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                        fold_first API Change Proposal
Proposal
Problem statement
Iterator::fold is an extremely useful API to process all the elements in an iterator.
Sometimes you don't have a sensible initial value. This is where Iterator::reduce comes in.
However, this removes some flexibility with the return type. It must be the same as the item stream.
There's a middle ground where you instead derive the initial fold value with the first element in the iterator.
Motivation, use-cases
The docs for fold presents this example
let numbers = [1, 2, 3, 4, 5];
let zero = "0".to_string();
let result = numbers.iter().fold(zero, |acc, &x| {
    format!("({acc} + {x})")
});
assert_eq!(result, "(((((0 + 1) + 2) + 3) + 4) + 5)");
There's no way to avoid the (0 + 1) situation with either fold or reduce unless you fold over a Option<String> or reduce over String iterators.
With fold_first, this is easy
let numbers = [1, 2, 3, 4, 5];
let result = numbers.iter().fold_first(
    |first| first.to_string(),
    |acc, &x| format!("({acc} + {x})"),
).unwrap();
assert_eq!(result, "((((1 + 2) + 3) + 4) + 5)");
Solution sketches
https://github.com/rust-lang/rust/pull/106348
Links and related work
What happens now?
This issue is part of the libs-api team API change proposal process. Once this issue is filed the libs-api team will review open proposals in its weekly meeting. You should receive feedback within a week or two.
That example exists in the docs mostly to emphasize the order in which the accumulator is applied.
Can you put more about your real-life situations where this is something you need?
My instinct is that we might not want another of these consumers, especially with a called-at-most-once closure.  reduce existing for the homogeneous case is one thing, but even that wasn't an obvious addition, showing up many years after the more critical fold.  It might be fine for people to just do the next-then-fold approach for this themselves.
The next-then-fold pattern feels like a more general tap-like thing where you have a pile of adapter calls, then want to apply something to that temporary and then want to apply something else.
I recently wrote some code that would have benefited from this API (and I'm pretty sure I've looked for it in the past too):
let mut messages = messages.into_iter();
let initial = Error::msg(messages.next().ok_or_else(|| eyre!("missing initial message"))?);
messages.fold(initial, |err, msg| err.wrap_err(msg))
with fold_first I find it much more readable to not switch back and forth between the imperative and functional APIs:
messages
  .into_iter()
  .fold_first(Error::msg, |err, msg| acc.wrap_err(msg))
  .ok_or_else(|| eyre!("missing initial message"))?
(code context: messages: Vec<String>, Error is eyre::Report, this is rebuilding a chained report from serialized messages sent over the network)
We discussed this briefly during this week's libs-api meeting. There weren't many strong opinions, but nobody wanted to second this addition, so we're going to close it.
The recommendation is to call it.next().map(|first| it.fold(first.to_string(), ...)) or let first = it.next(); it.fold(...).