Vert patterns

docs/archive/descriptor.md

@@ -110,25 +110,25 @@ Edges in the graph can be stored in various ways depending on graph structure:
 - MUST be a template with a single parameter for the underlying container's iterator type
 - Iterator category constraints:
   - **Random Access Iterator** (e.g., vector, deque): Used for index-based vertex storage
-  - **Bidirectional Iterator** (e.g., map, unordered_map): Used for key-value based vertex storage
-    - When bidirectional: the iterator's `value_type` MUST satisfy a pair-like concept where:
+  - **Forward Iterator** (e.g., map, unordered_map, unordered_set): Used for key-value based vertex storage
+    - When forward (non-random-access): the iterator's `value_type` MUST satisfy a pair-like concept where:
       - The type MUST have at least 2 members (accessible via tuple protocol or pair interface)
       - The first element serves as the vertex ID (key)
       - This can be checked using `std::tuple_size<value_type>::value >= 2` or by requiring `.first` and `.second` members
 - MUST have a single member variable that:
   - MUST be `size_t index` when the iterator is a random access iterator
-  - MUST be the iterator type itself when the iterator is a bidirectional iterator (non-random access)
+  - MUST be the iterator type itself when the iterator is a forward iterator (non-random access)
 - MUST provide a `vertex_id()` member function that returns the vertex's unique identifier:
   - When the vertex iterator is random access: MUST return the `size_t` member value (the index)
-  - When the vertex iterator is bidirectional: MUST return the key (first element) from the pair-like `value_type`
+  - When the vertex iterator is forward (non-random-access): MUST return the key (first element) from the pair-like `value_type`
   - Return type SHOULD be deduced appropriately based on iterator category
 - MUST provide a public `value()` member function that returns the underlying storage handle:
   - When the vertex iterator is random access: `value()` MUST return the stored `size_t` index
-  - When the vertex iterator is bidirectional: `value()` MUST return the stored iterator
+  - When the vertex iterator is forward (non-random-access): `value()` MUST return the stored iterator
   - Return type SHOULD be the exact type of the underlying member (copy by value)
 - MUST provide pre-increment and post-increment operators (`operator++` / `operator++(int)`) whose behavior mirrors the underlying storage:
   - For random access iterators: increment operations MUST advance the `size_t` index by one
-  - For bidirectional iterators: increment operations MUST advance the stored iterator
+  - For forward iterators: increment operations MUST advance the stored iterator
 - MUST be efficiently passable by value
 - SHOULD support conversion to/from underlying index type (for random access case)
 - MUST integrate with std::hash for unordered containers

docs/reference/concepts.md

@@ -285,7 +285,7 @@ for full documentation.
 | Concept | Purpose |
 |---------|---------|
 | `direct_vertex_type<Iter>` | Random-access, index-based vertex |
-| `keyed_vertex_type<Iter>` | Bidirectional, key-based vertex |
+| `keyed_vertex_type<Iter>` | Forward, key-based vertex |
 | `vertex_iterator<Iter>` | Either direct or keyed |
 | `random_access_vertex_pattern<Iter>` | Inner value: return whole element |
 | `pair_value_vertex_pattern<Iter>` | Inner value: return `.second` |

docs/reference/vertex-patterns.md

@@ -8,7 +8,7 @@
 > This page documents two complementary concept families for vertex types:
 **inner value patterns** (how vertex data is accessed) and
 **storage patterns** (how vertex IDs are stored/extracted). Both families live
-in `graph::adj_list::detail` and are re-exported via `<graph/graph.hpp>`.
+in `graph::adj_list` and are re-exported via `<graph/graph.hpp>`.
 
 </td>
 </tr></table>
@@ -17,6 +17,25 @@ in `graph::adj_list::detail` and are re-exported via `<graph/graph.hpp>`.
 
 ---
 
+## Foundation Concepts
+
+These building-block concepts determine whether a type is "pair-like" and
+are used internally by both the inner value and storage pattern concepts.
+
+| Concept | Definition |
+|---------|------------|
+| `pair_like<T>` | Has `std::tuple_size<T>::value >= 2` and supports `std::get<0>`, `std::get<1>` (tuple protocol) |
+| `has_first_second<T>` | Has `.first` and `.second` members |
+| `pair_like_value<T>` | `pair_like<T> \|\| has_first_second<T>` — disjunction of both |
+
+```cpp
+// Used to constrain keyed_vertex_type, pair_value_vertex_pattern, etc.
+template <typename T>
+concept pair_like_value = pair_like<T> || has_first_second<T>;
+```
+
+---
+
 ## Inner Value Patterns
 
 The `inner_value()` method on a vertex descriptor returns the vertex data
@@ -33,8 +52,8 @@ container type.
 | Concept | Iterator Requirements | `inner_value()` Returns | Typical Containers |
 |---------|----------------------|------------------------|--------------------|
 | `random_access_vertex_pattern<Iter>` | Random-access iterator | `container[index]` — the whole element | `std::vector`, `std::deque` |
-| `pair_value_vertex_pattern<Iter>` | Bidirectional, pair-like value type | `.second` — the mapped value | `std::map`, `std::unordered_map` |
-| `whole_value_vertex_pattern<Iter>` | Bidirectional, non-pair value type | `*iter` — the whole dereferenced value | Custom bidirectional containers |
+| `pair_value_vertex_pattern<Iter>` | Forward, pair-like value type | `.second` — the mapped value | `std::map`, `std::unordered_map` |
+| `whole_value_vertex_pattern<Iter>` | Forward, non-pair value type | `*iter` — the whole dereferenced value | Custom forward containers |
 
 ```cpp
 // Disjunction of all three
@@ -104,7 +123,7 @@ stored and extracted:
 | Concept | Iterator Requirements | Vertex ID Type | Access Pattern |
 |---------|----------------------|---------------|----------------|
 | `direct_vertex_type<Iter>` | Random-access | `std::size_t` (the index) | `container[index]` |
-| `keyed_vertex_type<Iter>` | Bidirectional, pair-like value | Key type (`.first`) | `(*iter).first` for ID, `.second` for data |
+| `keyed_vertex_type<Iter>` | Forward, pair-like value | Key type (`.first`) | `(*iter).first` for ID, `.second` for data |
 
 ```cpp
 // Disjunction
@@ -123,8 +142,10 @@ matches exactly one.
 | `vertex_storage_pattern<Iter>` | Struct with `::is_direct`, `::is_keyed` booleans |
 | `vertex_storage_pattern_v<Iter>` | Variable template shortcut |
 | `vertex_pattern` (enum) | `direct`, `keyed` |
+| `vertex_pattern_type<Iter>` | Struct with `::value` of type `vertex_pattern` |
 | `vertex_pattern_type_v<Iter>` | Variable template returning the enum value |
-| `vertex_id_type_t<Iter>` | Extracts the vertex ID type: `size_t` for direct, key type for keyed |
+| `vertex_id_type<Iter>` | Struct with `::type` alias; specializations for direct (`.first`/`.second`) and keyed (tuple protocol) |
+| `vertex_id_type_t<Iter>` | Alias for `vertex_id_type<Iter>::type`: `size_t` for direct, key type for keyed |
 
 ### Examples
 
@@ -146,11 +167,11 @@ static_assert(std::same_as<vertex_id_type_t<MapIter>, std::string>);
 The `vertex_id()` function in `vertex_descriptor` dispatches at compile time:
 
 ```cpp
-constexpr auto vertex_id() const noexcept {
+constexpr decltype(auto) vertex_id() const noexcept {
     if constexpr (std::random_access_iterator<VertexIter>) {
         return storage_;  // direct: return index (size_t)
     } else {
-        return std::get<0>(*storage_);  // keyed: extract key
+        return std::get<0>(*storage_);  // keyed: return const& to key
     }
 }
 ```
@@ -172,6 +193,98 @@ Both families work together to give `vertex_descriptor` complete type safety:
 
 ---
 
+## `vertex_descriptor<VertexIter>` Class Reference
+
+Defined in `<graph/adj_list/vertex_descriptor.hpp>`.
+A lightweight, type-safe handle to a vertex stored in a container.
+Constrained by `vertex_iterator<VertexIter>`.
+
+### Type Aliases
+
+| Alias | Definition |
+|-------|------------|
+| `iterator_type` | `VertexIter` |
+| `value_type` | `typename std::iterator_traits<VertexIter>::value_type` |
+| `storage_type` | `std::size_t` for random-access iterators, `VertexIter` otherwise |
+
+### Constructors
+
+| Signature | Notes |
+|-----------|-------|
+| `constexpr vertex_descriptor() noexcept` | Default; requires `std::default_initializable<storage_type>` |
+| `constexpr explicit vertex_descriptor(storage_type val) noexcept` | Construct from index or iterator |
+
+### Member Functions
+
+| Function | Returns | Description |
+|----------|---------|-------------|
+| `value()` | `storage_type` | The raw storage: index (`size_t`) or iterator |
+| `vertex_id()` | `decltype(auto)` | Vertex ID — index by value for direct, `const&` to key for keyed |
+| `underlying_value(Container&)` | `decltype(auto)` | Full container element (`container[i]` or `*iter`); const overload provided |
+| `inner_value(Container&)` | `decltype(auto)` | Vertex data excluding the key (`.second` for maps, whole value for vectors); const overload provided |
+| `operator++()` / `operator++(int)` | `vertex_descriptor&` / `vertex_descriptor` | Pre/post-increment |
+| `operator<=>` / `operator==` | | Defaulted three-way and equality comparison |
+
+### `std::hash` Specialization
+
+A `std::hash<vertex_descriptor<VertexIter>>` specialization is provided,
+hashing the index for direct storage or the `vertex_id()` for keyed storage.
+This enables use in `std::unordered_set` and `std::unordered_map`.
+
+---
+
+## `vertex_descriptor_view<VertexIter>` Class Reference
+
+Defined in `<graph/adj_list/vertex_descriptor_view.hpp>`.
+A forward-only view over vertex storage that synthesizes `vertex_descriptor`
+objects on-the-fly. Inherits from `std::ranges::view_interface`.
+
+### Type Aliases
+
+| Alias | Definition |
+|-------|------------|
+| `vertex_desc` | `vertex_descriptor<VertexIter>` |
+| `storage_type` | `typename vertex_desc::storage_type` |
+
+### Constructors
+
+| Signature | Notes |
+|-----------|-------|
+| `constexpr vertex_descriptor_view() noexcept` | Default |
+| `constexpr vertex_descriptor_view(storage_type begin, storage_type end) noexcept` | From index/iterator range; requires random-access |
+| `constexpr explicit vertex_descriptor_view(Container&) noexcept` | From mutable container; requires `sized_range` or random-access |
+| `constexpr explicit vertex_descriptor_view(const Container&) noexcept` | From const container |
+
+### Member Functions
+
+| Function | Description |
+|----------|-------------|
+| `begin()` / `end()` | Forward iterators yielding `vertex_descriptor` by value |
+| `cbegin()` / `cend()` | Const equivalents |
+| `size()` | O(1) — cached at construction |
+
+### Inner `iterator` Class
+
+| Property | Value |
+|----------|-------|
+| `iterator_category` | `std::forward_iterator_tag` |
+| `value_type` | `vertex_descriptor<VertexIter>` |
+| Dereference | Returns descriptor **by value** (synthesized) |
+
+### Deduction Guides
+
+```cpp
+vertex_descriptor_view(Container&)       -> vertex_descriptor_view<typename Container::iterator>;
+vertex_descriptor_view(const Container&) -> vertex_descriptor_view<typename Container::const_iterator>;
+```
+
+### Range Traits
+
+`std::ranges::enable_borrowed_range` is specialized to `true` — the view
+does not own the underlying data.
+
+---
+
 ## Compile-Time Dispatch Pattern
 
 ```cpp

include/graph/adj_list/descriptor.hpp

@@ -20,7 +20,7 @@ struct in_edge_tag {};
 /**
  * @brief Concept to check if a type is pair-like (has at least 2 members accessible via tuple protocol)
  * 
- * This is used to constrain bidirectional iterator value_types for vertex storage.
+ * This is used to constrain forward iterator value_types for vertex storage.
  */
 template <typename T>
 concept pair_like = requires {
@@ -89,7 +89,7 @@ concept keyed_vertex_type = std::forward_iterator<Iter> && !std::random_access_i
  * 
  * A vertex iterator must be either:
  * - Random access (direct/indexed storage)
- * - Bidirectional with pair-like value_type (keyed storage)
+ * - Forward with pair-like value_type (keyed storage)
  */
 template <typename Iter>
 concept vertex_iterator = direct_vertex_type<Iter> || keyed_vertex_type<Iter>;
@@ -111,25 +111,25 @@ concept random_access_vertex_pattern = std::random_access_iterator<Iter>;
 /**
  * @brief Concept for pair-value vertex pattern (map-like)
  * 
- * Used with bidirectional iterators where the value_type is pair-like.
+ * Used with forward iterators where the value_type is pair-like.
  * inner_value returns the .second part (the data, excluding the key).
  * Pattern: *iterator -> pair{key, data}, inner_value returns data&
- * Example: std::map<int, VertexData> where inner_value returns VertexData& (.second)
+ * Example: std::map<int, VertexData> or std::unordered_map<int, VertexData> where inner_value returns VertexData& (.second)
  */
 template <typename Iter>
-concept pair_value_vertex_pattern = std::bidirectional_iterator<Iter> && !std::random_access_iterator<Iter> &&
+concept pair_value_vertex_pattern = std::forward_iterator<Iter> && !std::random_access_iterator<Iter> &&
                                     pair_like_value<typename std::iterator_traits<Iter>::value_type>;
 
 /**
- * @brief Concept for whole-value vertex pattern (custom bidirectional)
+ * @brief Concept for whole-value vertex pattern (custom forward)
  * 
- * Used with bidirectional iterators where the value_type is NOT pair-like.
+ * Used with forward iterators where the value_type is NOT pair-like.
  * inner_value returns the entire element (same as underlying_value).
  * Pattern: *iterator -> value, inner_value returns value&
- * Example: Custom bidirectional container with non-pair value_type
+ * Example: Custom forward container with non-pair value_type
  */
 template <typename Iter>
-concept whole_value_vertex_pattern = std::bidirectional_iterator<Iter> && !std::random_access_iterator<Iter> &&
+concept whole_value_vertex_pattern = std::forward_iterator<Iter> && !std::random_access_iterator<Iter> &&
                                      !pair_like_value<typename std::iterator_traits<Iter>::value_type>;
 
 /**
@@ -274,6 +274,36 @@ template <typename Iter>
 requires vertex_iterator<Iter>
 using vertex_id_type_t = typename vertex_id_type<Iter>::type;
 
+// =============================================================================
+// Index-Only Vertex Detection
+// =============================================================================
+
+/**
+ * @brief Concept for index-only vertex iterators (no physical container backing)
+ *
+ * An index-only vertex iterator is a random-access iterator whose value_type
+ * is integral AND whose reference type is not an actual reference (i.e., it
+ * returns by value, like iota_view iterators). This distinguishes generated
+ * index sequences from container iterators over integral types (e.g.,
+ * vector<int>::iterator has reference = int&, so it is NOT index-only).
+ *
+ * For these iterators, inner_value() and underlying_value() are not meaningful
+ * because there is no physical container to index into.
+ */
+template <typename Iter>
+concept index_only_vertex = std::random_access_iterator<Iter> &&
+                            std::integral<std::iter_value_t<Iter>> &&
+                            !std::is_reference_v<std::iter_reference_t<Iter>>;
+
+/**
+ * @brief Concept for container-backed vertex iterators
+ *
+ * The inverse of index_only_vertex. These iterators reference elements in
+ * a physical container, so inner_value() and underlying_value() are valid.
+ */
+template <typename Iter>
+concept container_backed_vertex = vertex_iterator<Iter> && !index_only_vertex<Iter>;
+
 // =============================================================================
 // Edge Value Type Concepts for target_id() Extraction
 // =============================================================================

include/graph/adj_list/detail/graph_cpo.hpp

@@ -343,7 +343,7 @@ namespace _cpo_impls {
              * The descriptor default works for standard containers:
              * - Random-access containers (vector, deque): returns the index
              * - Associative containers (map): returns the key
-             * - Bidirectional containers: returns the iterator position
+             * - Forward containers: returns the iterator position
              * 
              * @tparam G Graph type
              * @tparam U Vertex descriptor type (constrained to be a vertex_descriptor_type)
@@ -391,7 +391,7 @@ inline namespace _cpo_instances {
  * The type of the unique identifier returned by vertex_id(g, u), with references stripped.
  * - For random-access containers (vector, deque): size_t (index)
  * - For associative containers (map): key type (e.g. std::string)
- * - For bidirectional containers: iterator-based ID
+ * - For forward containers: iterator-based ID
  */
 template <typename G>
 using vertex_id_t = std::remove_cvref_t<
@@ -3005,7 +3005,7 @@ namespace _cpo_impls {
              * - Uses u.inner_value(g) which returns the actual vertex data
              * - For random-access containers (vector): returns container[index]
              * - For associative containers (map): returns the .second value
-             * - For bidirectional containers: returns the dereferenced value
+             * - For forward containers: returns the dereferenced value
              * 
              * This provides access to user-defined vertex properties/data stored in the graph.
              *