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

24.3.6.2 Indirect callable traits [indirectcallable.traits]

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To implement algorithms taking projections, it is necessary to determine the projected type of an iterator's value type.
For the exposition-only alias template indirect-value-t, indirect-value-t<T> denotes
  • (1.1)
    invoke_result_t<Proj&, indirect-value-t<I>> if T names projected<I, Proj>, and
  • (1.2)
    iter_value_t<T>& otherwise.

24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]

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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 = indirectly_readable<I> && copy_constructible<F> && invocable<F&, indirect-value-t<I>> && invocable<F&, iter_reference_t<I>> && common_reference_with< invoke_result_t<F&, indirect-value-t<I>>, invoke_result_t<F&, iter_reference_t<I>>; template<class F, class I> concept indirectly_regular_unary_invocable = indirectly_readable<I> && copy_constructible<F> && regular_invocable<F&, indirect-value-t<I>> && regular_invocable<F&, iter_reference_t<I>> && common_reference_with< invoke_result_t<F&, indirect-value-t<I>>, invoke_result_t<F&, iter_reference_t<I>>; template<class F, class I> concept indirect_unary_predicate = indirectly_readable<I> && copy_constructible<F> && predicate<F&, indirect-value-t<I>> && predicate<F&, iter_reference_t<I>>; template<class F, class I1, class I2> concept indirect_binary_predicate = indirectly_readable<I1> && indirectly_readable<I2> && copy_constructible<F> && predicate<F&, indirect-value-t<I1>, indirect-value-t<I2>> && predicate<F&, indirect-value-t<I1>, iter_reference_t<I2>> && predicate<F&, iter_reference_t<I1>, indirect-value-t<I2>> && predicate<F&, iter_reference_t<I1>, iter_reference_t<I2>>; template<class F, class I1, class I2 = I1> concept indirect_equivalence_relation = indirectly_readable<I1> && indirectly_readable<I2> && copy_constructible<F> && equivalence_relation<F&, indirect-value-t<I1>, indirect-value-t<I2>> && equivalence_relation<F&, indirect-value-t<I1>, iter_reference_t<I2>> && equivalence_relation<F&, iter_reference_t<I1>, indirect-value-t<I2>> && equivalence_relation<F&, iter_reference_t<I1>, iter_reference_t<I2>>; template<class F, class I1, class I2 = I1> concept indirect_strict_weak_order = indirectly_readable<I1> && indirectly_readable<I2> && copy_constructible<F> && strict_weak_order<F&, indirect-value-t<I1>, indirect-value-t<I2>> && strict_weak_order<F&, indirect-value-t<I1>, iter_reference_t<I2>> && strict_weak_order<F&, iter_reference_t<I1>, indirect-value-t<I2>> && strict_weak_order<F&, iter_reference_t<I1>, iter_reference_t<I2>>; }

24.3.6.4 Alias template projected [projected]

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Alias template projected is used to constrain algorithms that accept callable objects and projections ([defns.projection]).
It combines an indirectly_readable type I and a callable object type Proj into a new indirectly_readable type whose reference type is the result of applying Proj to the iter_reference_t of I.
🔗
namespace std { template<class I, class Proj> struct projected-impl { / exposition only struct type { / exposition only using value_type = remove_cvref_t<indirect_result_t<Proj&, I>>; using difference_type = iter_difference_t<I>; / present only if I / models weakly_incrementable indirect_result_t<Proj&, I> operator*() const; / not defined }; }; template<indirectly_readable I, indirectly_regular_unary_invocable<I> Proj> using projected = projected-impl<I, Proj>::type; }

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