1 Synopsis

Currently, the Ranges TS uses function-style concepts. That’s because in a few places, concept names
are “overloaded”. Rather than have some variable concepts and some function concepts, the Ranges TS
opted for function concepts everywhere. The has proven unsatisfactory, because it fills function
signatures with useless syntactic noise (e.g., ()).

Also, committee in Kona (2016) expressed concern at there being multiple ways to define a concept.
There seemed interest in eliminating function-style concept definitions. The Ranges TS was given as
an example of where function-style concepts were used. But the Ranges TS does not need them and
would in fact probably be better off without them.

The reasons for dropping function-style concepts from the Ranges TS then are:

1. To eliminate syntactic noise.
2. To eliminate user confusion that comes at a concept’s point-of-use, where sometimes parens are
   needed (in requires clauses) and sometimes not (when the concept is used as a placeholder).
3. To avoid depending on a feature that may get dropped.
4. To avoid becoming a reason to keep a little-loved feature.

There is really only one reason for keeping function-style concepts in the Ranges TS:

1. In several places, the Ranges TS defines concepts with similar semantic meaning but different
   numbers of parameters; function-style concepts neatly captures this intent by allowing these
   concepts to share a name.

2 Revision History

2.1 R1

• Restore the () that were inadvertently ommitted from the Swappable constraints on the members of class tagged, and then strike them.

3 Proposed Solution

We propose respecifying the Ranges TS in terms of variable-style concepts. There are three cases
to handle:

1. Non-overloaded concepts
2. Cross-type concepts
3. Variable-argument concepts

3.1 Non-overloaded concepts

In the case of concepts that are not overloaded, changing to variable concepts is purely a
syntactic rewrite. For example, the following function-style concept:

template <class T>
concept bool Movable() {
  return MoveConstructible<T>() &&
    Assignable<T&, T>() &&
    Swappable<T&>();
}

would become:

template <class T>
concept bool Movable =
  MoveConstructible<T> &&
  Assignable<T&, T> &&
  Swappable<T&>;

Obviously, all uses of this concept would also need to be changed to drop the trailing empty parens
(“()”), if any.

3.2 Cross-type concepts

Some binary concepts offer a unary form to mean “same type”, such that Concept<A>() is
semantically identical to Concept<A, A>() (e.g., EqualityComparable). In these cases, a simple
rewrite into a variable form will not result in valid code, since variable concepts cannot be
overloaded. In these cases, we must find a different spelling for the unary and binary forms.

The suggestion is to use the suffix With for the binary form. So, EqualityComparable<int> would
be roughly equivalent to EqualityComparableWith<int, int>. This follows the precedent set by the
type traits is_swappable and is_swappable_with.

The concepts in the Ranges TS to which this applies are:

• EqualityComparable
• Swappable
• StrictTotallyOrdered

This pattern also appears in the relation concepts:

• Relation
• StrictWeakOrder

However, the forms Relation<R, T>() and StrictWeakOrder<R, T>() are used nowhere in the Ranges
TS and can simply be dropped with no impact.

3.3 Variable-argument concepts

The concepts that have to do with callables naturally permit a variable number of arguments and
are best expressed using variadic parameters packs. However, the indirect callable concepts used
to constrain the higher-order STL algorithms are fixed-arity (not variadic) so as to be able to
check callability with the cross-product of the iterators’ associated types. The STL algorithms
only ever deal with unary and binary callables, so the indirect callable concepts are “overloaded”
on zero, one, or two arguments.

The affected concepts are:

• IndirectInvocable
• IndirectRegularInvocable
• IndirectPredicate

(The concepts IndirectRelation and IndirectStrictWeakOrder are unaffected because they are not
overloaded.)

The concept IndirectInvocable is used to constrain the for_each algorithm, where the function
object it constrains is unary. So, we suggest dropping the nullary and binary forms of this concept
and renaming IndirectInvocable to IndirectUnaryInvocable.

Likewise, the concept IndirectRegularInvocable is used to constrain the projected class
template, where the function object it constrains is unary. So, we suggest dropping the nullary and
binary forms of this concept and renaming IndirectRegularInvocable to
IndirectRegularUnaryInvocable.

We observe that IndirectPredicate is only ever used to constrain unary predicates (once we fix
ericniebler/stl2#411), so we suggest dropping the binary form and renaming IndirectPredicate
to IndirectUnaryPredicate.

4 Discussion

Should the committee ever decide to permit variable-style concepts to be overloaded, we could
decide to revert the name changes proposed in this document. For example, we could offer
EqualityComparable<A, B> as an alternate syntax for EqualityComparableWith<A, B>, and deprecate
EqualityComparableWith.

4.1 Alternative Solutions

The following solutions have been considered and dismissed.

4.1.1 Leave Function-Style Intact

There is nothing wrong per se with leaving the concepts as function-style. The Ranges TS
is based on the Concepts TS as published, which supports the syntax. Giving up function-style
concepts forces us to come up with unique names for semantically similar things, including the
admittedly awful IndirectUnaryInvocable and friends.

This option comes with a few lasting costs, already discussed above. We feel the costs of sticking
with function-style concepts outweigh the benefits of being able to “overload” concept names.

5 Implementation Experience

All the interface changes suggested in this document have been implemented and tested in the
Ranges TS’s reference implementation at https://github.com/CaseyCarter/cmcstl2. The change was
straightforward and unsurprising.

6 Proposed Design

[ Editorial note: In places where a purely mechanical transformation is sufficient, rather
than show all the diffs (which would be overwhelming and tend to obsure the more meaningful edits),
we describe the transformation, give an example, and instruct the editor to make the mechanical
change everywhere applicable. In other cases, where concepts change name or need to be respecified,
the changes are shown explicitly with diff marks. ]

In all places in the document where concept checks are applied with a trailing set of empty parens
(“()”), remove the parens.

6.1 Section “Concepts library” ([concepts.lib])

In “Header <experimental/ranges/concepts> synopsis” ([concepts.lib.synopsis]), except where noted
below, change all the concept definitions from function-style concepts to variable-style concepts,
following the pattern for Same shown below:

template <class T, class U>
concept bool Same() { =
  return see below;
}

Change the second (binary) forms of Swappable, EqualityComparable, and StrictTotallyOrdered as
follows:

template <class T, class U>
concept bool SwappableWith() { =
  return see below;
}

template <class T, class U>
concept bool EqualityComparableWith() { =
  return see below;
}

template <class T, class U>
concept bool StrictTotallyOrderedWith() { =
  return see below;
}

In addition, remove the following two concept declarations:

template <class R, class T>
concept bool Relation() {
  return see below;
}

template <class R, class T>
concept bool StrictWeakOrder() {
  return see below;
}

Make the corresponding edits in sections 7.3 [concepts.lib.corelang] through section 7.6
[Callable concepts], except as follows.

In the section “Concept Movable ([concepts.lib.object.movable]), change the definition of
Movable as follows (includes changes from P0547R1 and
ericniebler/stl2#174 “Swappable concept and P0185 swappable traits”):

template <class T>
concept bool Movable() { =
  return std::is_object<T>::value && // see below
    MoveConstructible<T> &&
    Assignable<T&, T> &&
    Swappable<T&>;
}

In section “Concept Swappable” ([concepts.lib.corelang.swappable]), change the name of the binary
form of Swappable to SwappableWith as follows:

[ Editorial note: This includes the resolutions of ericniebler/stl2#155 “Comparison
concepts and reference types” and
ericniebler/stl2#174 “Swappable concept and P0185 swappable traits”. ]

template <class T>
concept bool Swappable() { =
  return requires(T&& a, T&& b) {
    ranges::swap(std::forward<T>(a), std::forward<T>(b));
  };
}

template <class T, class U>
concept bool SwappableWith =() {
  return Swappable<T>() &&
    Swappable<U>() &&
    CommonReference<
      const remove_reference_t<T>&,
      const remove_reference_t<U>&>() &&
    requires(T&& t, U&& u) {
      ranges::swap(std::forward<T>(t), std::forward<T>(t));
      ranges::swap(std::forward<U>(u), std::forward<U>(u));
      ranges::swap(std::forward<T>(t), std::forward<U>(u));
      ranges::swap(std::forward<U>(u), std::forward<T>(t));
    };
}

In [concepts.lib.corelang.swappable]/p2, change the two occurrences of Swappable<T, U>() to
SwappableWith<T, U>.

Change section “Concept EqualityComparable” ([concepts.lib.compare.equalitycomparable])/p3-4 as
follows:

3 [ Note: The requirement that the expression a == b is equality preserving implies that
== is reflexive, transitive, and symmetric. -- end note ]

template <class T, class U>
concept bool EqualityComparableWith() { =
  return
    EqualityComparable<T>() &&
    EqualityComparable<U>() &&
    CommonReference<
      const remove_reference_t<T>&,
      const remove_reference_t<U>&>() &&
    EqualityComparable<
      common_reference_t<
        const remove_reference_t<T>&,
        const remove_reference_t<U>&>>() &&
    WeaklyEqualityComparable<T, U>();
}

4 Let a be a const lvalue of type remove_reference_t<T>, b be a const lvalue of type
remove_reference_t<U>, and C be common_reference_t<const remove_reference_t<T>&,
const remove_reference_t<U>&>. Then EqualityComparableWith<T, U>() is satisfied if
and only if:

(4.1) -- bool(t == u) == bool(C(t) == C(u)).

[Note:This includes the resolution of ericniebler/stl2#155. ]

In section “Concept StrictTotallyOrdered” ([concepts.lib.corelang.stricttotallyordered]), change the name of the binary
form of StrictTotallyOrdered to StrictTotallyOrderedWith as follows:

[ Editorial note: This includes the resolution of ericniebler/stl2#155 “Comparison
concepts and reference types”. ]

template <class T>
concept bool StrictTotallyOrderedWith() { =
  return
    StrictTotallyOrdered<T>() &&
    StrictTotallyOrdered<U>() &&
    CommonReference<
      const remove_reference_t<T>&,
      const remove_reference_t<U>&>() &&
    StrictTotallyOrdered<
      common_reference_t<
        const remove_reference_t<T>&,
        const remove_reference_t<U>&>>() &&
    EqualityComparableWith<T, U>() &&
    requires(const remove_reference_t<T>& t,
             const remove_reference_t<U>& u) {
      { t < u } -> Boolean&&;
      { t > u } -> Boolean&&;
      { t <= u } -> Boolean&&;
      { t >= u } -> Boolean&&;
      { u < t } -> Boolean&&;
      { u > t } -> Boolean&&;
      { u <= t } -> Boolean&&;
      { u >= t } -> Boolean&&;
    };
}

In [concepts.lib.corelang.stricttotallyordered]/p2, change the occurrence of
StrictTotallyOrdered<T, U>() to StrictTotallyOrderedWith<T, U>.

Change section “Concept Relation” ([concepts.lib.callable.relation]) as follows:

[ Editorial note: This includes the resolution of ericniebler/stl2#155 “Comparison
concepts and reference types”. ]

template <class R, class T>
concept bool Relation() {
  return Predicate<R, T, T>;
}

template <class R, class T, class U>
concept bool Relation() { =
  return RelationPredicate<R, T, T>() &&
    RelationPredicate<R, U, U>() &&
    CommonReference<
      const remove_reference_t<T>&,
      const remove_reference_t<U>&>() &&
    RelationPredicate<R,
      common_reference_t<
        const remove_reference_t<T>&,
        const remove_reference_t<U>&>,
      common_reference_t<
        const remove_reference_t<T>&,
        const remove_reference_t<U>&>>() &&
    Predicate<R, T, U>() &&
    Predicate<R, U, T>();
}

Change section “Concept StrictWeakOrder” ([concepts.lib.callable.strictweakorder]) as follows:

template <class R, class T>
concept bool StrictWeakOrder() {
  return Relation<R, T>();
}

template <class R, class T, class U>
concept bool StrictWeakOrder() { =
  return Relation<R, T, U>();
}

6.2 Section “General utilities library” ([utilities])

Change section “Header <experimental/ranges/utility> synopsis” ([utility]/p2) as follows
(includes the resolution of ericniebler/stl2#174 “Swappable concept and P0185 swappable traits”):

// 8.5.2, struct with named accessors
template <class T>
concept bool TagSpecifier() { =
  return see below ;
}

template <class F>
concept bool TaggedType() { =
  return see below ;
}

template <class Base, TagSpecifier... Tags>
  requires sizeof...(Tags) <= tuple_size<Base>::value
struct tagged :
  [...]
  tagged& operator=(U&& u) noexcept(see below);
  void swap(tagged& that) noexcept(see below)
    requires Swappable<Base&>();
  friend void swap(tagged&, tagged&) noexcept(see below)
    requires Swappable<Base&>();
};

Make the accompanying edit to the definitions of TagSpecifier and TaggedType in section
“Class template tagged” [taggedtup.tagged]/p2, and to the detailed specifications of
tagged::swap and the non-member swap(tagged&, tagged&) overload in
[taggedtup.tagged]/p20 and p23

In the declarations of equal_to<void>::operator() and not_equal_to<void>::operator() in section
“Comparisons” [comparisons]/p8-9, change EqualityComparable<T, U>() to
EqualityComparableWith<T, U>.

In the declarations of greater<void>::operator(), less<void>::operator(),
greater_equal<void>::operator(), and less_equal<void>::operator() in section
“Comparisons” [comparisons]/p10-13, change StrictTotallyOrdered<T, U>() to
StrictTotallyOrderedWith<T, U>.

6.3 Section “Iterators library” ([iterators])

In “Header <experimental/ranges/iterators> synopsis” ([concepts.lib.synopsis]), except where noted
below, change all the function-style concept definitions to variable-style concepts.

In section “Header <experimental/ranges/iterator> synopsis” ([iterator.synopsis]), make the
following changes:

// 9.4, indirect callable requirements:
// 9.4.2, indirect callables:
template <class F>
concept bool IndirectInvocable() {
  return see below ;
}
template <class F, class I>
concept bool IndirectUnaryInvocable() { =
  return see below ;
}
template <class F, class I1, class I2>
concept bool IndirectInvocable() {
  return see below ;
}
template <class F>
concept bool IndirectRegularInvocable() {
  return see below ;
}
template <class F, class I>
concept bool IndirectRegularUnaryInvocable() { =
  return see below ;
}
template <class F, class I1, class I2>
concept bool IndirectRegularInvocable() {
  return see below ;
}
template <class F, class I>
concept bool IndirectUnaryPredicate() { =
  return see below ;
}
template <class F, class I1, class I2>
concept bool IndirectPredicate() {
  return see below ;
}

[...]

// 9.4.3, projected:
template <Readable I, IndirectRegularUnaryInvocable<I> Proj>
struct projected;

[...]

// 9.7, predefined iterators and sentinels:
// 9.7.1, reverse iterators:
template <BidirectionalIterator I> class reverse_iterator;

template <class I1, class I2>
    requires EqualityComparableWith<I1, I2>()
  bool operator==(
    const reverse_iterator<I1>& x,
    const reverse_iterator<I2>& y);
template <class I1, class I2>
    requires EqualityComparableWith<I1, I2>()
  bool operator!=(
    const reverse_iterator<I1>& x,
    const reverse_iterator<I2>& y);
template <class I1, class I2>
    requires StrictTotallyOrderedWith<I1, I2>()
  bool operator<(
    const reverse_iterator<I1>& x,
    const reverse_iterator<I2>& y);
template <class I1, class I2>
requires StrictTotallyOrderedWith<I1, I2>()
  bool operator>(
    const reverse_iterator<I1>& x,
    const reverse_iterator<I2>& y);
template <class I1, class I2>
requires StrictTotallyOrderedWith<I1, I2>()
  bool operator>=(
    const reverse_iterator<I1>& x,
    const reverse_iterator<I2>& y);
template <class I1, class I2>
requires StrictTotallyOrderedWith<I1, I2>()
  bool operator<=(
    const reverse_iterator<I1>& x,
    const reverse_iterator<I2>& y);

[...]

// 9.7.3, move iterators and sentinels:
template <InputIterator I> class move_iterator;
template <class I1, class I2>
    requires EqualityComparableWith<I1, I2>()
  bool operator==(
    const move_iterator<I1>& x, const move_iterator<I2>& y);
template <class I1, class I2>
    requires EqualityComparableWith<I1, I2>()
  bool operator!=(
    const move_iterator<I1>& x, const move_iterator<I2>& y);
template <class I1, class I2>
    requires StrictTotallyOrderedWith<I1, I2>()
  bool operator<(
    const move_iterator<I1>& x, const move_iterator<I2>& y);
template <class I1, class I2>
    requires StrictTotallyOrderedWith<I1, I2>()
  bool operator<=(
    const move_iterator<I1>& x, const move_iterator<I2>& y);
template <class I1, class I2>
    requires StrictTotallyOrderedWith<I1, I2>()
  bool operator>(
    const move_iterator<I1>& x, const move_iterator<I2>& y);
template <class I1, class I2>
    requires StrictTotallyOrderedWith<I1, I2>()
  bool operator>=(
    const move_iterator<I1>& x, const move_iterator<I2>& y);

[...]

template <class I1, class I2, Sentinel<I2> S1, Sentinel<I1> S2>
  bool operator==(
    const common_iterator<I1, S1>& x, const common_iterator<I2, S2>& y);
template <class I1, class I2, Sentinel<I2> S1, Sentinel<I1> S2>
    requires EqualityComparableWith<I1, I2>()
  bool operator==(
    const common_iterator<I1, S1>& x, const common_iterator<I2, S2>& y);
template <class I1, class I2, Sentinel<I2> S1, Sentinel<I1> S2>
  bool operator!=(
    const common_iterator<I1, S1>& x, const common_iterator<I2, S2>& y);

[Editorial note: The resolution of ericniebler/stl2#286 changes indirect_result_of to no longer use
IndirectInvocable, so no change is necessary there. – end note]

Change section “Indirect callables” [indirectcallable.indirectinvocable] as follows:

template <class F>
concept bool IndirectInvocable() {
  return CopyConstructible<F>() &&
    Invocable<F&>();
}
template <class F, class I>
concept bool IndirectUnaryInvocable() { =
  return Readable<I>() &&
    CopyConstructible<F>() &&
    Invocable<F&, value_type_t<I>&>() &&
    Invocable<F&, reference_t<I>>() &&
    Invocable<F&, iter_common_reference_t<I>>();
}
template <class F, class I1, class I2>
concept bool IndirectInvocable() {
  return Readable<I1>() && Readable<I2>() &&
    CopyConstructible<F>() &&
    Invocable<F&, value_type_t<I1>&, value_type_t<I2>&>() &&
    Invocable<F&, value_type_t<I1>&, reference_t<I2>>() &&
    Invocable<F&, reference_t<I1>, value_type_t<I2>&>() &&
    Invocable<F&, reference_t<I1>, reference_t<I2>>() &&
    Invocable<F&, iter_common_reference_t<I1>, iter_common_reference_t<I2>>();
}

template <class F>
concept bool IndirectRegularInvocable() {
  return CopyConstructible<F>() &&
    RegularInvocable<F&>();
}
template <class F, class I>
concept bool IndirectRegularUnaryInvocable() { =
  return Readable<I>() &&
    CopyConstructible<F>() &&
    RegularInvocable<F&, value_type_t<I>&>() &&
    RegularInvocable<F&, reference_t<I>>() &&
    RegularInvocable<F&, iter_common_reference_t<I>>();
}
template <class F, class I1, class I2>
concept bool IndirectRegularInvocable() {
  return Readable<I1>() && Readable<I2>() &&
    CopyConstructible<F>() &&
    RegularInvocable<F&, value_type_t<I1>&, value_type_t<I2>&>() &&
    RegularInvocable<F&, value_type_t<I1>&, reference_t<I2>>() &&
    RegularInvocable<F&, reference_t<I1>, value_type_t<I2>&>() &&
    RegularInvocable<F&, reference_t<I1>, reference_t<I2>>() &&
    RegularInvocable<F&, iter_common_reference_t<I1>, iter_common_reference_t<I2>>();
}

template <class F, class I>
concept bool IndirectUnaryPredicate() { =
  return Readable<I>() &&
    CopyConstructible<F>() &&
    Predicate<F&, value_type_t<I>&>() &&
    Predicate<F&, reference_t<I>>() &&
    Predicate<F&, iter_common_reference_t<I>>();
}
template <class F, class I1, class I2>
concept bool IndirectPredicate() {
  return Readable<I1>() && Readable<I2>() &&
    CopyConstructible<F>() &&
    Predicate<F&, value_type_t<I1>&, value_type_t<I2>&>() &&
    Predicate<F&, value_type_t<I1>&, reference_t<I2>>() &&
    Predicate<F&, reference_t<I1>, value_type_t<I2>&>() &&
    Predicate<F&, reference_t<I1>, reference_t<I2>>() &&
    Predicate<F&, iter_common_reference_t<I1>, iter_common_reference_t<I2>>();
}

In section “Class template projected” ([projected]), change the occurrence of
IndirectRegularInvocable to IndirectRegularUnaryInvocable.

In [commonalgoreq.general]/p2, change the note to read:

[…] equal_to<> requires its arguments satisfy EqualityComparableWith (7.4.3), and
less<> requires its arguments satisfy StrictTotallyOrderedWith (7.4.4). […]

In section “Class template reverse_iterator” ([reverse.iterator]), in the synopsis and in definitions
of the relational operators ([reverse.iter.op==] through [reverse.iter.op<=]), change
EqualityComparable<I1, I2>() to EqualityComparableWith<I1, I2>, and change
StrictTotallyOrdered<I1, I2>() to StrictTotallyOrderedWith<I1, I2> as shown above in the
<experimental/ranges/iterator> synopsis ([iterator.synopsis]).

In section “Class template move_iterator” ([move.iterator]), in the synopsis (p2) and in definitions
of the relational operators ([[move.iter.op.comp]]), change EqualityComparable<I1, I2>() to
EqualityComparableWith<I1, I2>, and change StrictTotallyOrdered<I1, I2>() to
StrictTotallyOrderedWith<I1, I2> as shown above in the <experimental/ranges/iterator> synopsis
([iterator.synopsis]).

In section “Class template move_sentinel” ([move.sentinel]), in the move_if example in para 2,
change IndirectPredicate to IndirectUnaryPredicate.

In section “Class template common_iterator” ([common.iterator]), in the synopsis (p2) and in definitions
of the relational operators ([[common.iter.op.comp]]), change EqualityComparable<I1, I2>() to
EqualityComparableWith<I1, I2> as shown above in the <experimental/ranges/iterator> synopsis
([iterator.synopsis]).

In section “Range requirements” ([ranges.requirements]), change all function-style concept definitions
to variable-style concept definitions.

6.4 Section “Algorithms library” [algorithms]

In “Header <experimental/ranges/algorithm> synopsis” ([algorithms.general]/p2), make the following
changes:

template <InputIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  bool all_of(I first, S last, Pred pred, Proj proj = Proj{});
template <InputRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  bool all_of(Rng&& rng, Pred pred, Proj proj = Proj{});

template <InputIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  bool any_of(I first, S last, Pred pred, Proj proj = Proj{});
template <InputRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  bool any_of(Rng&& rng, Pred pred, Proj proj = Proj{});

template <InputIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  bool none_of(I first, S last, Pred pred, Proj proj = Proj{});
template <InputRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  bool none_of(Rng&& rng, Pred pred, Proj proj = Proj{});

template <InputIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryInvocable<projected<I, Proj>> Fun>
  tagged_pair<tag::in(I), tag::fun(Fun)>
    for_each(I first, S last, Fun f, Proj proj = Proj{});
template <InputRange Rng, class Proj = identity,
    IndirectUnaryInvocable<projected<iterator_t<Rng>, Proj>> Fun>
  tagged_pair<tag::in(safe_iterator_t<Rng>), tag::fun(Fun)>
    for_each(Rng&& rng, Fun f, Proj proj = Proj{});

[...]

template <InputIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  I find_if(I first, S last, Pred pred, Proj proj = Proj{});
template <InputRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  safe_iterator_t<Rng>
    find_if(Rng&& rng, Pred pred, Proj proj = Proj{});

template <InputIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  I find_if_not(I first, S last, Pred pred, Proj proj = Proj{});
template <InputRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  safe_iterator_t<Rng>
    find_if_not(Rng&& rng, Pred pred, Proj proj = Proj{});

[...]

template <InputIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  difference_type_t<I>
    count_if(I first, S last, Pred pred, Proj proj = Proj{});
template <InputRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  difference_type_t<iterator_t<Rng>>
    count_if(Rng&& rng, Pred pred, Proj proj = Proj{});

[...]

template <InputIterator I, Sentinel<I> S, WeaklyIncrementable O, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  requires IndirectlyCopyable<I, O>()
  tagged_pair<tag::in(I), tag::out(O)>
    copy_if(I first, S last, O result, Pred pred, Proj proj = Proj{});
template <InputRange Rng, WeaklyIncrementable O, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  requires IndirectlyCopyable<iterator_t<Rng>, O>()
  tagged_pair<tag::in(safe_iterator_t<Rng>), tag::out(O)>
    copy_if(Rng&& rng, O result, Pred pred, Proj proj = Proj{});

[...]

template <ForwardIterator I, Sentinel<I> S, class T, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  requires Writable<I, const T&>()
  I
    replace_if(I first, S last, Pred pred, const T& new_value, Proj proj = Proj{});
template <ForwardRange Rng, class T, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  requires Writable<iterator_t<Rng>, const T&>()
  safe_iterator_t<Rng>
    replace_if(Rng&& rng, Pred pred, const T& new_value, Proj proj = Proj{});

[...]

template <InputIterator I, Sentinel<I> S, class T, OutputIterator<const T&> O,
    class Proj = identity, IndirectUnaryPredicate<projected<I, Proj>> Pred>
  requires IndirectlyCopyable<I, O>()
  tagged_pair<tag::in(I), tag::out(O)>
    replace_copy_if(I first, S last, O result, Pred pred, const T& new_value,
                    Proj proj = Proj{});
template <InputRange Rng, class T, OutputIterator<const T&> O, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  requires IndirectlyCopyable<iterator_t<Rng>, O>()
  tagged_pair<tag::in(safe_iterator_t<Rng>), tag::out(O)>
    replace_copy_if(Rng&& rng, O result, Pred pred, const T& new_value,
                    Proj proj = Proj{});

[...]

template <ForwardIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  requires Permutable<I>()
  I remove_if(I first, S last, Pred pred, Proj proj = Proj{});
template <ForwardRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  requires Permutable<iterator_t<Rng>>()
  safe_iterator_t<Rng>
    remove_if(Rng&& rng, Pred pred, Proj proj = Proj{});

[...]

template <InputIterator I, Sentinel<I> S, WeaklyIncrementable O,
    class Proj = identity, IndirectUnaryPredicate<projected<I, Proj>> Pred>
  requires IndirectlyCopyable<I, O>()
  tagged_pair<tag::in(I), tag::out(O)>
    remove_copy_if(I first, S last, O result, Pred pred, Proj proj = Proj{});
template <InputRange Rng, WeaklyIncrementable O, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  requires IndirectlyCopyable<iterator_t<Rng>, O>()
  tagged_pair<tag::in(safe_iterator_t<Rng>), tag::out(O)>
    remove_copy_if(Rng&& rng, O result, Pred pred, Proj proj = Proj{});

[...]

template <InputIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  bool is_partitioned(I first, S last, Pred pred, Proj proj = Proj{});
template <InputRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  bool
  is_partitioned(Rng&& rng, Pred pred, Proj proj = Proj{});

template <ForwardIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  requires Permutable<I>()
  I partition(I first, S last, Pred pred, Proj proj = Proj{});
template <ForwardRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  requires Permutable<iterator_t<Rng>>()
  safe_iterator_t<Rng>
    partition(Rng&& rng, Pred pred, Proj proj = Proj{});

template <BidirectionalIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  requires Permutable<I>()
  I stable_partition(I first, S last, Pred pred, Proj proj = Proj{});
template <BidirectionalRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  requires Permutable<iterator_t<Rng>>()
  safe_iterator_t<Rng>
    stable_partition(Rng&& rng, Pred pred, Proj proj = Proj{});

template <InputIterator I, Sentinel<I> S, WeaklyIncrementable O1, WeaklyIncrementable O2,
    class Proj = identity, IndirectUnaryPredicate<projected<I, Proj>> Pred>
  requires IndirectlyCopyable<I, O1>() && IndirectlyCopyable<I, O2>()
  tagged_tuple<tag::in(I), tag::out1(O1), tag::out2(O2)>
    partition_copy(I first, S last, O1 out_true, O2 out_false, Pred pred,
                   Proj proj = Proj{});
template <InputRange Rng, WeaklyIncrementable O1, WeaklyIncrementable O2,
    class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  requires IndirectlyCopyable<iterator_t<Rng>, O1>() &&
    IndirectlyCopyable<iterator_t<Rng>, O2>()
  tagged_tuple<tag::in(safe_iterator_t<Rng>), tag::out1(O1), tag::out2(O2)>
    partition_copy(Rng&& rng, O1 out_true, O2 out_false, Pred pred, Proj proj = Proj{});

template <ForwardIterator I, Sentinel<I> S, class Proj = identity,
    IndirectUnaryPredicate<projected<I, Proj>> Pred>
  I partition_point(I first, S last, Pred pred, Proj proj = Proj{});
template <ForwardRange Rng, class Proj = identity,
    IndirectUnaryPredicate<projected<iterator_t<Rng>, Proj>> Pred>
  safe_iterator_t<Rng>
  partition_point(Rng&& rng, Pred pred, Proj proj = Proj{});

In section “All of” ([alg.all_of]), change the signature of the all_of algorithm to match those
shown in <experimental/ranges/algorithm> synopsis ([algorithms.general]/p2) above.

Likewise, do the same for the following algorithms:

• any_of in section “Any of” ([alg.any_of])
• none_of in section “None of” ([alg.none_of])
• for_each in section “For each” ([alg.for_each])
• find_if in section “Find” ([alg.find])
• find_if_not in section “Find” ([alg.find])
• count_if in section “Count” ([alg.count])
• copy_if in section “Copy” ([alg.copy])
• replace_if in section “Replace” ([alg.replace])
• replace_copy_if in section “Replace” ([alg.replace])
• remove_if in section “Remove” ([alg.remove])
• remove_copy_if in section “Remove” ([alg.remove])
• is_partitioned in section “Partitions” ([alg.partitions])
• partition in section “Partitions” ([alg.partitions])
• stable_partition in section “Partitions” ([alg.partitions])
• partition_copy in section “Partitions” ([alg.partitions])
• partition_point in section “Partitions” ([alg.partitions])

7 Acknowledgements

I would like to thank Casey Carter for his review feedback.