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diff --git a/library/core/src/iter/sources/once_with.rs b/library/core/src/iter/sources/once_with.rs
new file mode 100644
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+++ b/library/core/src/iter/sources/once_with.rs
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+use crate::iter::{FusedIterator, TrustedLen};
+
+/// Creates an iterator that lazily generates a value exactly once by invoking
+/// the provided closure.
+///
+/// This is commonly used to adapt a single value generator into a [`chain()`] of
+/// other kinds of iteration. Maybe you have an iterator that covers almost
+/// everything, but you need an extra special case. Maybe you have a function
+/// which works on iterators, but you only need to process one value.
+///
+/// Unlike [`once()`], this function will lazily generate the value on request.
+///
+/// [`chain()`]: Iterator::chain
+/// [`once()`]: crate::iter::once
+///
+/// # Examples
+///
+/// Basic usage:
+///
+/// ```
+/// use std::iter;
+///
+/// // one is the loneliest number
+/// let mut one = iter::once_with(|| 1);
+///
+/// assert_eq!(Some(1), one.next());
+///
+/// // just one, that's all we get
+/// assert_eq!(None, one.next());
+/// ```
+///
+/// Chaining together with another iterator. Let's say that we want to iterate
+/// over each file of the `.foo` directory, but also a configuration file,
+/// `.foorc`:
+///
+/// ```no_run
+/// use std::iter;
+/// use std::fs;
+/// use std::path::PathBuf;
+///
+/// let dirs = fs::read_dir(".foo").unwrap();
+///
+/// // we need to convert from an iterator of DirEntry-s to an iterator of
+/// // PathBufs, so we use map
+/// let dirs = dirs.map(|file| file.unwrap().path());
+///
+/// // now, our iterator just for our config file
+/// let config = iter::once_with(|| PathBuf::from(".foorc"));
+///
+/// // chain the two iterators together into one big iterator
+/// let files = dirs.chain(config);
+///
+/// // this will give us all of the files in .foo as well as .foorc
+/// for f in files {
+///     println!("{f:?}");
+/// }
+/// ```
+#[inline]
+#[stable(feature = "iter_once_with", since = "1.43.0")]
+pub fn once_with<A, F: FnOnce() -> A>(gen: F) -> OnceWith<F> {
+    OnceWith { gen: Some(gen) }
+}
+
+/// An iterator that yields a single element of type `A` by
+/// applying the provided closure `F: FnOnce() -> A`.
+///
+/// This `struct` is created by the [`once_with()`] function.
+/// See its documentation for more.
+#[derive(Clone, Debug)]
+#[stable(feature = "iter_once_with", since = "1.43.0")]
+pub struct OnceWith<F> {
+    gen: Option<F>,
+}
+
+#[stable(feature = "iter_once_with", since = "1.43.0")]
+impl<A, F: FnOnce() -> A> Iterator for OnceWith<F> {
+    type Item = A;
+
+    #[inline]
+    fn next(&mut self) -> Option<A> {
+        let f = self.gen.take()?;
+        Some(f())
+    }
+
+    #[inline]
+    fn size_hint(&self) -> (usize, Option<usize>) {
+        self.gen.iter().size_hint()
+    }
+}
+
+#[stable(feature = "iter_once_with", since = "1.43.0")]
+impl<A, F: FnOnce() -> A> DoubleEndedIterator for OnceWith<F> {
+    fn next_back(&mut self) -> Option<A> {
+        self.next()
+    }
+}
+
+#[stable(feature = "iter_once_with", since = "1.43.0")]
+impl<A, F: FnOnce() -> A> ExactSizeIterator for OnceWith<F> {
+    fn len(&self) -> usize {
+        self.gen.iter().len()
+    }
+}
+
+#[stable(feature = "iter_once_with", since = "1.43.0")]
+impl<A, F: FnOnce() -> A> FusedIterator for OnceWith<F> {}
+
+#[stable(feature = "iter_once_with", since = "1.43.0")]
+unsafe impl<A, F: FnOnce() -> A> TrustedLen for OnceWith<F> {}