[Boost-commit] svn:boost r7034

From: huseyinakcan_at_[hidden]
Date: 2007-06-13 16:47:14

Author: huseyinakcan
Date: 2007-06-13 16:47:14 EDT (Wed, 13 Jun 2007)
New Revision: 7034
URL: http://svn.boost.org/trac/boost/changeset/7034

Log:
*_list_hds_concept concept definitions and classes added.

Added:
   sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/facet_list_hds_concept.hpp
   sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/halfedge_list_hds_concept.hpp
   sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/vertex_list_hds_concept.hpp
Text files modified: 
   sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts.hpp |    25 +++++++++++++------------               
   1 files changed, 13 insertions(+), 12 deletions(-)

Modified: sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts.hpp
==============================================================================
--- sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts.hpp	(original)
+++ sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts.hpp	2007-06-13 16:47:14 EDT (Wed, 13 Jun 2007)
@@ -1,18 +1,18 @@
+//hds_concepts.hpp   -*- C++ -*-
+//
+//@PURPOSE: Provides concept checking classes for HDS-related concepts.
+//
+///HDS Introduction
+///----------------
+// FILLME
+//
+///HDS Concepts
+///------------
+// FILLME
+
 #ifndef HDSTL_HDS_CONCEPTS_HPP
 #define HDSTL_HDS_CONCEPTS_HPP
 
-/**
- * @file hds_concepts.hpp
- *
- * @brief This file provides a number of concept checking classes for
- * HDS-related concepts.
- *
- * @par HDS Introduction
- * FILLME
- *
- * @par HDS Concepts
- * FILLME
- */
 #include <hds_concepts/hds_concept.hpp>
 #include <hds_concepts/forward_hds_concept.hpp>
 #include <hds_concepts/backward_hds_concept.hpp>
@@ -20,4 +20,5 @@
 #include <hds_concepts/vertex_hds_concept.hpp>
 #include <hds_concepts/facet_hds_concept.hpp>
 #include <hds_concepts/mutable_hds_concept.hpp>
+
 #endif

Added: sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/facet_list_hds_concept.hpp
==============================================================================
--- (empty file)
+++ sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/facet_list_hds_concept.hpp	2007-06-13 16:47:14 EDT (Wed, 13 Jun 2007)
@@ -0,0 +1,191 @@
+//facet_list_hds_concept.hpp    -*- C++ -*- 
+//
+//@PURPOSE: Provide 'FacetListHDS' concept definition, and concept checking class.
+//
+//@DESCRIPTION: This file provides a single class template that,
+// when used with the following concept-checking utilities:
+//..
+//  boost::function_requires<FacetListHDSConcept<HDS> >();
+//..
+// inside a function body, or
+//..
+//  BOOST_CLASS_REQUIRE(HDS, boost::hdstl,FacetListHDSConcept);
+//..
+// inside a class body, checks whether the type given as template
+// argument is a model of the HDS concept described on the page 
+// [facetlisthds].
+//
+//@CONCEPT: [facetlisthds] Facet List HDS concept
+//
+///Definition
+///----------
+// This concept refines the 'HDSConcept', and specifies additional accessors
+// to handle facets in the 'HDS' data structure. 
+//
+///Refinement of:
+///--------------
+//  - 'HDSConcept'
+//
+///Notation
+///--------
+//  - 'HDS'  A type that is a model of FacetListHDSConcept
+//  - 'hds'  A non-modifiable instance of HDS
+//  - 'f'    Facet descriptor, of type 'hds_traits<HDS>::facet_descriptor'
+//  - 'p'    Facet iterator pair, of type 
+//           'std::pair<facet_iterator,facet_iterator>'
+//  - 'F'    Facet size type, of type 'hds_traits<HDS>::facet_size_type'
+//
+///Associated types
+///----------------
+//  - 'hds_traits<HDS>::facet_descriptor': must be 'DefaultConstructible', 
+//    'CopyConstructible', 'EqualityComparable', and 'Assignable'.
+//  - 'hds_traits<HDS>::facet_iterator': must be 'MultiPassInputIterator'.
+//  - 'hds_traits<HDS>::facet_size_type': facet size type.
+//
+///Definitions
+///-----------
+//  - 'facet_descriptor' is a type that contains information to access 
+//     the facet.  (See the 'HDSConcept' for a full definition.)
+//  - 'facet_iterator' is an iterator type for the facets.
+//  - 'facet_size_type' defines the size type.
+//
+///Valid Expressions
+///-----------------
+// In addition to the valid expressions of the 'HDS' concept:
+//  - 'facets(hds)' must return a value assignable to 'p'.  
+//  - '*p.first' must return a value assignable to 'f'.
+//  - 'num_facets(HDS)' must return a value assignable to 'F'.
+//
+///Expression Semantics
+///--------------------
+// In addition to the valid expression semantics of the 'HDS' concept:
+//  - 'facets(hds)' returns a 'facet_iterator' pair 'p', consistent 
+//    with the STL style iterator ranges, which means all the facets
+//    can be accessed by increasing the first part of the pair until the second
+//    part is reached.
+//  - '*p.first' returns a 'facet_descriptor'.
+//  - 'num_facets(HDS)' returns the number of facets in the 'HDS' data
+//    structure.
+//
+///Complexity guarantees
+///---------------------
+//  - 'facets(hds)'    : amortized constant time. (for just getting the 
+//    'facet_iterator' pair, accessing the facets takes linear time.)
+//  - '*p.first'       : amortized constant time.
+//  - 'num_facets(HDS)': amortized constant time.
+//
+///Invariants 
+///----------
+// 'FacetListHDSConcept' should validate all the invariants for the 
+// 'HDSConcept'.
+//
+///Concept-checking class
+///----------------------
+//..
+// template <class HDS> 
+// struct FacetListHDSConcept {
+//     typedef typename hds_traits<HDS>::facet_iterator  facet_iterator;
+//     typedef typename hds_traits<HDS>::facet_descriptor facet_descriptor;
+//     typedef typename hds_traits<HDS>::facets_size_type facets_size_type;
+//     void constraints() 
+//     {
+//         using namespace boost;
+//         function_requires<HDSConcept>();
+//         function_requires<DefaultConstructibleConcept<facet_descriptor> >();
+//         function_requires<CopyConstructibleConcept<facet_descriptor> >();
+//         function_requires<EqualityComparableConcept<facet_descriptor> >();
+//         function_requires<AssignableConcept<facet_descriptor> >();
+//         function_requires<hdstl_detail::MultiPassInputIteratorConcept<facet_iterator> >();
+//         p = facets(hds);
+//         f = *p.first;
+//         F = num_facets(hds);
+//         const_constraints(hds);
+//     }
+//     void const_constraints(HDS const& hds) 
+//     {
+//         p = facets(hds);
+//         f = *p.first;
+//         F = num_facets(hds);
+//     }
+//     private:
+//     FacetListHDS hds;   
+//     facet_descriptor f;
+//     std::pair<facet_iterator,facet_iterator> p;
+//     facet_size_type F; 
+
+// };
+//..
+
+#ifdef BOOST_HDSTL_CONCEPTS_FACETLISTHDSCONCEPT_HPP
+#define BOOST_HDSTL_CONCEPTS_FACETLISTHDSCONCEPT_HPP 1
+
+#include <boost/concepts.h>
+
+namespace hdstl{
+namespace concepts {
+
+   template <class HDS> 
+   struct FacetListHDSConcept {
+       // This class provides a concept checking class for the 
+       // 'FacetListHDSConcept', i.e., using the statement
+       //..
+       //  boost::function_requires<FacetListHDSConcept<HDS>()
+       //..
+       // inside a function body, or
+       //..
+       //  BOOST_CLASS_REQUIRE(HDS, boost::hdstl, FacetListHDSConcept);
+       //..
+       // inside a class definition body, should trigger a compile-time error
+       // if the type HDS does not model the 'FacetListHDSConcept'.
+
+       // TYPES
+       typedef typename hds_traits<HDS>::facet_iterator  facet_iterator;
+       typedef typename hds_traits<HDS>::facet_descriptor facet_descriptor;
+       typedef typename hds_traits<HDS>::facets_size_type facets_size_type;
+       // The specialization of 'hds_traits<HDS>' must have these required
+       // types, obeying the types requirements stated in the detailed
+       // description of the 'FacetListHDS' concept on page 
+       // [facetlisthdsconcept].
+
+       //MANIPULATORS
+       void constraints() 
+           // Check that the 'HDS' template parameters satisfies all the
+           // constraints of 'FacetListHDSConcept' on page 
+           // [facetlisthdsconcept].
+       {
+           using namespace boost;
+           function_requires<HDSConcept>();
+           function_requires<DefaultConstructibleConcept<facet_descriptor> >();
+           function_requires<CopyConstructibleConcept<facet_descriptor> >();
+           function_requires<EqualityComparableConcept<facet_descriptor> >();
+           function_requires<AssignableConcept<facet_descriptor> >();
+           function_requires<hdstl_detail::MultiPassInputIteratorConcept<facet_iterator> >();
+           p = facets(hds);
+           f = *p.first;
+           F = num_facets(hds);
+           const_constraints(hds);
+       }
+
+       // ACCESSORS
+       void const_constraints(HDS const& hds) 
+           // Check that the non-modifiable 'HDS' template parameters
+           // satisfies all the constraints of 'FacetListHDSConcept'.
+       {
+           p = facets(hds);
+           f = *p.first;
+           F = num_facets(hds);
+       }
+
+       private:
+       //DATA
+       FacetListHDS hds;     // a halfedge data structure object
+       facet_descriptor f;   // a facet descriptor
+       std::pair<facet_iterator,facet_iterator> p; // a facet iterator pair
+       facet_size_type F;    // facet size type
+
+   };
+
+}  // close namespace concepts
+}  // close namespace hdstl
+
+#endif

Added: sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/halfedge_list_hds_concept.hpp
==============================================================================
--- (empty file)
+++ sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/halfedge_list_hds_concept.hpp	2007-06-13 16:47:14 EDT (Wed, 13 Jun 2007)
@@ -0,0 +1,191 @@
+//halfedge_list_hds_concept.hpp    -*- C++ -*- 
+//
+//@PURPOSE: Provide 'HalfedgeListHDS' concept definition, and concept checking class.
+//
+//@DESCRIPTION: This file provides a single class template that,
+// when used with the following concept-checking utilities:
+//..
+//  boost::function_requires<HalfedgeListHDSConcept<HDS> >();
+//..
+// inside a function body, or
+//..
+//  BOOST_CLASS_REQUIRE(HDS, boost::hdstl,HalfedgeListHDSConcept);
+//..
+// inside a class body, checks whether the type given as template
+// argument is a model of the HDS concept described on the page 
+// [halfedgelisthds].
+//
+//@CONCEPT: [halfedgelisthds] Halfedge List HDS concept
+//
+///Definition
+///----------
+// This concept refines the 'HDSConcept', and specifies additional accessors
+// to handle halfedges in the 'HDS' data structure. 
+//
+///Refinement of:
+///--------------
+//  - 'HDSConcept'
+//
+///Notation
+///--------
+//  - 'HDS'  A type that is a model of HalfedgeListHDSConcept
+//  - 'hds'  A non-modifiable instance of HDS
+//  - 'h'    Halfedge descriptor, of type 'hds_traits<HDS>::halfedge_descriptor'
+//  - 'p'    Halfedge iterator pair, of type 
+//           'std::pair<halfedge_iterator,halfedge_iterator>'
+//  - 'H'    Halfedge size type, of type 'hds_traits<HDS>::halfedge_size_type'
+//
+///Associated types
+///----------------
+//  - 'hds_traits<HDS>::halfedge_descriptor': must be 'DefaultConstructible', 
+//    'CopyConstructible', 'EqualityComparable', and 'Assignable'.
+//  - 'hds_traits<HDS>::halfedge_iterator': must be 'MultiPassInputIterator'.
+//  - 'hds_traits<HDS>::halfedge_size_type': halfedge size type.
+//
+///Definitions
+///-----------
+//  - 'halfedge_descriptor' is a type that contains information to access 
+//     the halfedge.  (See the 'HDSConcept' for a full definition.)
+//  - 'halfedge_iterator' is an iterator type for the halfedges.
+//  - 'halfedge_size_type' defines the size type.
+//
+///Valid Expressions
+///-----------------
+// In addition to the valid expressions of the 'HDS' concept:
+//  - 'halfedges(hds)' must return a value assignable to 'p'.  
+//  - '*p.first' must return a value assignable to 'h'.
+//  - 'num_halfedges(HDS)' must return a value assignable to 'H'.
+//
+///Expression Semantics
+///--------------------
+// In addition to the valid expression semantics of the 'HDS' concept:
+//  - 'halfedges(hds)' returns a 'halfedge_iterator' pair 'p', consistent 
+//    with the STL style iterator ranges, which means all the halfedges
+//    can be accessed by increasing the first part of the pair until the second
+//    part is reached.
+//  - '*p.first' returns a 'halfedge_descriptor'.
+//  - 'num_halfedges(HDS)' returns the number of halfedges in the 'HDS' data
+//    structure.
+//
+///Complexity guarantees
+///---------------------
+//  - 'halfedges(hds)'    : amortized constant time. (for just getting the 
+//    'halfedge_iterator' pair, accessing the halfedges takes linear time.)
+//  - '*p.first'          : amortized constant time.
+//  - 'num_halfedges(HDS)': amortized constant time.
+//
+///Invariants 
+///----------
+// 'HalfedgeListHDSConcept' should validate all the invariants for the 
+// 'HDSConcept'.
+//
+///Concept-checking class
+///----------------------
+//..
+// template <class HDS> 
+// struct HalfedgeListHDSConcept {
+//    typedef typename hds_traits<HDS>::halfedge_iterator  halfedge_iterator;
+//    typedef typename hds_traits<HDS>::halfedge_descriptor halfedge_descriptor;
+//    typedef typename hds_traits<HDS>::halfedges_size_type halfedges_size_type;
+//     void constraints() 
+//     {
+//         using namespace boost;
+//         function_requires<HDSConcept>();
+//         function_requires<DefaultConstructibleConcept<halfedge_descriptor> >();
+//         function_requires<CopyConstructibleConcept<halfedge_descriptor> >();
+//         function_requires<EqualityComparableConcept<halfedge_descriptor> >();
+//         function_requires<AssignableConcept<halfedge_descriptor> >();
+//         function_requires<hdstl_detail::MultiPassInputIteratorConcept<halfedge_iterator> >();
+//         p = halfedges(hds);
+//         h = *p.first;
+//         H = num_halfedges(hds);
+//         const_constraints(hds);
+//     }
+//     void const_constraints(HDS const& hds) 
+//     {
+//         p = halfedges(hds);
+//         h = *p.first;
+//         H = num_halfedges(hds);
+//     }
+
+//     private:
+//     HalfedgeListHDS hds;
+//     halfedge_descriptor h;
+//     std::pair<halfedge_iterator,halfedge_iterator> p;
+//     halfedge_size_type H;
+// };
+//..
+
+#ifdef BOOST_HDSTL_CONCEPTS_HALFEDGELISTHDSCONCEPT_HPP
+#define BOOST_HDSTL_CONCEPTS_HALFEDGELISTHDSCONCEPT_HPP 1
+
+#include <boost/concepts.h>
+
+namespace hdstl{
+namespace concepts {
+
+   template <class HDS> 
+   struct HalfedgeListHDSConcept {
+       // This class provides a concept checking class for the 
+       // 'HalfedgeListHDSConcept', i.e., using the statement
+       //..
+       //  boost::function_requires<HalfedgeListHDSConcept<HDS>()
+       //..
+       // inside a function body, or
+       //..
+       //  BOOST_CLASS_REQUIRE(HDS, boost::hdstl, HalfedgeListHDSConcept);
+       //..
+       // inside a class definition body, should trigger a compile-time error
+       // if the type HDS does not model the 'HalfedgeListHDSConcept'.
+
+       // TYPES
+       typedef typename hds_traits<HDS>::halfedge_iterator  halfedge_iterator;
+       typedef typename hds_traits<HDS>::halfedge_descriptor halfedge_descriptor;
+       typedef typename hds_traits<HDS>::halfedges_size_type halfedges_size_type;
+       // The specialization of 'hds_traits<HDS>' must have these required
+       // types, obeying the types requirements stated in the detailed
+       // description of the 'HalfedgeListHDS' concept on page 
+       // [halfedgelisthdsconcept].
+
+       //MANIPULATORS
+       void constraints() 
+           // Check that the 'HDS' template parameters satisfies all the
+           // constraints of 'HalfedgeListHDSConcept' on page 
+           // [halfedgelisthdsconcept].
+       {
+           using namespace boost;
+           function_requires<HDSConcept>();
+           function_requires<DefaultConstructibleConcept<halfedge_descriptor> >();
+           function_requires<CopyConstructibleConcept<halfedge_descriptor> >();
+           function_requires<EqualityComparableConcept<halfedge_descriptor> >();
+           function_requires<AssignableConcept<halfedge_descriptor> >();
+           function_requires<hdstl_detail::MultiPassInputIteratorConcept<halfedge_iterator> >();
+           p = halfedges(hds);
+           h = *p.first;
+           H = num_halfedges(hds);
+           const_constraints(hds);
+       }
+
+       // ACCESSORS
+       void const_constraints(HDS const& hds) 
+           // Check that the non-modifiable 'HDS' template parameters
+           // satisfies all the constraints of 'HalfedgeListHDSConcept'.
+       {
+           p = halfedges(hds);
+           h = *p.first;
+           H = num_halfedges(hds);
+       }
+
+       private:
+       //DATA
+       HalfedgeListHDS hds;         // a halfedge data structure object
+       halfedge_descriptor h;   // a halfedge descriptor
+       std::pair<halfedge_iterator,halfedge_iterator> p; // a halfedge iterator pair
+       halfedge_size_type H; // halfedge size type
+
+   };
+
+}  // close namespace concepts
+}  // close namespace hdstl
+
+#endif

Added: sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/vertex_list_hds_concept.hpp
==============================================================================
--- (empty file)
+++ sandbox/SOC/2007/geometry/libs/hdstl/dev/hds_concepts/vertex_list_hds_concept.hpp	2007-06-13 16:47:14 EDT (Wed, 13 Jun 2007)
@@ -0,0 +1,190 @@
+//vertex_list_hds_concept.hpp    -*- C++ -*- 
+//
+//@PURPOSE: Provide 'VertexListHDS' concept definition, and concept checking class.
+//
+//@DESCRIPTION: This file provides a single class template that,
+// when used with the following concept-checking utilities:
+//..
+//  boost::function_requires<VertexListHDSConcept<HDS> >();
+//..
+// inside a function body, or
+//..
+//  BOOST_CLASS_REQUIRE(HDS, boost::hdstl,VertexListHDSConcept);
+//..
+// inside a class body, checks whether the type given as template
+// argument is a model of the HDS concept described on the page 
+// [vertexlisthds].
+//
+//@CONCEPT: [vertexlisthds] Vertex List HDS concept
+//
+///Definition
+///----------
+// This concept refines the 'HDSConcept', and specifies additional accessors
+// to handle vertices in the 'HDS' data structure. 
+//
+///Refinement of:
+///--------------
+//  - 'HDSConcept'
+//
+///Notation
+///--------
+//  - 'HDS'  A type that is a model of VertexListHDSConcept
+//  - 'hds'  A non-modifiable instance of HDS
+//  - 'v'    Vertex descriptor, of type 'hds_traits<HDS>::vertex_descriptor'
+//  - 'p'    Vertex iterator pair, of type 
+//           'std::pair<vertex_iterator,vertex_iterator>'
+//  - 'V'    Vertex size type, of type 'hds_traits<HDS>::vertex_size_type'
+//
+///Associated types
+///----------------
+//  - 'hds_traits<HDS>::vertex_descriptor': must be 'DefaultConstructible', 
+//    'CopyConstructible', 'EqualityComparable', and 'Assignable'.
+//  - 'hds_traits<HDS>::vertex_iterator': must be 'MultiPassInputIterator'.
+//  - 'hds_traits<HDS>::vertex_size_type': vertex size type.
+//
+///Definitions
+///-----------
+//  - 'vertex_descriptor' is a type that contains information to access 
+//     the vertex.  (See the 'HDSConcept' for a full definition.)
+//  - 'vertex_iterator' is an iterator type for the vertices.
+//  - 'vertex_size_type' defines the size type.
+//
+///Valid Expressions
+///-----------------
+// In addition to the valid expressions of the 'HDS' concept:
+//  - 'vertices(hds)' must return a value assignable to 'p'.  
+//  - '*p.first' must return a value assignable to 'v'.
+//  - 'num_vertices(HDS)' must return a value assignable to 'V'.
+//
+///Expression Semantics
+///--------------------
+// In addition to the valid expression semantics of the 'HDS' concept:
+//  - 'vertices(hds)' returns a 'vertex_iterator' pair 'p', consistent 
+//    with the STL style iterator ranges, which means all the vertices
+//    can be accessed by increasing the first part of the pair until the second
+//    part is reached.
+//  - '*p.first' returns a 'vertex_descriptor'.
+//  - 'num_vertices(HDS)' returns the number of vertices in the 'HDS' data
+//    structure.
+//
+///Complexity guarantees
+///---------------------
+//  - 'vertices(hds)'    : amortized constant time. (for just getting the 
+//    'vertex_iterator' pair, accessing the vertices takes linear time.)
+//  - '*p.first'         : amortized constant time.
+//  - 'num_vertices(HDS)': amortized constant time.
+//
+///Invariants 
+///----------
+// 'VertexListHDSConcept' should validate all the invariants for the 
+// 'HDSConcept'.
+//
+///Concept-checking class
+///----------------------
+//..
+// template <class HDS> 
+// struct VertexListHDSConcept {
+//     typedef typename hds_traits<HDS>::vertex_iterator  vertex_iterator;
+//     typedef typename hds_traits<HDS>::vertex_descriptor vertex_descriptor;
+//     typedef typename hds_traits<HDS>::vertices_size_type vertices_size_type;
+//     void constraints() 
+//     {
+//         using namespace boost;
+//         function_requires<HDSConcept>();
+//         function_requires<DefaultConstructibleConcept<vertex_descriptor> >();
+//         function_requires<CopyConstructibleConcept<vertex_descriptor> >();
+//         function_requires<EqualityComparableConcept<vertex_descriptor> >();
+//         function_requires<AssignableConcept<vertex_descriptor> >();
+//         function_requires<hdstl_detail::MultiPassInputIteratorConcept<vertex_iterator> >();
+//         p = vertices(hds);
+//         v = *p.first;
+//         V = num_vertices(hds);
+//         const_constraints(hds);
+//     }
+//     void const_constraints(HDS const& hds) 
+//     {
+//         p = vertices(hds);
+//         v = *p.first;
+//         V = num_vertices(hds);
+//     }
+//     private:
+//     VertexListHDS hds; 
+//     vertex_descriptor v;
+//     std::pair<vertex_iterator,vertex_iterator> p;
+//     vertex_size_type V;  
+// };
+//..
+
+#ifdef BOOST_HDSTL_CONCEPTS_VERTEXLISTHDSCONCEPT_HPP
+#define BOOST_HDSTL_CONCEPTS_VERTEXLISTHDSCONCEPT_HPP 1
+
+#include <boost/concepts.h>
+
+namespace hdstl{
+namespace concepts {
+
+   template <class HDS> 
+   struct VertexListHDSConcept {
+       // This class provides a concept checking class for the 
+       // 'VertexListHDSConcept', i.e., using the statement
+       //..
+       //  boost::function_requires<VertexListHDSConcept<HDS>()
+       //..
+       // inside a function body, or
+       //..
+       //  BOOST_CLASS_REQUIRE(HDS, boost::hdstl, VertexListHDSConcept);
+       //..
+       // inside a class definition body, should trigger a compile-time error
+       // if the type HDS does not model the 'VertexListHDSConcept'.
+
+       // TYPES
+       typedef typename hds_traits<HDS>::vertex_iterator  vertex_iterator;
+       typedef typename hds_traits<HDS>::vertex_descriptor vertex_descriptor;
+       typedef typename hds_traits<HDS>::vertices_size_type vertices_size_type;
+       // The specialization of 'hds_traits<HDS>' must have these required
+       // types, obeying the types requirements stated in the detailed
+       // description of the 'VertexListHDS' concept on page 
+       // [vertexlisthdsconcept].
+
+       //MANIPULATORS
+       void constraints() 
+           // Check that the 'HDS' template parameters satisfies all the
+           // constraints of 'VertexListHDSConcept' on page 
+           // [vertexlisthdsconcept].
+       {
+           using namespace boost;
+           function_requires<HDSConcept>();
+           function_requires<DefaultConstructibleConcept<vertex_descriptor> >();
+           function_requires<CopyConstructibleConcept<vertex_descriptor> >();
+           function_requires<EqualityComparableConcept<vertex_descriptor> >();
+           function_requires<AssignableConcept<vertex_descriptor> >();
+           function_requires<hdstl_detail::MultiPassInputIteratorConcept<vertex_iterator> >();
+           p = vertices(hds);
+           v = *p.first;
+           V = num_vertices(hds);
+           const_constraints(hds);
+       }
+
+       // ACCESSORS
+       void const_constraints(HDS const& hds) 
+           // Check that the non-modifiable 'HDS' template parameters
+           // satisfies all the constraints of 'VertexListHDSConcept'.
+       {
+           p = vertices(hds);
+           v = *p.first;
+           V = num_vertices(hds);
+       }
+
+       private:
+       //DATA
+       VertexListHDS hds;     // a halfedge data structure object
+       vertex_descriptor v;   // a vertex descriptor
+       std::pair<vertex_iterator,vertex_iterator> p; // a vertex iterator pair
+       vertex_size_type V;    // vertex size type
+
+   };
+
+}  // close namespace concepts
+}  // close namespace hdstl
+
+#endif