ranges::fold
Document #:  P2322R5 
Date:  20211018 
Project:  Programming Language C++ 
Audience: 
LEWG 
Replyto: 
Barry Revzin <barry.revzin@gmail.com> 
Since [P2322R4], removed the shortcircuiting fold with one that simply returns the end iterator in addition to the value. Also removed the projections, see the discussion.
LEWG also reconfirmed having foldl
and foldl1
under different names, polling “fold with an initial value and fold with no initial value should have the same name (presumably just foldl)” (since once the projections were removed, there is no more ambiguity between the two algorithms)
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0  3  4  8  3 
LEWG also voted to rename the *1
suffix to *_first
. fold_left
was also preferred to foldl
(106), but there was no consensus between choosing the name fold
for the simple left fold (as previously preferred) or fold_left
(for symmetry). This revision has been tentatively updated to use the symmetric names fold_left
, fold_left_first
, fold_right
, and fold_right_last
, although this will need further discussion.
Since [P2322R3], no changes in actual proposal, just some improvements in the description.
[P2322R2] used the names fold_left
and fold_right
to refer to the left and right folds and used the same names for the initial value and noinitial value algorithms. LEWG took the following polls [P2322minutes]:
fold
with an initial value, and fold
with no initial value and nonempty range should have different names (presumably fold
and fold_first
)
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F

N

A

SA


6  6  3  2  1 
fold_left
to fold
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2  10  8  3  1 
This revision uses different names for the initial value and noinitial value algorithms, although rather than using fold
and fold_right
(and coming up with how to name the noinitial value versions), this paper uses the names foldl
and foldr
and then foldl1
and foldr1
. This revision also changes the noinitial value versions from having a nonempty range as a precondition to instead returning optional<T>
.
There was also discussion around having these algorithms return an end iterator.
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2  3  5  4  6 
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4  9  3  3  1 
But the primary algorithms (foldl
and foldl1
for leftfold) will definitely solely return a value. This revision adds further discussion on the flavors of fold
that can be provided, and ultimately adds another pair that satisfies this desire.
[P2322R1] used weaklyassignablefrom
as the constraint, this elevates it to assignable_from
. This revision also changes the return type of fold
to no longer be the type of the initial value, see the discussion.
[P2322R0] used regular_invocable
as the constraint in the foldable
concept, but we don’t need that for this algorithm and it prohibits reasonable uses like a mutating operation. invocable
is the sufficient constraint here (in the same way that it is for for_each
). Also restructured the API to overload on providing the initial value instead of having differently named algorithms.
As described in [P2214R0], there is one very important rangified algorithm missing from the standard library: fold
.
While we do have an iteratorbased version of fold
in the standard library, it is currently named accumulate
, defaults to performing +
on its operands, and is found in the header <numeric>
. But fold
is much more than addition, so as described in the linked paper, it’s important to give it the more generic name and to avoid a default operator.
Also as described in the linked paper, it is important to avoid overconstraining fold
in a way that prevents using it for heterogeneous folds. As such, the fold
specified in this paper only requires one particular invocation of the binary operator and there is no common_reference
requirement between any of the types involved.
Lastly, the fold
here is proposed to go into <algorithm>
rather than <numeric>
since there is nothing especially numeric about it.
Consider the example:
What is the type and value of r
? There are two choices, which I’ll demonstrate with implementations (with incomplete constraints).
T
We implement like so:
template <range R, movable T, typename F>
auto fold(R&& r, T init, F op) > T
{
ranges::iterator_t<R> first = ranges::begin(r);
ranges::sentinel_t<R> last = ranges::end(r);
for (; first != last; ++first) {
init = invoke(op, move(init), *first);
}
return init;
}
Here, fold(v, 1, std::plus())
is an int
because the initial value is 1
. Since our accumulator is an int
, the result here is 1
. This is a consistent with std::accumulate
and is simple to reason about and specify. But it is also a common gotcha with std::accumulate
.
Note that if we use assignable_from<T&, invoke_result_t<F&, T, range_reference_t<R>>>
as the constraint on this algorithm, in this example this becomes assignable_from<int&, double>
. We would be violating the semantic requirements of assignable_from
, which state 18.4.8 [concept.assignable]/1.5:
(1.5) After evaluating
lhs = rhs
:
 (1.5.1)
lhs
is equal torcopy
, unlessrhs
is a nonconst xvalue that refers tolcopy
.
This only holds if all the double
s happen to be whole numbers, which is not the case for our example. This invocation would be violating the semantic constraints of the algorithm.
When we talk about the mathematical definition of fold, that’s f(f(f(f(init, x1), x2), ...), xn)
. If we actually evaluate this expression in this context, that’s ((1 + 0.25) + 0.75)
which would be 2.0
.
We cannot in general get this type correctly. A hypothetical f
could actually change its type every time which we cannot possibly implement, so we can’t exactly mirror the mathematical definition regardless. But let’s just put that case aside as being fairly silly.
We could at least address the gotcha from std::accumulate
by returning the decayed result of invoking the binary operation with T
(the initial value) and the reference type of the range. That is, U = decay_t<invoke_result_t<F&, T, ranges::range_reference_t<R>>>
. There are two possible approaches to implementing a fold that returns U
instead of T
:
Either way, our set of requirements is:
invocable<F&, T, range_reference_t<R>>
(even though the implementation on the right does not actually invoke the function using these arguments, we still need this to determine the type U
)invocable<F&, U, range_reference_t<R>>
convertible_to<T, U>
assignable_from<U&, invoke_result_t<F&, U, range_reference_t<R>>>
While the lefthand side also needs convertible_to<invoke_result_t<F&, T, range_reference_t<R>>, U>
.
This is a fairly complicated set of requirements.
But it means that our example, fold(v, 1, std::plus())
yields the more likely expected result of 2.0
. So this is the version this paper proposes.
fold
algorithms[P2214R0] proposed a single fold algorithm that takes an initial value and a binary operation and performs a left fold over the range. But there are a couple variants that are also quite valuable and that we should adopt as a family.
fold1
Sometimes, there is no good choice for the initial value of the fold and you want to use the first element of the range. For instance, if I want to find the smallest string in a range, I can already do that as ranges::min(r)
but the only way to express this in terms of fold
is to manually pull out the first element, like so:
auto b = ranges::begin(r);
auto e = ranges::end(r);
ranges::fold(ranges::next(b), e, *b, ranges::min);
But this is both tedious to write, and subtly wrong for input ranges anyway since if the next(b)
is evaluated before *b
, we have a dangling iterator. This comes up enough that this paper proposes a version of fold
that uses the first element in the range as the initial value (and thus has a precondition that the range is not empty).
This algorithm exists in Scala and Kotlin (which call the noninitializer version reduce
but the initializer version fold
), Haskell (under the name fold1
), and Rust (in the Itertools
crate under the name fold1
and recently finalized under the name reduce
to match Scala and Kotlin [iterator_fold_self], although at some point it was fold_first
).
In Python, the single algorithm functools.reduce
supports both forms (the initializer
is an optional argument). In Julia, foldl
and foldr
both take an optional initial value as well (though it is mandatory in certain cases).
There are two questions to ask about the version of fold
that does not take an extra initializer.
Should we give this algorithm a different name (e.g. fold_first
or fold1
, since reduce
is clearly not an option for us) or provide it as an overload of fold
? To answer that question, we have to deal with the question of ambiguity. For two arguments, fold(xs, a)
can only be interpreted as a fold
with no initial value using a
as the binary operator. For four arguments, fold(xs, a, b, c)
can only be interpreted as a fold
with a
as the initial value, b
as the binary operation that is the reduction function, and c
as a unary projection.
What about fold(xs, a, b)
? It could be:
a
as the initial value and b
as a binary reduction of the form (A, X) > A
.a
as a binary reduction of the form (X, Y) > X
and b
as a unary projection of the form X > Y
.Is it possible for these to collide? It would be an uncommon situation, since b
would have to be both a unary and a binary function. But it is definitely possible:
This call is ambiguous! This works with either interpretation. It would either just return first
(the lambda) in the first case or the first element of the range in the second case, which makes it either completely useless or just mostly useless.
It’s possible to force either the function or projection to ensure that it can only be interpreted one way or the other, but since the algorithm is sufficiently different (see following section), even if such ambiguity is going to be extremely rare (and possible to deal with even if it does arise), we may as well avoid the issue entirely.
As such, this paper proposes a differently named algorithm for the version that takes no initial value rather than adding an overload under the same name.
optional
or UB?The result of ranges::foldl(empty_range, init, f)
is just init
. That is straightforward. But what would the result of ranges::foldl1(empty_range, f)
be? There are two options:
optional<T>
, orT
, but this case is undefined behaviorIn other words: empty range is either a valid input for the algorithm, whose result is nullopt
, or there is a precondition that the range is nonempty.
Users can always recover the undefined behavior case if they want, by writing *foldl1(empty_range, f)
, and the optional
return allows for easy addition of other functionality, such as providing a sentinel value for the empty range case (foldl1(empty_range, f).value_or(sentinel)
reads better than not ranges::empty(r) ? foldl1(r, f) : sentinel
, at least to me). It’s also much safer to use in the context where you may not know if the range is empty or not, because it’s adapted: foldl1(r  filter(f), op)
.
However, this would be the very first algorithm in the standard library that meaningful interacts with one of the sum types. And goes against the convention of algorithms simply being undefined for empty ranges (such as max
). Although it’s worth pointing out that max_element
is not UB for an empty range, it simply returns the end iterator, and the distinction there is likely due to simply not having had an available sentinel to return. But now we do.
This paper proposes returning optional<T>
. Which is added motivation for a name distinct from the fold
algorithm that takes an initializer.
fold_right
While ranges::fold
would be a leftfold, there is also occasionally the need for a rightfold. As with the previous section, we should also provide overloads of fold_right
that do not take an initial value.
There are three questions that would need to be asked about fold_right
.
First, the order of operations of to the function. Given fold_right([1, 2, 3], z, f)
, is the evaluation f(f(f(z, 3), 2), 1)
or is the evaluation f(1, f(2, f(3, z)))
? Note that either way, we’re choosing the 3
then 2
then 1
, both are right folds. It’s a question of if the initial element is the lefthand operand (as it is in the left fold
) or the righthand operand (as it would be if consider the right fold as a flip of the left fold).
One advantage of the former  where the initial call is f(z, 3)
 is that we can specify fold_right(r, z, op)
as precisely fold_left(views::reverse(r), z, op)
and leave it at that. Notably with the same op
. With the latter  where the initial call is f(3, z)
 we would need slightly more specification and would want to avoid saying flip(op)
since directly invoking the operation with the arguments in the correct order is a little better in the case of ranges of prvalues.
If we take a look at how other languages handle leftfold and rightfold, and whether the accumulator is on the same side (and, in these cases, the accumulator is always on the right) or opposite side (the accumulator is on the lefthand side for left fold and on the righthand side for right fold):
Same Side  Opposite Side 

Scheme  Haskell 
Elixir  F# 
Elm  Julia 
Kotlin  
OCaml  
Scala 
This paper chooses what appears to be the more common approach: the accumulator is on the lefthand side for left fold and the righthand side for right fold. That is, foldr(r, z, op)
is equivalent to foldl(reverse(r), z, flip(op))
.
Second, supporting bidirectional ranges is straightforward. Supporting forward ranges involves recursion of the size of the range. Supporting input ranges involves recursion and also copying the whole range first. Are either of these worth supporting? The paper simply supports bidirectional ranges.
Third, the naming question.
There are roughly four different choices that we could make here:
fold
(a leftfold) and fold_right
.fold_left
and fold_right
.fold_left
and fold_right
and also provide an alias fold
which is also fold_left
.foldl
and foldr
.There’s language precedents for any of these cases. F# and Kotlin both provide fold
as a leftfold and suffixed rightfold (foldBack
in F#, foldRight
in Kotlin). Elm, Haskell, Julia, and OCaml provide symmetrically named algorithms (foldl
/foldr
for the first three and fold_left
/fold_right
for the third). Scala provides a foldLeft
and foldRight
while also providing fold
to also mean foldLeft
.
In C++, we don’t have precedent in the library at this point for providing an alias for an algorithm, although we do have precedent in the library for providing an alias for a range adapter (keys
and values
for elements<0>
and elements<1>
, and [P2321R0] proposes pairwise
and pairwise_transform
as aliases for adjacent<2>
and adjacent_transform<2>
). We also have precedent in the library for asymmetric names (sort
vs stable_sort
vs partial_sort
) and symmetric ones (shift_left
vs shift_right
), even symmetric ones with terse names (rotl
and rotr
, although the latter are basically instructions).
All of which is to say, I don’t think there’s a clear answer to this question. I think at this point, all possible options have appeared in some revision of this paper. This current revision uses Option 2.
With the versions of algorithms that use an element from the range as the initializer, there’s a further choice. LEWG recently voted to prefer _first
as a suffix to 1
, which is fine for a left fold but with a right fold _first
seems like a poor choice of suffix because it’s really the last element that is the initializer. If we drop Option 4 above (LEWG prefers _left
and _right
as suffixes to l
and r
), we additionally have two options:
fold_right_first
fold_right_last
Or, putting it all together, we have the following name banks:
Left Folds  Right Folds  

With Init  No Init  With Init  No Init  
A 
fold

fold_first

fold_right

fold_right_first

B 
fold

fold_first

fold_right

fold_right_last

C 
fold_left

fold_left_first

fold_right

fold_right_first

D 
fold_left

fold_left_first

fold_right

fold_right_last

E 
fold == fold_left

fold_first == fold_left_first

fold_right

fold_right_first

F 
fold == fold_left

fold_first == fold_left_first

fold_right

fold_right_last

The current revision of this paper proposes Option D: the symmetric names (no fold
by itself, whether an alias or not) and _last
as the suffix rather than _first
. There was previously preference for fold
over fold_left
, but this will have to be discussed again separately.
The folds discussed up until now have always evaluated the entirety of the range. That’s very useful in of itself, and several other algorithms that we have in the standard library can be implemented in terms of such a fold (e.g. min
or count_if
).
But for some algorithms, we really want to short circuit. For instance, we don’t want to define all_of(r, pred)
as fold(r, true, logical_and(), pred)
. This formulation would give the correct answer, but we really don’t want to keep evaluating pred
once we got our first false
. To do this correctly, we really need short circuiting.
There are (at least) three different approaches for how to have a shortcircuiting fold. Here are different approaches to implementing any_of
in terms of a shortcircuiting fold:
You could provide a function that mutates the accumulator and returns true
to continue and false
to break. That is, all_of(r, pred)
would look like
and the main loop of the fold_while
algorithm would look like:
Same as #1, except return an enum class instead of a bool
(like control_flow::continue_
vs control_flow::break_
).
You could provide a function that returns a variant<continue_<T>, break_<U>>
. The algorithm would then return this variant (rather than a T
). Rust’s Itertools
crate provides this under the name fold_while
:
template <typename T> struct continue_ { T value; };
template <typename T> struct break_ { T value; };
template <> struct break_<void> { };
break_() > break_<void>;
template <typename T, typename U>
using fold_while_t = variant<continue_<T>, break_<U>>;
return fold_while(r, true, [&](bool, auto&& elem) > fold_while_t<bool, void> {
if (pred(elem)) {
return continue_{true};
} else {
return break_();
}
}).index() == 0;
and the main loop of the fold_while
algorithm would look like:
You could provide a function that returns an expected<T, E>
, which then the algorithm would return an expected<T, E>
(rather than a T
). Rust Iterator
trait provides this under the name try_fold
:
return fold_while(r, true, [&](bool, auto&& elem) > expected<bool, bool> {
if (pred(FWD(elem))) {
return true;
} else {
return unexpected(false);
}
}).has_value();
and the main loop of the fold_while
algorithm would look like:
Option (1) is a questionable option because of mutating state (note that we cannot use predicate
as the constraint on the type, because predicate
s are not allowed to mutate their arguments), but this approach is probably the most efficient due to not moving the accumulator at all.
Option (2) seems like a strictly worse version than Option (1) for C++, due to not being able to use existing predicates.
Option (3) is an awkward option for C++ because of general ergonomics. The provided lambda couldn’t just return continue_{x}
in one case and break_{y}
in another since those have different types, so you’d basically always have to provide > fold_while_t<T, U>
as a trailingreturntype. This would also be the first (or second, see above) algorithm which actually meaningfully uses one of the standard library’s sum types.
Option (4) isn’t a great option for C++ because we don’t even have expected<T, E>
in the standard library yet (although hopefully imminent at this point, as [P0323R10] is already being discussed in LWG), and ergonomically it has the same issues as described earlier  you can’t just return a T
and an unexpected<E>
for a lambda, you need to have a trailing return type. We’d also want to generalize this approach to any “truthy” type which would require coming up with a way to conceptualize (in the concept
sense) “truthy” (since optional<T>
would be a valid type as well, as well as any other the various userdefined versions out there. Rust’s name for this is Try
, with a new revision in progress). Because the implementation would have to wrap and unwrap the accumulator, it could potentially be less efficient than Option (1) as well.
Or, to put these all in a table, given that the accumulator has type T
:
Callable is Pure?  Callable returns…  Algorithm returns…  

1  ❌ 
bool

T

2  ❌ 
enum class control_flow

T

3  ✔️ 
variant<continue_<T>, break_<U>>

variant<continue_<T>, break_<U>>

4  ✔️ 
expected<T, E> optional<T>

expected<T, E> optional<T>

Option (3) is far too unergonomic in C++ to be reasonable, but Option (4) does have the benefit that it would allow different return types for the earlyreturn and fullconsume cases.
None of these options stand out as particularly promising. Moreover, I’ve been unable to find any other other than Rust which provides such an algorithm (even though basically every language provides algorithms that reduce to a shortcircuiting fold, like any
and all
), and in Rust, this algorithm is quite ergonomic due to language features that C++ does not possess. As such, while a previous revision of this paper proposed a shortcircuiting fold (specifically, Option 1), this paper does not.
Up until this point, this paper has only discussed returning a value from fold
: whatever we get as the result of f(f(f(f(init, e0), e1), e2), e3)
. But there is another value that we compute along the way that is thrown out: the end iterator.
An alternative formulation of fold
would preserve that information. Rather than returning R
, we could do something like this:
template <input_iterator I, typename R>
struct fold_result {
I in;
R value;
};
template <input_iterator I, sentinel_for<I> S, class T, class Proj = identity,
indirectlybinaryleftfoldable<T, projected<I, Proj>> F,
typename R = invoke_result_t<F&, T, indirect_result_t<Proj&, I>>>
constexpr auto fold_left(I first, S last, T init, F f, Proj proj = {})
> fold_result<I, R>;
But the problem with that direction is, quoting from [P2214R0]:
[T]he above definition definitely follows Alexander Stepanov’s law of useful return [stepanov] (emphasis ours):
When writing code, it’s often the case that you end up computing a value that the calling function doesn’t currently need. Later, however, this value may be important when the code is called in a different situation. In this situation, you should obey the law of useful return: A procedure should return all the potentially useful information it computed.
But it makes the usage of the algorithm quite cumbersome. The point of a fold is to return the single value. We would just want to write:
Rather than:
or:
ranges::fold
should just return T
. This would be consistent with what the other rangebased folds already return in C++20 (e.g. ranges::count
returns a range_difference_t<R>
, ranges::any_of
 which can’t quite be a fold
due to wanting to shortcircuit  just returns bool
).
Moreover, even if we added a version of this algorithm that returned an iterator (let’s call it fold_with_iterator
), we wouldn’t want fold(first, last, init, f)
to be defined as
since this would have to incur an extra move of the accumulated result, due to lack of copy elision (we have different return types). So we’d want need this algorithm to be specified separately (or, perhaps, the “Effects: equivalent to” formulation is sufficiently permissive as to allow implementations to do the right thing?)
From a usability perspective, I think it’s important that fold
just return the value.
The problem going past that is that we end up with this combinatorial explosion of algorithms based on a lot of orthogonal choices:
T
or (iterator, T)
Which would be… 32 distinct functions (under 16 different names) if we go all out. And these really are basically orthogonal choices. Indeed, a shortcircuiting fold seems even more likely to want the iterator that the algorithm stopped at! Do we need to provide all of them? Maybe we do!
This brings with it its own naming problem. That’s a lot of names. One approach there could be a suffix system:
fold_left
is a nonshortcircuiting leftfold with an initial value that returns T
fold_left_first
is a nonshortcircuiting leftfold with no initial value that returns T
fold_left_first_while
is a shortcircuiting leftfold with no initial value that returns T
fold_right_with_iter
is a nonshortcircuiting rightfold with an initial value that returns (iterator, T)
fold_right_last_while_with_iter
is a shortcircuiting rightfold with no initial value that returns (iterator, T)
with_iter
is not the best suffix, but the rest seem to work out ok.
One solution to the combinatorial explosion problem, as suggested by Tristan Brindle, is to simply not consider all of these options as being necessarily orthogonal. That is, providing a leftfold that returns a value is very valuable and highly desired. But having both a left and rightfold that return an iterator?
In other words, if you want the common and convenient thing, we’ll provide that: foldl
and foldl1
will exist and just return a value. But if you want a more complex tool, it’ll be a little more complicated to use. In other words, what this paper is proposing is six algorithms (with two overloads each):
fold_left
(a leftfold with an initial value that returns T
)fold_left_first
(a leftfold with no initial value that returns T
)fold_right
(a rightfold with an initial value that returns T
)fold_right_last
(a rightfold with no initial value that returns T
)fold_left_with_iter
(a leftfold with an initial value that returns (iterator, T)
)fold_left_first_with_iter
(a leftfold with no initial value that returns (iterator, T)
)There is no rightfold that returns an iterator, since you can use views::reverse
. This is a little harder to use since the transition from a fold that just returns T
to a fold that actually produces an iterator
as well isn’t as easy as going from:
to:
Instead, you have to flip the binary operation  and we have no flip
function adapter (Boost.HOF does though).
All the algorithms in std::ranges
take a projection, but there’s a problem in this case. For fold_left
, there’s no problem  we just look over the iterators and do invoke(proj, *first)
before passing that into the call to f
.
But for fold_left_first
, we need to produce an initial value, rather than an initial reference. And with a projection, we can’t… do that for iterators that give proxy references. Let’s start by writing out what fold_left_first
would be implemented as, without a projection, and then try to add it in:
template <input_iterator I, sentinel_for<I> S, indirectlybinaryleftfoldable<iter_value_t<I>, I> F> requires constructible_from<iter_value_t<I>, iter_reference_t<I>> constexpr auto fold_left_first(I first, S last, F f) { using U = decltype(ranges::fold_left(first, last, iter_value_t<I>(*first), f)); if (first == last) { return optional<U>(nullopt); } iter_value_t<I> init(*first); // <== ++first; return optional<U>(in_place, ranges::fold_left(std::move(first), std::move(last), std::move(init), std::move(f))); }
Now, how do we replace the commented line with a projected version of the same? We need a value. Imagine if *first
yielded a tuple<T&>
(as it does for zip
) and our projection is identity
(the common case). If we did:
We’d still end up with a tuple<T&>
, whereas we’d need to end up with a tuple<T>
. The only way to get this right is to project the value type first:
But that’s not actually required to be valid. The projection is required to take either iter_reference_t<I>
or iter_value_t<I>&
(specifically an lvalue of the value type). So you have to write this:
Which means that the only way to get this right is to incur an extra copy.
Which means we’re performing an extra copy in the typical case (the iterator does not yield a proxy reference and there is no projection) simply to be able to support the rare case. That seems problematic. And we don’t have any other algorithm where we’d need to get a projected value, we only ever need projected references (algorithms like min
which return a value type return the value type of the original range, not the projected range).
This suggests dropping the projections for the *_first
/*_last
variants (fold_left_first
, fold_right_last
, and fold_left_first_with_iter
). But then they’re more inconsistent with the other variants, so this paper suggests simply not having projections at all. This doesn’t cost you anything for some of the algorithms, since projections in these case can always be provided either as range adaptors or function adaptors.
The expression that I’m not supporting:
means the same as either this version using a range adaptor:
or this version using a function adaptor. Boost.HOF defines an adaptor proj
such that proj(p, f)(xs...)
means f(p(xs)...)
. We need to project only the right hand argument, so here proj_rhs(p, f)(x, y)
means f(x, p(y))
as desired. One way to implement this is std::bind(f, _1, std::bind(proj, _2))
.
The version using views::transform
is probably more familiar, but it won’t work as well for fold_left_with_iter
since this would return dangling
(since transform
is never a borrowed range) but even with adjustment would return an iterator into the transformed range rather than the original range. This issue is one of the original cited motivations for projections in [N4128]. The version using the function adaptor has no such issue, although proposing more function adaptors into the standard library is out of scope for this paper.
In short, there are good reasons to avoid projections for fold_left_first
, fold_right_last
, and fold_left_first_with_iter
. For consistency, I’m also removing the projections for fold_left
, fold_right
, and fold_left_with_iter
. This makes the folds inconsistent with the rest of the standard library algorithms (although at least internally consistent), but it doesn’t actually cost them functionality.
Part of this paper (naming the algorithms foldl
, foldl1
, foldr
, and foldr1
, where the *1
algorithms return an optional
) has been implemented in rangev3 [rangev3fold] (with projections, although not quite correctly as it turns out).
The algorithms returning an iterator have not been implemented in rangev3 yet, but they’re exactly the same as their noniteratorreturning counterparts.
Add a featuretest macro to 17.3.2 [version.syn]:
Append to 25.4 [algorithm.syn], first a new result type:
#include <initializer_list> namespace std { namespace ranges { // [algorithms.results], algorithm result types template<class I, class F> struct in_fun_result; template<class I1, class I2> struct in_in_result; template<class I, class O> struct in_out_result; template<class I1, class I2, class O> struct in_in_out_result; template<class I, class O1, class O2> struct in_out_out_result; template<class T> struct min_max_result; template<class I> struct in_found_result; + template<class I, class T> + struct in_value_result; } // ... }
and then also a bunch of fold algorithms:
namespace std { // ... // [alg.fold], folds namespace ranges { template<class F> struct flipped { // exposition only F f; template<class T, class U> requires invocable<F&, U, T> invoke_result_t<F&, U, T> operator()(T&&, U&&); }; template <class F, class T, class I, class U> concept indirectlybinaryleftfoldableimpl = // exposition only movable<T> && movable<U> && convertible_to<T, U> && invocable<F&, U, iter_reference_t<I>> && assignable_from<U&, invoke_result_t<F&, U, iter_reference_t<I>>>; template <class F, class T, class I> concept indirectlybinaryleftfoldable = // exposition only copy_constructible<F> && indirectly_readable<I> && invocable<F&, T, iter_reference_t<I>> && convertible_to<invoke_result_t<F&, T, iter_reference_t<I>>, decay_t<invoke_result_t<F&, T, iter_reference_t<I>>>> && indirectlybinaryleftfoldableimpl<F, T, I, decay_t<invoke_result_t<F&, T, iter_reference_t<I>>>>; template <class F, class T, class I> concept indirectlybinaryrightfoldable = // exposition only indirectlybinaryleftfoldable<flipped<F>, T, I>; template<input_iterator I, sentinel_for<I> S, class T, indirectlybinaryleftfoldable<T, I> F> constexpr auto fold_left(I first, S last, T init, F f); template<input_range R, class T, indirectlybinaryleftfoldable<T, iterator_t<R>> F> constexpr auto fold_left(R&& r, T init, F f); template <input_iterator I, sentinel_for<I> S, indirectlybinaryleftfoldable<iter_value_t<I>, I> F> requires constructible_from<iter_value_t<I>, iter_reference_t<I>> constexpr auto fold_left_first(I first, S last, F f); template <input_range R, indirectlybinaryleftfoldable<range_value_t<R>, iterator_t<R>> F> requires constructible_from<range_value_t<R>, range_reference_t<R>> constexpr auto fold_left_first(R&& r, F f); template<bidirectional_iterator I, sentinel_for<I> S, class T, indirectlybinaryrightfoldable<T, I> F> constexpr auto fold_right(I first, S last, T init, F f); template<bidirectional_range R, class T, indirectlybinaryrightfoldable<T, iterator_t<R>> F> constexpr auto fold_right(R&& r, T init, F f); template <bidirectional_iterator I, sentinel_for<I> S, indirectlybinaryrightfoldable<iter_value_t<I>, I> F> requires constructible_from<iter_value_t<I>, iter_reference_t<I>> constexpr auto fold_right_last(I first, S last, F f); template <bidirectional_range R, indirectlybinaryrightfoldable<range_value_t<R>, iterator_t<R>> F> requires constructible_from<range_value_t<R>, range_reference_t<R>> constexpr auto fold_right_last(R&& r, F f); template<class I, class T> using fold_left_with_iter_result = in_value_result<I, T>; template<class I, class T> using fold_left_first_with_iter_result = in_value_result<I, T>; template<input_iterator I, sentinel_for<I> S, class T, indirectlybinaryleftfoldable<T, I> F> constexpr see below fold_left_with_iter(I first, S last, T init, F f); template<input_range R, class T, indirectlybinaryleftfoldable<T, iterator_t<R>> F> constexpr see below fold_left_with_iter(R&& r, T init, F f); template <input_iterator I, sentinel_for<I> S, indirectlybinaryleftfoldable<iter_value_t<I>, I> F> requires constructible_from<iter_value_t<I>, iter_reference_t<I>> constexpr see below fold_left_first_with_iter(I first, S last, F f); template <input_range R, indirectlybinaryleftfoldable<range_value_t<R>, iterator_t<R>> F> requires constructible_from<range_value_t<R>, range_reference_t<R>> constexpr see below fold_left_first_with_iter(R&& r, F f); } }
Add a new result type to 25.5 [algorithms.results]:
namespace std::ranges { // ... template<class I> struct in_found_result { [[no_unique_address]] I in; bool found; template<class I2> requires convertible_to<const I&, I2> constexpr operator in_found_result<I2>() const & { return {in, found}; } template<class I2> requires convertible_to<I, I2> constexpr operator in_found_result<I2>() && { return {std::move(in), found}; } }; + template<class I, class T> + struct in_value_result { + [[no_unique_address]] I in; + [[no_unique_address]] T value; + + template<class I2, class T2> + requires convertible_to<const I&, I2> && convertible_to<const T&, T2> + constexpr operator in_value_result<I2, T2>() const & { + return {in, value}; + } + + template<class I2, class T2> + requires convertible_to<I, I2> && convertible_to<T, T2> + constexpr operator in_value_result<I2, T2>() && { + return {std::move(in), std::move(value)}; + } + }; }
And add a new clause, [alg.fold]:
template<input_iterator I, sentinel_for<I> S, class T, indirectlybinaryleftfoldable<T, I> F> constexpr auto ranges::fold_left(I first, S last, T init, F f); template<input_range R, class T, indirectlybinaryleftfoldable<T, iterator_t<R>> F> constexpr auto ranges::fold_left(R&& r, T init, F f);
1 Returns:
ranges::fold_left_with_iter(std::move(first), last, std::move(init), f).value
.template <input_iterator I, sentinel_for<I> S, indirectlybinaryleftfoldable<iter_value_t<I>, I> F> requires constructible_from<iter_value_t<I>, iter_reference_t<I>> constexpr auto ranges::fold_left_first(I first, S last, F f); template <input_range R, indirectlybinaryleftfoldable<range_value_t<R>, iterator_t<R>> F> requires constructible_from<range_value_t<R>, range_reference_t<R>> constexpr auto ranges::fold_left_first(R&& r, F f);
2 Returns:
ranges::fold_left_first_with_iter(std::move(first), last, f).value
.template<bidirectional_iterator I, sentinel_for<I> S, class T, indirectlybinaryrightfoldable<T, I> F> constexpr auto ranges::fold_right(I first, S last, T init, F f); template<bidirectional_range R, class T, indirectlybinaryrightfoldable<T, iterator_t<R>> F> constexpr auto ranges::fold_right(R&& r, T init, F f);
3 Effects: Equivalent to:
template <bidirectional_iterator I, sentinel_for<I> S, indirectlybinaryrightfoldable<iter_value_t<I>, I> F> requires constructible_from<iter_value_t<I>, iter_reference_t<I>> constexpr auto ranges::fold_right_last(I first, S last, F f); template <bidirectional_range R, indirectlybinaryrightfoldable<range_value_t<R>, iterator_t<R>> F> requires constructible_from<range_value_t<R>, range_reference_t<R>> constexpr auto ranges::fold_right_last(R&& r, F f);
4 Let
U
bedecltype(ranges::fold_right(first, last, iter_value_t<I>(*first), f))
.5 Effects: Equivalent to:
template<input_iterator I, sentinel_for<I> S, class T, indirectlybinaryleftfoldable<T, I> F> constexpr see below fold_left_with_iter(I first, S last, T init, F f); template<input_range R, class T, indirectlybinaryleftfoldable<T, iterator_t<R>> F> constexpr see below fold_left_with_iter(R&& r, T init, F f);
6 Let
U
bedecay_t<invoke_result_t<F&, T, iter_reference_t<I>>>
.7 Effects: Equivalent to:
8 Remarks: The return type is
fold_left_with_iter_result<I, U>
for the first overload andfold_left_with_iter_result<borrowed_iterator_t<R>, U>
for the second overload.template <input_iterator I, sentinel_for<I> S, indirectlybinaryleftfoldable<iter_value_t<I>, I> F> requires constructible_from<iter_value_t<I>, iter_reference_t<I>> constexpr see below fold_left_first_with_iter(I first, last, F f) template <input_range R, indirectlybinaryleftfoldable<range_value_t<R>, iterator_t<R>> F> requires constructible_from<range_value_t<R>, range_reference_t<R>> constexpr see below fold_left_first_with_iter(R&& r, F f);
9 Let
U
bedecltype(ranges::fold_left(std::move(first), last, iter_value_t<I>(*first), f))
.10 Effects: Equivalent to:
11 Remarks: The return type is
fold_left_first_with_iter_result<I, optional<U>>
for the first overload andfold_left_first_with_iter_result<borrowed_iterator_t<R>, optional<U>>
for the second overload.
[iterator_fold_self] Ashley Mannix. 2020. Tracking issue for iterator_fold_self
.
https://github.com/rustlang/rust/issues/68125
[N4128] E. Niebler, S. Parent, A. Sutton. 20141010. Ranges for the Standard Library, Revision 1.
https://wg21.link/n4128
[P0323R10] JF Bastien, Vicente Botet. 20210415. std::expected.
https://wg21.link/p0323r10
[P2214R0] Barry Revzin, Conor Hoekstra, Tim Song. 20201015. A Plan for C++23 Ranges.
https://wg21.link/p2214r0
[P2321R0] Tim Song. 20210221. zip.
https://wg21.link/p2321r0
[P2322minutes] LEWG. 2021. P2322 Minutes.
https://wiki.edg.com/bin/view/Wg21telecons2021/P2322#20210503
[P2322R0] Barry Revzin. 20210218. ranges::fold.
https://wg21.link/p2322r0
[P2322R1] Barry Revzin. 20210317. ranges::fold.
https://wg21.link/p2322r1
[P2322R2] Barry Revzin. 20210415. ranges::fold.
https://wg21.link/p2322r2
[P2322R3] Barry Revzin. 20210613. ranges::fold.
https://wg21.link/p2322r3
[P2322R4] Barry Revzin. 20210913. ranges::fold.
https://wg21.link/p2322r4
[rangev3fold] Barry Revzin. 2021. Fold algos.
https://github.com/ericniebler/rangev3/pull/1628
[stepanov] Alexander A. Stepanov. 2014. From Mathematics to Generic Programming.