal_range(inter_val);
+    if(exterior.first == exterior.second)
+        return;
+
+    iterator last_  = prior(exterior.second);
+    iterator it_    = exterior.first;
+    subtract_front          (inter_val,         it_       );
+    subtract_main <Combiner>(           co_val, it_, last_);
+    subtract_rear <Combiner>(inter_val, co_val, it_       );
+}
+
+//==============================================================================
+//= Insertion
+//==============================================================================
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::insert_main(const interval_type& inter_val, const CodomainT& co_val, 
+                  iterator& it_, const iterator& last_)
+{
+    iterator end_   = boost::next(last_);
+    iterator prior_ = it_, inserted_;
+    if(prior_ != this->_map.end())
+        --prior_;
+    interval_type rest_interval = inter_val, left_gap, cur_itv;
+    interval_type last_interval = last_ ->first;
+
+    while(it_ != end_  )
+    {
+        cur_itv = (*it_).first ;            
+        left_gap = right_subtract(rest_interval, cur_itv);
+
+        if(!icl::is_empty(left_gap))
+        {
+            inserted_ = this->_map.insert(prior_, value_type(left_gap, co_val));
+            it_ = that()->handle_inserted(inserted_);
+        }
+
+        // shrink interval
+        rest_interval = left_subtract(rest_interval, cur_itv);
+        prior_ = it_;
+        ++it_;
+    }
+
+    //insert_rear(rest_interval, co_val, last_):
+    interval_type end_gap = left_subtract(rest_interval, last_interval);
+    if(!icl::is_empty(end_gap))
+    {
+        inserted_ = this->_map.insert(prior_, value_type(end_gap, co_val));
+        it_ = that()->handle_inserted(inserted_);
+    }
+    else
+        it_ = prior_;
+}
+
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+inline typename interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>::iterator
+    interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::_insert(const segment_type& addend)
+{
+    interval_type inter_val = addend.first;
+    if(icl::is_empty(inter_val)) 
+        return this->_map.end();
+
+    const codomain_type& co_val = addend.second;
+    if(on_codomain_absorbtion::is_absorbable(co_val)) 
+        return this->_map.end();
+
+    std::pair<iterator,bool> insertion = this->_map.insert(addend);
+
+    if(insertion.second)
+        return that()->handle_inserted(insertion.first);
+    else
+    {
+        // Detect the first and the end iterator of the collision sequence
+        iterator first_ = this->_map.lower_bound(inter_val),
+                 last_  = insertion.first;
+        //assert((++last_) == this->_map.upper_bound(inter_val));
+        iterator it_ = first_;
+        insert_main(inter_val, co_val, it_, last_);
+        return it_;
+    }
+}
+
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+inline typename interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>::iterator
+    interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::_insert(iterator prior_, const segment_type& addend)
+{
+    interval_type inter_val = addend.first;
+    if(icl::is_empty(inter_val)) 
+        return prior_;
+
+    const codomain_type& co_val = addend.second;
+    if(on_codomain_absorbtion::is_absorbable(co_val)) 
+        return prior_;
+
+    std::pair<iterator,bool> insertion = insert_at(prior_, inter_val, co_val);
+
+    if(insertion.second)
+        return that()->handle_inserted(insertion.first);
+    {
+        // Detect the first and the end iterator of the collision sequence
+        std::pair<iterator,iterator> overlap = equal_range(inter_val);
+        iterator it_    = overlap.first,
+                 last_  = prior(overlap.second);
+        insert_main(inter_val, co_val, it_, last_);
+        return it_;
+    }
+}
+
+//==============================================================================
+//= Erasure segment_type
+//==============================================================================
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+inline void interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::erase_rest(interval_type& inter_val, const CodomainT& co_val, 
+                 iterator& it_, const iterator& last_)
+{
+    // For all intervals within loop: (*it_).first are contained_in inter_val
+    while(it_ != last_)
+        if((*it_).second == co_val)
+            this->_map.erase(it_++); 
+        else it_++;
+
+    //erase_rear:
+    if((*it_).second == co_val)
+    {
+        interval_type right_resid = left_subtract((*it_).first, inter_val);
+        if(icl::is_empty(right_resid))
+            this->_map.erase(it_);
+        else
+            const_cast<interval_type&>((*it_).first) = right_resid;
+    }
+}
+
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+inline SubType& interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::erase(const segment_type& minuend)
+{
+    interval_type inter_val = minuend.first;
+    if(icl::is_empty(inter_val)) 
+        return *that();
+
+    const codomain_type& co_val = minuend.second;
+    if(on_codomain_absorbtion::is_absorbable(co_val))
+        return *that();
+
+    std::pair<iterator,iterator> exterior = equal_range(inter_val);
+    if(exterior.first == exterior.second)
+        return *that();
+
+    iterator first_ = exterior.first, end_ = exterior.second, 
+             last_  = cyclic_prior(*this, end_);
+    iterator second_= first_; ++second_;
+
+    if(first_ == last_) 
+    {   //     [----inter_val----)
+        //   .....first_==last_.....
+        // only for the last there can be a right_resid: a part of *it_ right of minuend
+        interval_type right_resid = left_subtract((*first_).first, inter_val);
+
+        if((*first_).second == co_val)
+        {   
+            interval_type left_resid = right_subtract((*first_).first, inter_val);
+            if(!icl::is_empty(left_resid)) //            [----inter_val----)
+            {                              // [left_resid)..first_==last_......
+                const_cast<interval_type&>((*first_).first) = left_resid;
+                if(!icl::is_empty(right_resid))
+                    this->_map.insert(first_, value_type(right_resid, co_val));
+            }
+            else if(!icl::is_empty(right_resid))
+                const_cast<interval_type&>((*first_).first) = right_resid;
+            else
+                this->_map.erase(first_);
+        }
+    }
+    else
+    {
+        // first AND NOT last
+        if((*first_).second == co_val)
+        {
+            interval_type left_resid = right_subtract((*first_).first, inter_val);
+            if(icl::is_empty(left_resid))
+                this->_map.erase(first_);
+            else
+                const_cast<interval_type&>((*first_).first) = left_resid;
+        }
+
+        erase_rest(inter_val, co_val, second_, last_);
+    }
+
+     return *that();
+}
+
+//==============================================================================
+//= Erasure key_type
+//==============================================================================
+template <class SubType, class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc>
+inline SubType& interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc>
+    ::erase(const interval_type& minuend)
+{
+    if(icl::is_empty(minuend)) 
+        return *that();
+
+    std::pair<iterator, iterator> exterior = equal_range(minuend);
+    if(exterior.first == exterior.second)
+        return *that();
+
+    iterator first_ = exterior.first,
+             end_   = exterior.second,
+             last_  = prior(end_);
+
+    interval_type left_resid  = right_subtract((*first_).first, minuend);
+    interval_type right_resid =  left_subtract(last_ ->first, minuend);
+
+    if(first_ == last_ )
+        if(!icl::is_empty(left_resid))
+        {
+            const_cast<interval_type&>((*first_).first) = left_resid;
+            if(!icl::is_empty(right_resid))
+                this->_map.insert(first_, value_type(right_resid, (*first_).second));
+        }
+        else if(!icl::is_empty(right_resid))
+            const_cast<interval_type&>((*first_).first) = left_subtract((*first_).first, minuend);
+        else
+            this->_map.erase(first_);
+    else
+    {   //            [-------- minuend ---------)
+        // [left_resid   fst)   . . . .    [lst  right_resid)
+        iterator second_= first_; ++second_;
+
+        iterator start_ = icl::is_empty(left_resid)? first_: second_;
+        iterator stop_  = icl::is_empty(right_resid)? end_  : last_ ;
+        this->_map.erase(start_, stop_); //erase [start_, stop_)
+
+        if(!icl::is_empty(left_resid))
+            const_cast<interval_type&>((*first_).first) = left_resid;
+
+        if(!icl::is_empty(right_resid))
+            const_cast<interval_type&>(last_ ->first) = right_resid;
+    }
+
+    return *that();
+}
+
+//-----------------------------------------------------------------------------
+// type traits
+//-----------------------------------------------------------------------------
+template 
+<
+    class SubType,
+    class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE)  Interval, ICL_ALLOC Alloc
+>
+struct is_map<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> >
+{ 
+    typedef is_map<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> > type;
+    BOOST_STATIC_CONSTANT(bool, value = true); 
+};
+
+template 
+<
+    class SubType,
+    class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE)  Interval, ICL_ALLOC Alloc
+>
+struct has_inverse<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> >
+{ 
+    typedef has_inverse<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> > type;
+    BOOST_STATIC_CONSTANT(bool, value = (has_inverse<CodomainT>::value)); 
+};
+
+template 
+<
+    class SubType,
+    class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE)  Interval, ICL_ALLOC Alloc
+>
+struct is_interval_container<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> >
+{ 
+    typedef is_interval_container<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> > type;
+    BOOST_STATIC_CONSTANT(bool, value = true); 
+};
+
+template 
+<
+    class SubType,
+    class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE)  Interval, ICL_ALLOC Alloc
+>
+struct absorbs_identities<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> >
+{
+    typedef absorbs_identities<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> > type;
+    BOOST_STATIC_CONSTANT(bool, value = (Traits::absorbs_identities)); 
+};
+
+template 
+<
+    class SubType,
+    class DomainT, class CodomainT, class Traits, ICL_COMPARE Compare, ICL_COMBINE Combine, ICL_SECTION Section, ICL_INTERVAL(ICL_COMPARE) Interval, ICL_ALLOC Alloc
+>
+struct is_total<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> >
+{
+    typedef is_total<icl::interval_base_map<SubType,DomainT,CodomainT,Traits,Compare,Combine,Section,Interval,Alloc> > type;
+    BOOST_STATIC_CONSTANT(bool, value = (Traits::is_total)); 
+};
+
+
+
+}} // namespace icl boost
+
+#endif
+
+