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[indirectcallable]
# 24 Iterators library [[iterators]](./#iterators)
## 24.3 Iterator requirements [[iterator.requirements]](iterator.requirements#indirectcallable)
### 24.3.6 Indirect callable requirements [indirectcallable]
#### [24.3.6.1](#general) General [[indirectcallable.general]](indirectcallable.general)
[1](#general-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/iterators.tex#L2430)
There are several concepts that group requirements of algorithms that
take callable objects ([[func.def]](func.def "22.10.3 Definitions")) as arguments[.](#general-1.sentence-1)
#### [24.3.6.2](#traits) Indirect callable traits [[indirectcallable.traits]](indirectcallable.traits)
[1](#traits-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/iterators.tex#L2436)
To implement algorithms taking projections,
it is necessary to determine the projected type of an iterator's value type[.](#traits-1.sentence-1)
For the exposition-only alias template *indirect-value-t*,*indirect-value-t*<T> denotes
- [(1.1)](#traits-1.1)
invoke_result_t<Proj&, *indirect-value-t*<I>> if T names projected<I, Proj>, and
- [(1.2)](#traits-1.2)
iter_value_t<T>& otherwise[.](#traits-1.sentence-2)
#### [24.3.6.3](#indirectinvocable) Indirect callables [[indirectcallable.indirectinvocable]](indirectcallable.indirectinvocable)
[1](#indirectinvocable-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/iterators.tex#L2451)
The indirect callable concepts are used to constrain those algorithms
that accept callable objects ([[func.def]](func.def "22.10.3 Definitions")) as arguments[.](#indirectinvocable-1.sentence-1)
namespace std {template<class F, class I>concept [indirectly_unary_invocable](#concept:indirectly_unary_invocable "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]") =[indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I> &&[copy_constructible](concept.copyconstructible#concept:copy_constructible "18.4.14 Concept copy_­constructible [concept.copyconstructible]")<F> &&[invocable](concept.invocable#concept:invocable "18.7.2 Concept invocable [concept.invocable]")<F&, *indirect-value-t*<I>> &&[invocable](concept.invocable#concept:invocable "18.7.2 Concept invocable [concept.invocable]")<F&, iter_reference_t<I>> &&[common_reference_with](concept.commonref#concept:common_reference_with "18.4.5 Concept common_­reference_­with [concept.commonref]")< 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](#concept:indirectly_regular_unary_invocable "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]") =[indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I> &&[copy_constructible](concept.copyconstructible#concept:copy_constructible "18.4.14 Concept copy_­constructible [concept.copyconstructible]")<F> &&[regular_invocable](concept.regularinvocable#concept:regular_invocable "18.7.3 Concept regular_­invocable [concept.regularinvocable]")<F&, *indirect-value-t*<I>> &&[regular_invocable](concept.regularinvocable#concept:regular_invocable "18.7.3 Concept regular_­invocable [concept.regularinvocable]")<F&, iter_reference_t<I>> &&[common_reference_with](concept.commonref#concept:common_reference_with "18.4.5 Concept common_­reference_­with [concept.commonref]")< 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](#concept:indirect_unary_predicate "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]") =[indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I> &&[copy_constructible](concept.copyconstructible#concept:copy_constructible "18.4.14 Concept copy_­constructible [concept.copyconstructible]")<F> &&[predicate](concept.predicate#concept:predicate "18.7.4 Concept predicate [concept.predicate]")<F&, *indirect-value-t*<I>> &&[predicate](concept.predicate#concept:predicate "18.7.4 Concept predicate [concept.predicate]")<F&, iter_reference_t<I>>; template<class F, class I1, class I2>concept [indirect_binary_predicate](#concept:indirect_binary_predicate "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]") =[indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I1> && [indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I2> &&[copy_constructible](concept.copyconstructible#concept:copy_constructible "18.4.14 Concept copy_­constructible [concept.copyconstructible]")<F> &&[predicate](concept.predicate#concept:predicate "18.7.4 Concept predicate [concept.predicate]")<F&, *indirect-value-t*<I1>, *indirect-value-t*<I2>> &&[predicate](concept.predicate#concept:predicate "18.7.4 Concept predicate [concept.predicate]")<F&, *indirect-value-t*<I1>, iter_reference_t<I2>> &&[predicate](concept.predicate#concept:predicate "18.7.4 Concept predicate [concept.predicate]")<F&, iter_reference_t<I1>, *indirect-value-t*<I2>> &&[predicate](concept.predicate#concept:predicate "18.7.4 Concept predicate [concept.predicate]")<F&, iter_reference_t<I1>, iter_reference_t<I2>>; template<class F, class I1, class I2 = I1>concept [indirect_equivalence_relation](#concept:indirect_equivalence_relation "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]") =[indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I1> && [indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I2> &&[copy_constructible](concept.copyconstructible#concept:copy_constructible "18.4.14 Concept copy_­constructible [concept.copyconstructible]")<F> &&[equivalence_relation](concept.equiv#concept:equivalence_relation "18.7.6 Concept equivalence_­relation [concept.equiv]")<F&, *indirect-value-t*<I1>, *indirect-value-t*<I2>> &&[equivalence_relation](concept.equiv#concept:equivalence_relation "18.7.6 Concept equivalence_­relation [concept.equiv]")<F&, *indirect-value-t*<I1>, iter_reference_t<I2>> &&[equivalence_relation](concept.equiv#concept:equivalence_relation "18.7.6 Concept equivalence_­relation [concept.equiv]")<F&, iter_reference_t<I1>, *indirect-value-t*<I2>> &&[equivalence_relation](concept.equiv#concept:equivalence_relation "18.7.6 Concept equivalence_­relation [concept.equiv]")<F&, iter_reference_t<I1>, iter_reference_t<I2>>; template<class F, class I1, class I2 = I1>concept [indirect_strict_weak_order](#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]") =[indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I1> && [indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]")<I2> &&[copy_constructible](concept.copyconstructible#concept:copy_constructible "18.4.14 Concept copy_­constructible [concept.copyconstructible]")<F> &&[strict_weak_order](concept.strictweakorder#concept:strict_weak_order "18.7.7 Concept strict_­weak_­order [concept.strictweakorder]")<F&, *indirect-value-t*<I1>, *indirect-value-t*<I2>> &&[strict_weak_order](concept.strictweakorder#concept:strict_weak_order "18.7.7 Concept strict_­weak_­order [concept.strictweakorder]")<F&, *indirect-value-t*<I1>, iter_reference_t<I2>> &&[strict_weak_order](concept.strictweakorder#concept:strict_weak_order "18.7.7 Concept strict_­weak_­order [concept.strictweakorder]")<F&, iter_reference_t<I1>, *indirect-value-t*<I2>> &&[strict_weak_order](concept.strictweakorder#concept:strict_weak_order "18.7.7 Concept strict_­weak_­order [concept.strictweakorder]")<F&, iter_reference_t<I1>, iter_reference_t<I2>>;}
#### [24.3.6.4](#projected) Alias template projected [[projected]](projected)
[1](#projected-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/iterators.tex#L2515)
Alias template projected is used to constrain algorithms
that accept callable objects and projections ([[defns.projection]](defns.projection "3.44 projection"))[.](#projected-1.sentence-1)
It combines an [indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]") type I and
a callable object type Proj into a new [indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]") type
whose reference type is the result of applyingProj to the iter_reference_t of I[.](#projected-1.sentence-2)
[🔗](#lib:projected)
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](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") indirect_result_t<Proj&, I> operator*() const; // *not defined*}; }; template<[indirectly_readable](iterator.concept.readable#concept:indirectly_readable "24.3.4.2 Concept indirectly_­readable [iterator.concept.readable]") I, [indirectly_regular_unary_invocable](#concept:indirectly_regular_unary_invocable "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<I> Proj>using projected = *projected-impl*<I, Proj>::*type*;}