Domain concepts (details)
=========================

.. contents:: Table of Contents
    :local:


.. _concept-details-Domain:

Domain
------

.. cpp:concept:: template<typename D> Domain

    #. Refines the :cpp:concept:`template <typename T> Regular` concept.
    #. ``Dom::point_type`` models :cpp:concept:`template <typename Pnt> Point` concept.
    #. ``Dom::const_point_range`` models the :cpp:concept:`template <typename BidirRng> BidirectionalRange` concept
    #. ``Dom::codomain_type`` models :cpp:concept:`template <typename Val> Value` concept, is non-const and is not a reference.
    #. ``Dom`` provides methods `has`, `shape`, `empty`, `is_continuous`, `is_discrete` and `points`.

    **Notation**

    .. cpp:type::   Dom
    .. cpp:type::   point_type = Dom::point_type
    .. cpp:type::   const_point_range = Dom::const_point_range
    .. cpp:var::    Dom dom
    .. cpp:var::    Dom dom_cpy
    .. cpp:var::    const Dom cdom
    .. cpp:var::    const Dom lhs
    .. cpp:var::    const Dom rhs
    .. cpp:var::    point_type p

    **Valid Expressions**

    - :cpp:expr:`dom()` returns an instance of :cpp:expr:`Dom`.
    - :cpp:expr:`cdom()` returns an instance of :cpp:expr:`const Dom`.

    - :cpp:expr:`dom_cpy(dom)` returns an instance of :cpp:expr:`Dom`.
    - :cpp:expr:`dom_cpy(cdom)` returns an instance of :cpp:expr:`Dom`.
    - :cpp:expr:`dom_cpy(move(dom))` returns an instance of :cpp:expr:`Dom`.

    - :cpp:expr:`dom_cpy = dom` returns an instance of :cpp:expr:`Dom&`.
    - :cpp:expr:`dom_cpy = cdom` returns an instance of :cpp:expr:`Dom&`.
    - :cpp:expr:`dom_cpy = move(dom)` returns an instance of :cpp:expr:`Dom&`.

    - :cpp:expr:`lhs == rhs` return-type models :cpp:concept:`template <typename B> Boolean`.
    - :cpp:expr:`lhs != rhs` return-type models :cpp:concept:`template <typename B> Boolean`.
    - :cpp:expr:`rhs == lhs` return-type models :cpp:concept:`template <typename B> Boolean`.
    - :cpp:expr:`rhs != lhs` return-type models :cpp:concept:`template <typename B> Boolean`.

    - :cpp:expr:`cdom.has(p)` return-type models :cpp:concept:`template <typename B> Boolean`.
    - :cpp:expr:`cdom.empty()` return-type models :cpp:concept:`template <typename B> Boolean`.
    - :cpp:expr:`cdom.is_continuous()` return-type models :cpp:concept:`template <typename B> Boolean`.
    - :cpp:expr:`cdom.is_discrete()` return-type models :cpp:concept:`template <typename B> Boolean`.
    - :cpp:expr:`cdom.points()` returns :cpp:expr:`const_point_range`.

    **Possible implementation**

    .. code:: cpp

        template<typename D, Dom = remove_cvref<D>>
        concept Domain =    Regular<Dom> &&

                            requires {
                                typename Dom::point_type;
                                typename Dom::const_point_range;
                                typename Dom::codomain_type;
                            } &&

                            Point<Dom::point_type> &&
                            BidirectionalRange<Dom::const_point_range> &&
                            Value<Dom::codomain_type> &&

                            Same<const Dom::point_type, Dom::const_point_range::value_type> &&

                            !is_const_v<Dom::codomain_type> &&
                            !is_reference_v<Dom::codomain_type> &&

                            requires(const Dom cdom, Dom::point_type p) {
                                { cdom.has(p) }             -> bool;
                                { cdom.empty() }            -> bool;
                                { cdom.is_continuous() }    -> bool;
                                { cdom.is_discrete() }      -> bool;
                                { cdom.points() }           -> Dom::const_point_range;
                            };