Domain concepts
===============

.. contents:: Table of Contents
    :local:


.. _concept-Domain:

Domain
------

Let `Dom` be a type that models :ref:`Domain (details) <concept-details-Domain>`.

Then `Dom` also models :ref:`Regular (fundamentals) <concept-fundamentals-object-Regular>`.

.. _concept-Domain-types:
.. rubric:: Types

Then we can define :

+--------------------------+-------------------------------------------------+--------------------------------------------------+
|        Definition        |                   Description                   |                   Requirement                    |
+==========================+=================================================+==================================================+
| `Dom::point_type`        | type of a point                                 | models :ref:`concept-Point` concept              |
+--------------------------+-------------------------------------------------+--------------------------------------------------+
| `Dom::const_point_range` | type of the range to iterate over all the point | models :ref:`concept-BidirectionalRange` concept |
+--------------------------+-------------------------------------------------+--------------------------------------------------+
| `Dom::value_type`        | type of a value                                 | - models :ref:`concept-Value` concept            |
|                          |                                                 | - non-const                                      |
|                          |                                                 | - not a reference                                |
+--------------------------+-------------------------------------------------+--------------------------------------------------+

.. _concept-Domain-expressions:
.. rubric:: Expressions

Let : 
    - ``dom`` be an instance of `Dom`.
    - ``dom_cpy`` be an instance of `Dom`.
    - ``cdom`` be an instance of `const Dom`.
    - ``lhs`` be an instance of `const Dom`.
    - ``rhs`` be an instance of `const Dom`.
    - ``p`` be an instance of `Dom::point_type`.

Then we have the following valid expressions :

+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
|        Expression        |     Return type     | Pre-condition | Post-condition |                    Description                     |
+==========================+=====================+===============+================+====================================================+
| ``dom()``                | `Dom`               | none          | none           | Constructs a domain ``dom`` of type `Dom`          |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``cdom()``               | `const Dom`         | none          | none           | Constructs a domain ``cdom`` of type `Dom`         |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``dom_cpy(dom)``         | `Dom`               | none          | none           | Copy-constructs a domain ``dom_cpy`` from ``dom``  |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``dom_cpy(cdom)``        | `Dom`               | none          | none           | Copy-constructs a domain ``dom_cpy`` from ``cdom`` |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``dom_cpy(move(dom))``   | `Dom`               | none          | none           | Move-constructs a domain ``dom_cpy`` from ``dom``  |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``dom_cpy = dom``        | `Dom&`              | none          | none           | Assign ``dom`` to ``dom_cpy``                      |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``dom_cpy = cdom``       | `Dom&`              | none          | none           | Assign ``cdom`` to ``dom_cpy``                     |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``dom_cpy = move(dom)``  | `Dom&`              | none          | none           | Move-assign ``dom`` to ``dom_cpy``                 |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``lhs == rhs``           | `bool`              | none          | none           | Compare wether two domains are equal               |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``lhs != rhs``           | `bool`              | none          | none           | Compare wether two domains are different           |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``rhs == lhs``           | `bool`              | none          | none           | Compare wether two domains are equal               |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``rhs != lhs``           | `bool`              | none          | none           | Compare wether two domains are different           |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``cdom.has(p)``          | `bool`              | none          | none           | Check wether ``p`` belongs to the domain ``cdom``  |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``cdom.empty()``         | `bool`              | none          | none           | Check wether ``cdom`` is an empty domain           |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``cdom.is_continuous()`` | `bool`              | none          | none           | Check wether ``cdom`` is a continuous domain       |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``cdom.is_discrete()``   | `bool`              | none          | none           | Check wether ``cdom`` is a discrete domain         |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+
| ``cdom.points()``        | `const_point_range` | none          | none           | Return a range of points to iterate over it        |
+--------------------------+---------------------+---------------+----------------+----------------------------------------------------+