diff --git a/main-settings/src/main/scala/sbt/std/InputConvert.scala b/main-settings/src/main/scala/sbt/std/InputConvert.scala
index 3a830fa54..59fe8794b 100644
--- a/main-settings/src/main/scala/sbt/std/InputConvert.scala
+++ b/main-settings/src/main/scala/sbt/std/InputConvert.scala
@@ -12,7 +12,6 @@ import sbt.internal.util.appmacro.{ Convert, ContextUtil }
 import sbt.internal.util.complete.Parser
 import Def.Initialize
 import sbt.util.Applicative
-import sbt.internal.util.Types.Compose
 import scala.quoted.*
 
 class InputInitConvert[C <: Quotes & scala.Singleton](override val qctx: C, valStart: Int)
@@ -94,7 +93,7 @@ class FullConvert[C <: Quotes & scala.Singleton](override val qctx: C, valStart:
     }
     Converted.success(t.asTerm)
 
-  def appExpr: Expr[Applicative[Compose[Initialize, Task]]] =
+  def appExpr: Expr[Applicative[[a] =>> Initialize[Task[a]]]] =
     '{ FullInstance.initializeTaskMonad }
 end FullConvert
 
diff --git a/main-settings/src/main/scala/sbt/std/Instances.scala b/main-settings/src/main/scala/sbt/std/Instances.scala
index 3ea614a4f..223372d65 100644
--- a/main-settings/src/main/scala/sbt/std/Instances.scala
+++ b/main-settings/src/main/scala/sbt/std/Instances.scala
@@ -10,7 +10,7 @@ package std
 
 import Def.Initialize
 import sbt.util.{ Applicative, Monad }
-import sbt.internal.util.Types.{ const, Compose }
+import sbt.internal.util.Types.const
 import sbt.internal.util.complete.{ DefaultParsers, Parser }
 
 object InitializeInstance:
@@ -28,8 +28,8 @@ end InitializeInstance
 private[std] object ComposeInstance:
   import InitializeInstance.initializeMonad
   val InitInstance = summon[Applicative[Initialize]]
-  val F1F2: Applicative[Compose[Initialize, Task]] =
-    summon[Applicative[Compose[Initialize, Task]]]
+  val F1F2: Applicative[[a] =>> Initialize[Task[a]]] =
+    summon[Applicative[[a] =>> Initialize[Task[a]]]]
 end ComposeInstance
 
 object ParserInstance:
@@ -60,8 +60,8 @@ object FullInstance:
   )
 
   given Monad[Initialize] = InitializeInstance.initializeMonad
-  val F1F2: Applicative[Compose[Initialize, Task]] = ComposeInstance.F1F2
-  given initializeTaskMonad: Monad[Compose[Initialize, Task]] with
+  val F1F2: Applicative[[a] =>> Initialize[Task[a]]] = ComposeInstance.F1F2
+  given initializeTaskMonad: Monad[[a] =>> Initialize[Task[a]]] with
     type F[x] = Initialize[Task[x]]
     override def pure[A1](x: () => A1): Initialize[Task[A1]] = F1F2.pure(x)
     override def ap[A1, A2](ff: Initialize[Task[A1 => A2]])(
diff --git a/util-collection/src/main/scala/sbt/internal/util/TypeFunctions.scala b/util-collection/src/main/scala/sbt/internal/util/TypeFunctions.scala
index 78712d7f5..78a46a933 100644
--- a/util-collection/src/main/scala/sbt/internal/util/TypeFunctions.scala
+++ b/util-collection/src/main/scala/sbt/internal/util/TypeFunctions.scala
@@ -11,15 +11,6 @@ trait TypeFunctions:
   type Id[X] = X
   type NothingK[X] = Nothing
 
-  /*
-  import TypeFunctions._
-  sealed trait Const[A] { type Apply[B] = A }
-  sealed trait ConstK[A] { type l[L[x]] = A }
-  type ConstK[A] = [F[_]] =>> A
-   */
-
-  type Compose[F1[_], F2[_]] = [a] =>> F1[F2[a]]
-
   sealed trait ∙[A[_], B[_]] { type l[T] = A[B[T]] }
   private type AnyLeft[A] = Left[A, Nothing]
   private type AnyRight[A] = Right[Nothing, A]
@@ -40,10 +31,6 @@ trait TypeFunctions:
   final def idK[F[_]]: [a] => F[a] => F[a] = [a] =>
     (fa: F[a]) => fa // .setToString("TypeFunctions.idK")
 
-  inline def nestCon[F1[_], F2[_], F3[_]](
-      f: [a] => F1[a] => F2[a]
-  ): [a] => Compose[F1, F3][a] => Compose[F2, F3][a] =
-    f.asInstanceOf[[a] => Compose[F1, F3][a] => Compose[F2, F3][a]]
 end TypeFunctions
 
 /*
diff --git a/util-collection/src/main/scala/sbt/util/Applicative.scala b/util-collection/src/main/scala/sbt/util/Applicative.scala
index 8d5c00a20..088ee3559 100644
--- a/util-collection/src/main/scala/sbt/util/Applicative.scala
+++ b/util-collection/src/main/scala/sbt/util/Applicative.scala
@@ -7,8 +7,6 @@
 
 package sbt.util
 
-import sbt.internal.util.Types.Compose
-
 trait Applicative[F[_]] extends Apply[F]:
   def pure[A1](x: () => A1): F[A1]
 
@@ -20,14 +18,12 @@ object Applicative:
   given Applicative[Option] = OptionInstances.optionMonad
   given Applicative[List] = ListInstances.listMonad
 
-  given [F1[_], F2[_]](using Applicative[F1], Applicative[F2]): Applicative[Compose[F1, F2]] with
+  given [F1[_], F2[_]](using Applicative[F1], Applicative[F2]): Applicative[[a] =>> F1[F2[a]]] with
     type F[x] = F1[F2[x]]
     val F1 = summon[Applicative[F1]]
     val F2 = summon[Applicative[F2]]
     override def pure[A1](x: () => A1): F1[F2[A1]] = F1.pure(() => F2.pure(x))
-    override def ap[A1, A2](f1f2f: Compose[F1, F2][A1 => A2])(
-        f1f2a: Compose[F1, F2][A1]
-    ): F1[F2[A2]] =
+    override def ap[A1, A2](f1f2f: F1[F2[A1 => A2]])(f1f2a: F1[F2[A1]]): F1[F2[A2]] =
       F1.ap(F1.map(f1f2f) { (f2f: F2[A1 => A2]) => (f2a: F2[A1]) => F2.ap(f2f)(f2a) })(f1f2a)
 
 end Applicative