diff --git a/compiler/rustc_data_structures/src/graph/iterate/mod.rs b/compiler/rustc_data_structures/src/graph/iterate/mod.rs
index bc3d1ce53bac5..5f42d46e28575 100644
--- a/compiler/rustc_data_structures/src/graph/iterate/mod.rs
+++ b/compiler/rustc_data_structures/src/graph/iterate/mod.rs
@@ -1,6 +1,7 @@
 use super::{DirectedGraph, WithNumNodes, WithStartNode, WithSuccessors};
 use rustc_index::bit_set::BitSet;
 use rustc_index::vec::IndexVec;
+use std::ops::ControlFlow;
 
 #[cfg(test)]
 mod tests;
@@ -86,10 +87,6 @@ where
     }
 }
 
-/// Allows searches to terminate early with a value.
-// FIXME (#75744): remove the alias once the generics are in a better order and `C=()`.
-pub type ControlFlow<T> = std::ops::ControlFlow<(), T>;
-
 /// The status of a node in the depth-first search.
 ///
 /// See the documentation of `TriColorDepthFirstSearch` to see how a node's status is updated
diff --git a/compiler/rustc_mir_build/src/lints.rs b/compiler/rustc_mir_build/src/lints.rs
index a9620b83124e0..576b537c01766 100644
--- a/compiler/rustc_mir_build/src/lints.rs
+++ b/compiler/rustc_mir_build/src/lints.rs
@@ -1,5 +1,5 @@
 use rustc_data_structures::graph::iterate::{
-    ControlFlow, NodeStatus, TriColorDepthFirstSearch, TriColorVisitor,
+    NodeStatus, TriColorDepthFirstSearch, TriColorVisitor,
 };
 use rustc_hir::intravisit::FnKind;
 use rustc_middle::hir::map::blocks::FnLikeNode;
@@ -8,6 +8,7 @@ use rustc_middle::ty::subst::{GenericArg, InternalSubsts};
 use rustc_middle::ty::{self, AssocItem, AssocItemContainer, Instance, TyCtxt};
 use rustc_session::lint::builtin::UNCONDITIONAL_RECURSION;
 use rustc_span::Span;
+use std::ops::ControlFlow;
 
 crate fn check<'tcx>(tcx: TyCtxt<'tcx>, body: &Body<'tcx>) {
     let def_id = body.source.def_id().expect_local();
diff --git a/library/core/src/iter/adapters/mod.rs b/library/core/src/iter/adapters/mod.rs
index bf30dcb7689fa..9c8e639c2d802 100644
--- a/library/core/src/iter/adapters/mod.rs
+++ b/library/core/src/iter/adapters/mod.rs
@@ -1280,7 +1280,7 @@ where
         #[inline]
         fn find<T, B>(
             f: &mut impl FnMut(T) -> Option<B>,
-        ) -> impl FnMut((), T) -> ControlFlow<(), B> + '_ {
+        ) -> impl FnMut((), T) -> ControlFlow<B> + '_ {
             move |(), x| match f(x) {
                 Some(x) => ControlFlow::Break(x),
                 None => ControlFlow::CONTINUE,
@@ -2059,7 +2059,7 @@ where
             flag: &'a mut bool,
             p: &'a mut impl FnMut(&T) -> bool,
             mut fold: impl FnMut(Acc, T) -> R + 'a,
-        ) -> impl FnMut(Acc, T) -> ControlFlow<Acc, R> + 'a {
+        ) -> impl FnMut(Acc, T) -> ControlFlow<R, Acc> + 'a {
             move |acc, x| {
                 if p(&x) {
                     ControlFlow::from_try(fold(acc, x))
@@ -2372,7 +2372,7 @@ where
         fn check<T, Acc, R: Try<Ok = Acc>>(
             mut n: usize,
             mut fold: impl FnMut(Acc, T) -> R,
-        ) -> impl FnMut(Acc, T) -> ControlFlow<Acc, R> {
+        ) -> impl FnMut(Acc, T) -> ControlFlow<R, Acc> {
             move |acc, x| {
                 n -= 1;
                 let r = fold(acc, x);
@@ -2496,7 +2496,7 @@ where
         fn check<'a, T, Acc, R: Try<Ok = Acc>>(
             n: &'a mut usize,
             mut fold: impl FnMut(Acc, T) -> R + 'a,
-        ) -> impl FnMut(Acc, T) -> ControlFlow<Acc, R> + 'a {
+        ) -> impl FnMut(Acc, T) -> ControlFlow<R, Acc> + 'a {
             move |acc, x| {
                 *n -= 1;
                 let r = fold(acc, x);
@@ -2681,7 +2681,7 @@ where
             state: &'a mut St,
             f: &'a mut impl FnMut(&mut St, T) -> Option<B>,
             mut fold: impl FnMut(Acc, B) -> R + 'a,
-        ) -> impl FnMut(Acc, T) -> ControlFlow<Acc, R> + 'a {
+        ) -> impl FnMut(Acc, T) -> ControlFlow<R, Acc> + 'a {
             move |acc, x| match f(state, x) {
                 None => ControlFlow::Break(try { acc }),
                 Some(x) => ControlFlow::from_try(fold(acc, x)),
diff --git a/library/core/src/iter/traits/double_ended.rs b/library/core/src/iter/traits/double_ended.rs
index 87fe3c210402e..6f8cb6b5a65b6 100644
--- a/library/core/src/iter/traits/double_ended.rs
+++ b/library/core/src/iter/traits/double_ended.rs
@@ -339,9 +339,7 @@ pub trait DoubleEndedIterator: Iterator {
         P: FnMut(&Self::Item) -> bool,
     {
         #[inline]
-        fn check<T>(
-            mut predicate: impl FnMut(&T) -> bool,
-        ) -> impl FnMut((), T) -> ControlFlow<(), T> {
+        fn check<T>(mut predicate: impl FnMut(&T) -> bool) -> impl FnMut((), T) -> ControlFlow<T> {
             move |(), x| {
                 if predicate(&x) { ControlFlow::Break(x) } else { ControlFlow::CONTINUE }
             }
diff --git a/library/core/src/iter/traits/iterator.rs b/library/core/src/iter/traits/iterator.rs
index 18b4adc23e8ef..7fc60caec2a73 100644
--- a/library/core/src/iter/traits/iterator.rs
+++ b/library/core/src/iter/traits/iterator.rs
@@ -2109,7 +2109,7 @@ pub trait Iterator {
         F: FnMut(Self::Item) -> bool,
     {
         #[inline]
-        fn check<T>(mut f: impl FnMut(T) -> bool) -> impl FnMut((), T) -> ControlFlow<(), ()> {
+        fn check<T>(mut f: impl FnMut(T) -> bool) -> impl FnMut((), T) -> ControlFlow<()> {
             move |(), x| {
                 if f(x) { ControlFlow::CONTINUE } else { ControlFlow::BREAK }
             }
@@ -2162,7 +2162,7 @@ pub trait Iterator {
         F: FnMut(Self::Item) -> bool,
     {
         #[inline]
-        fn check<T>(mut f: impl FnMut(T) -> bool) -> impl FnMut((), T) -> ControlFlow<(), ()> {
+        fn check<T>(mut f: impl FnMut(T) -> bool) -> impl FnMut((), T) -> ControlFlow<()> {
             move |(), x| {
                 if f(x) { ControlFlow::BREAK } else { ControlFlow::CONTINUE }
             }
@@ -2222,9 +2222,7 @@ pub trait Iterator {
         P: FnMut(&Self::Item) -> bool,
     {
         #[inline]
-        fn check<T>(
-            mut predicate: impl FnMut(&T) -> bool,
-        ) -> impl FnMut((), T) -> ControlFlow<(), T> {
+        fn check<T>(mut predicate: impl FnMut(&T) -> bool) -> impl FnMut((), T) -> ControlFlow<T> {
             move |(), x| {
                 if predicate(&x) { ControlFlow::Break(x) } else { ControlFlow::CONTINUE }
             }
@@ -2255,9 +2253,7 @@ pub trait Iterator {
         F: FnMut(Self::Item) -> Option<B>,
     {
         #[inline]
-        fn check<T, B>(
-            mut f: impl FnMut(T) -> Option<B>,
-        ) -> impl FnMut((), T) -> ControlFlow<(), B> {
+        fn check<T, B>(mut f: impl FnMut(T) -> Option<B>) -> impl FnMut((), T) -> ControlFlow<B> {
             move |(), x| match f(x) {
                 Some(x) => ControlFlow::Break(x),
                 None => ControlFlow::CONTINUE,
@@ -2296,7 +2292,7 @@ pub trait Iterator {
         R: Try<Ok = bool>,
     {
         #[inline]
-        fn check<F, T, R>(mut f: F) -> impl FnMut((), T) -> ControlFlow<(), Result<T, R::Error>>
+        fn check<F, T, R>(mut f: F) -> impl FnMut((), T) -> ControlFlow<Result<T, R::Error>>
         where
             F: FnMut(&T) -> R,
             R: Try<Ok = bool>,
diff --git a/library/core/src/ops/control_flow.rs b/library/core/src/ops/control_flow.rs
index 3bca3ff97332b..5ede1ba8e2c10 100644
--- a/library/core/src/ops/control_flow.rs
+++ b/library/core/src/ops/control_flow.rs
@@ -3,7 +3,7 @@ use crate::ops::Try;
 /// Used to make try_fold closures more like normal loops
 #[unstable(feature = "control_flow_enum", reason = "new API", issue = "75744")]
 #[derive(Debug, Clone, Copy, PartialEq)]
-pub enum ControlFlow<C, B> {
+pub enum ControlFlow<B, C = ()> {
     /// Continue in the loop, using the given value for the next iteration
     Continue(C),
     /// Exit the loop, yielding the given value
@@ -11,7 +11,7 @@ pub enum ControlFlow<C, B> {
 }
 
 #[unstable(feature = "control_flow_enum", reason = "new API", issue = "75744")]
-impl<C, B> Try for ControlFlow<C, B> {
+impl<B, C> Try for ControlFlow<B, C> {
     type Ok = C;
     type Error = B;
     #[inline]
@@ -31,7 +31,7 @@ impl<C, B> Try for ControlFlow<C, B> {
     }
 }
 
-impl<C, B> ControlFlow<C, B> {
+impl<B, C> ControlFlow<B, C> {
     /// Returns `true` if this is a `Break` variant.
     #[inline]
     #[unstable(feature = "control_flow_enum", reason = "new API", issue = "75744")]
@@ -58,7 +58,7 @@ impl<C, B> ControlFlow<C, B> {
     }
 }
 
-impl<R: Try> ControlFlow<R::Ok, R> {
+impl<R: Try> ControlFlow<R, R::Ok> {
     /// Create a `ControlFlow` from any type implementing `Try`.
     #[unstable(feature = "control_flow_enum", reason = "new API", issue = "75744")]
     #[inline]
@@ -80,7 +80,7 @@ impl<R: Try> ControlFlow<R::Ok, R> {
     }
 }
 
-impl<B> ControlFlow<(), B> {
+impl<B> ControlFlow<B, ()> {
     /// It's frequently the case that there's no value needed with `Continue`,
     /// so this provides a way to avoid typing `(())`, if you prefer it.
     ///
@@ -102,7 +102,7 @@ impl<B> ControlFlow<(), B> {
     pub const CONTINUE: Self = ControlFlow::Continue(());
 }
 
-impl<C> ControlFlow<C, ()> {
+impl<C> ControlFlow<(), C> {
     /// APIs like `try_for_each` don't need values with `Break`,
     /// so this provides a way to avoid typing `(())`, if you prefer it.
     ///