23 Iterators library [iterators]

23.3 Iterator requirements [iterator.requirements]

23.3.6 Indirect callable requirements [indirectcallable]

23.3.6.1 General [indirectcallable.general]

There are several concepts that group requirements of algorithms that take callable objects ([func.def]) as arguments.

23.3.6.2 Indirect callables [indirectcallable.indirectinvocable]

The indirect callable concepts are used to constrain those algorithms that accept callable objects ([func.def]) as arguments.
namespace std {
  template<class F, class I>
    concept indirectly_unary_invocable =
      readable<I> &&
      copy_constructible<F> &&
      invocable<F&, iter_value_t<I>&> &&
      invocable<F&, iter_reference_t<I>> &&
      invocable<F&, iter_common_reference_t<I>> &&
      common_reference_with<
        invoke_result_t<F&, iter_value_t<I>&>,
        invoke_result_t<F&, iter_reference_t<I>>>;

  template<class F, class I>
    concept indirectly_regular_unary_invocable =
      readable<I> &&
      copy_constructible<F> &&
      regular_invocable<F&, iter_value_t<I>&> &&
      regular_invocable<F&, iter_reference_t<I>> &&
      regular_invocable<F&, iter_common_reference_t<I>> &&
      common_reference_with<
        invoke_result_t<F&, iter_value_t<I>&>,
        invoke_result_t<F&, iter_reference_t<I>>>;

  template<class F, class I>
    concept indirect_unary_predicate =
      readable<I> &&
      copy_constructible<F> &&
      predicate<F&, iter_value_t<I>&> &&
      predicate<F&, iter_reference_t<I>> &&
      predicate<F&, iter_common_reference_t<I>>;

  template<class F, class I1, class I2 = I1>
    concept indirect_relation =
      readable<I1> && readable<I2> &&
      copy_constructible<F> &&
      relation<F&, iter_value_t<I1>&, iter_value_t<I2>&> &&
      relation<F&, iter_value_t<I1>&, iter_reference_t<I2>> &&
      relation<F&, iter_reference_t<I1>, iter_value_t<I2>&> &&
      relation<F&, iter_reference_t<I1>, iter_reference_t<I2>> &&
      relation<F&, iter_common_reference_t<I1>, iter_common_reference_t<I2>>;

  template<class F, class I1, class I2 = I1>
    concept indirect_strict_weak_order =
      readable<I1> && readable<I2> &&
      copy_constructible<F> &&
      strict_weak_order<F&, iter_value_t<I1>&, iter_value_t<I2>&> &&
      strict_weak_order<F&, iter_value_t<I1>&, iter_reference_t<I2>> &&
      strict_weak_order<F&, iter_reference_t<I1>, iter_value_t<I2>&> &&
      strict_weak_order<F&, iter_reference_t<I1>, iter_reference_t<I2>> &&
      strict_weak_order<F&, iter_common_reference_t<I1>, iter_common_reference_t<I2>>;
}

23.3.6.3 Class template projected [projected]

Class template projected is used to constrain algorithms that accept callable objects and projections ([defns.projection]).
It combines a readable type I and a callable object type Proj into a new readable type whose reference type is the result of applying Proj to the iter_­reference_­t of I.
namespace std {
  template<readable I, indirectly_regular_unary_invocable<I> Proj>
  struct projected {
    using value_type = remove_cvref_t<indirect_result_t<Proj&, I>>;
    indirect_result_t<Proj&, I> operator*() const;              // not defined
  };

  template<weakly_incrementable I, class Proj>
  struct incrementable_traits<projected<I, Proj>> {
    using difference_type = iter_difference_t<I>;
  };
}