Make the usage of kind projections more consistent.

core/src/main/scala/cats/Alternative.scala

@@ -3,7 +3,7 @@ package cats
 import simulacrum.typeclass
 
 @typeclass trait Alternative[F[_]] extends Applicative[F] with MonoidK[F] { self =>
-  override def compose[G[_]: Applicative]: Alternative[Lambda[A => F[G[A]]]] =
+  override def compose[G[_]: Applicative]: Alternative[λ[α => F[G[α]]]] =
     new ComposedAlternative[F, G] {
       val F = self
       val G = Applicative[G]

core/src/main/scala/cats/Applicative.scala

@@ -44,7 +44,7 @@ import simulacrum.typeclass
   def sequence[G[_], A](as: G[F[A]])(implicit G: Traverse[G]): F[G[A]] =
     G.sequence(as)(this)
 
-  def compose[G[_]: Applicative]: Applicative[Lambda[A => F[G[A]]]] =
+  def compose[G[_]: Applicative]: Applicative[λ[α => F[G[α]]]] =
     new ComposedApplicative[F, G] {
       val F = self
       val G = Applicative[G]

core/src/main/scala/cats/Apply.scala

@@ -58,7 +58,7 @@ trait Apply[F[_]] extends Functor[F] with Cartesian[F] with ApplyArityFunctions[
   def map2Eval[A, B, Z](fa: F[A], fb: Eval[F[B]])(f: (A, B) => Z): Eval[F[Z]] =
     fb.map(fb => map2(fa, fb)(f))
 
-  def compose[G[_]: Apply]: Apply[Lambda[A => F[G[A]]]] =
+  def compose[G[_]: Apply]: Apply[λ[α => F[G[α]]]] =
     new ComposedApply[F, G] {
       val F = self
       val G = Apply[G]

core/src/main/scala/cats/Bifoldable.scala

@@ -17,7 +17,7 @@ trait Bifoldable[F[_, _]] extends Any with Serializable { self =>
       (c: C, b: B) => C.combine(c, g(b))
     )
 
-  def compose[G[_, _]](implicit ev: Bifoldable[G]): Bifoldable[Lambda[(A, B) => F[G[A, B], G[A, B]]]] =
+  def compose[G[_, _]](implicit ev: Bifoldable[G]): Bifoldable[λ[(α, β) => F[G[α, β], G[α, β]]]] =
     new CompositeBifoldable[F, G] {
       val F = self
       val G = ev
@@ -28,7 +28,7 @@ object Bifoldable {
   def apply[F[_, _]](implicit F: Bifoldable[F]): Bifoldable[F] = F
 }
 
-trait CompositeBifoldable[F[_, _], G[_, _]] extends Bifoldable[Lambda[(A, B) => F[G[A, B], G[A, B]]]] {
+trait CompositeBifoldable[F[_, _], G[_, _]] extends Bifoldable[λ[(α, β) => F[G[α, β], G[α, β]]]] {
   implicit def F: Bifoldable[F]
   implicit def G: Bifoldable[G]
 

core/src/main/scala/cats/Bitraverse.scala

@@ -14,7 +14,7 @@ trait Bitraverse[F[_, _]] extends Bifoldable[F] with Bifunctor[F] { self =>
     bitraverse(fab)(identity, identity)
 
   /** If F and G are both [[cats.Bitraverse]] then so is their composition F[G[_, _], G[_, _]] */
-  def compose[G[_, _]](implicit ev: Bitraverse[G]): Bitraverse[Lambda[(A, B) => F[G[A, B], G[A, B]]]] =
+  def compose[G[_, _]](implicit ev: Bitraverse[G]): Bitraverse[λ[(α, β) => F[G[α, β], G[α, β]]]] =
     new CompositeBitraverse[F, G] {
       val F = self
       val G = ev
@@ -29,7 +29,7 @@ object Bitraverse {
 }
 
 trait CompositeBitraverse[F[_, _], G[_, _]]
-    extends Bitraverse[Lambda[(A, B) => F[G[A, B], G[A, B]]]]
+    extends Bitraverse[λ[(α, β) => F[G[α, β], G[α, β]]]]
     with    CompositeBifoldable[F, G] {
   def F: Bitraverse[F]
   def G: Bitraverse[G]

core/src/main/scala/cats/Composed.scala

@@ -2,23 +2,23 @@ package cats
 
 import cats.functor._
 
-private[cats] trait ComposedInvariant[F[_], G[_]] extends Invariant[Lambda[A => F[G[A]]]] { outer =>
+private[cats] trait ComposedInvariant[F[_], G[_]] extends Invariant[λ[α => F[G[α]]]] { outer =>
   def F: Invariant[F]
   def G: Invariant[G]
 
   override def imap[A, B](fga: F[G[A]])(f: A => B)(g: B => A): F[G[B]] =
     F.imap(fga)(ga => G.imap(ga)(f)(g))(gb => G.imap(gb)(g)(f))
 }
 
-private[cats] trait ComposedFunctor[F[_], G[_]] extends Functor[Lambda[A => F[G[A]]]] with ComposedInvariant[F, G] { outer =>
+private[cats] trait ComposedFunctor[F[_], G[_]] extends Functor[λ[α => F[G[α]]]] with ComposedInvariant[F, G] { outer =>
   def F: Functor[F]
   def G: Functor[G]
 
   override def map[A, B](fga: F[G[A]])(f: A => B): F[G[B]] =
     F.map(fga)(ga => G.map(ga)(f))
 }
 
-private[cats] trait ComposedApply[F[_], G[_]] extends Apply[Lambda[A => F[G[A]]]] with ComposedFunctor[F, G] { outer =>
+private[cats] trait ComposedApply[F[_], G[_]] extends Apply[λ[α => F[G[α]]]] with ComposedFunctor[F, G] { outer =>
   def F: Apply[F]
   def G: Apply[G]
 
@@ -29,30 +29,30 @@ private[cats] trait ComposedApply[F[_], G[_]] extends Apply[Lambda[A => F[G[A]]]
     F.map2(fga, fgb)(G.product)
 }
 
-private[cats] trait ComposedApplicative[F[_], G[_]] extends Applicative[Lambda[A => F[G[A]]]] with ComposedApply[F, G] { outer =>
+private[cats] trait ComposedApplicative[F[_], G[_]] extends Applicative[λ[α => F[G[α]]]] with ComposedApply[F, G] { outer =>
   def F: Applicative[F]
   def G: Applicative[G]
 
   override def pure[A](x: A): F[G[A]] = F.pure(G.pure(x))
 }
 
-private[cats] trait ComposedSemigroupK[F[_], G[_]] extends SemigroupK[Lambda[A => F[G[A]]]] { outer =>
+private[cats] trait ComposedSemigroupK[F[_], G[_]] extends SemigroupK[λ[α => F[G[α]]]] { outer =>
   def F: SemigroupK[F]
 
   override def combineK[A](x: F[G[A]], y: F[G[A]]): F[G[A]] = F.combineK(x, y)
 }
 
-private[cats] trait ComposedMonoidK[F[_], G[_]] extends MonoidK[Lambda[A => F[G[A]]]] with ComposedSemigroupK[F, G] { outer =>
+private[cats] trait ComposedMonoidK[F[_], G[_]] extends MonoidK[λ[α => F[G[α]]]] with ComposedSemigroupK[F, G] { outer =>
   def F: MonoidK[F]
 
   override def empty[A]: F[G[A]] = F.empty
 }
 
-private[cats] trait ComposedAlternative[F[_], G[_]] extends Alternative[Lambda[A => F[G[A]]]] with ComposedApplicative[F, G] with ComposedMonoidK[F, G] { outer =>
+private[cats] trait ComposedAlternative[F[_], G[_]] extends Alternative[λ[α => F[G[α]]]] with ComposedApplicative[F, G] with ComposedMonoidK[F, G] { outer =>
   def F: Alternative[F]
 }
 
-private[cats] trait ComposedFoldable[F[_], G[_]] extends Foldable[Lambda[A => F[G[A]]]] { outer =>
+private[cats] trait ComposedFoldable[F[_], G[_]] extends Foldable[λ[α => F[G[α]]]] { outer =>
   def F: Foldable[F]
   def G: Foldable[G]
 
@@ -63,15 +63,15 @@ private[cats] trait ComposedFoldable[F[_], G[_]] extends Foldable[Lambda[A => F[
     F.foldRight(fga, lb)((ga, lb) => G.foldRight(ga, lb)(f))
 }
 
-private[cats] trait ComposedTraverse[F[_], G[_]] extends Traverse[Lambda[A => F[G[A]]]] with ComposedFoldable[F, G] with ComposedFunctor[F, G] { outer =>
+private[cats] trait ComposedTraverse[F[_], G[_]] extends Traverse[λ[α => F[G[α]]]] with ComposedFoldable[F, G] with ComposedFunctor[F, G] { outer =>
   def F: Traverse[F]
   def G: Traverse[G]
 
   override def traverse[H[_]: Applicative, A, B](fga: F[G[A]])(f: A => H[B]): H[F[G[B]]] =
     F.traverse(fga)(ga => G.traverse(ga)(f))
 }
 
-private[cats] trait ComposedReducible[F[_], G[_]] extends Reducible[Lambda[A => F[G[A]]]] with ComposedFoldable[F, G] { outer =>
+private[cats] trait ComposedReducible[F[_], G[_]] extends Reducible[λ[α => F[G[α]]]] with ComposedFoldable[F, G] { outer =>
   def F: Reducible[F]
   def G: Reducible[G]
 
@@ -90,39 +90,39 @@ private[cats] trait ComposedReducible[F[_], G[_]] extends Reducible[Lambda[A =>
   }
 }
 
-private[cats] trait ComposedContravariant[F[_], G[_]] extends Functor[Lambda[A => F[G[A]]]] { outer =>
+private[cats] trait ComposedContravariant[F[_], G[_]] extends Functor[λ[α => F[G[α]]]] { outer =>
   def F: Contravariant[F]
   def G: Contravariant[G]
 
   override def map[A, B](fga: F[G[A]])(f: A => B): F[G[B]] =
     F.contramap(fga)(gb => G.contramap(gb)(f))
 }
 
-private[cats] trait ComposedContravariantCovariant[F[_], G[_]] extends Contravariant[Lambda[A => F[G[A]]]] { outer =>
+private[cats] trait ComposedContravariantCovariant[F[_], G[_]] extends Contravariant[λ[α => F[G[α]]]] { outer =>
   def F: Contravariant[F]
   def G: Functor[G]
 
   override def contramap[A, B](fga: F[G[A]])(f: B => A): F[G[B]] =
     F.contramap(fga)(gb => G.map(gb)(f))
 }
 
-private[cats] trait ComposedCovariantContravariant[F[_], G[_]] extends Contravariant[Lambda[A => F[G[A]]]] { outer =>
+private[cats] trait ComposedCovariantContravariant[F[_], G[_]] extends Contravariant[λ[α => F[G[α]]]] { outer =>
   def F: Functor[F]
   def G: Contravariant[G]
 
   override def contramap[A, B](fga: F[G[A]])(f: B => A): F[G[B]] =
     F.map(fga)(ga => G.contramap(ga)(f))
 }
 
-private[cats] trait ComposedInvariantCovariant[F[_], G[_]] extends Invariant[Lambda[A => F[G[A]]]] { outer =>
+private[cats] trait ComposedInvariantCovariant[F[_], G[_]] extends Invariant[λ[α => F[G[α]]]] { outer =>
   def F: Invariant[F]
   def G: Functor[G]
 
   override def imap[A, B](fga: F[G[A]])(f: A => B)(g: B => A): F[G[B]] =
     F.imap(fga)(ga => G.map(ga)(f))(gb => G.map(gb)(g))
 }
 
-private[cats] trait ComposedInvariantContravariant[F[_], G[_]] extends Invariant[Lambda[A => F[G[A]]]] { outer =>
+private[cats] trait ComposedInvariantContravariant[F[_], G[_]] extends Invariant[λ[α => F[G[α]]]] { outer =>
   def F: Invariant[F]
   def G: Contravariant[G]
 

core/src/main/scala/cats/Foldable.scala

@@ -269,7 +269,7 @@ import simulacrum.typeclass
   def nonEmpty[A](fa: F[A]): Boolean =
     !isEmpty(fa)
 
-  def compose[G[_]: Foldable]: Foldable[Lambda[A => F[G[A]]]] =
+  def compose[G[_]: Foldable]: Foldable[λ[α => F[G[α]]]] =
     new ComposedFoldable[F, G] {
       val F = self
       val G = Foldable[G]

core/src/main/scala/cats/Functor.scala

@@ -39,13 +39,13 @@ import simulacrum.typeclass
    */
   def as[A, B](fa: F[A], b: B): F[B] = map(fa)(_ => b)
 
-  def compose[G[_]: Functor]: Functor[Lambda[A => F[G[A]]]] =
+  def compose[G[_]: Functor]: Functor[λ[α => F[G[α]]]] =
     new ComposedFunctor[F, G] {
       val F = self
       val G = Functor[G]
     }
 
-  override def composeContravariant[G[_]: Contravariant]: Contravariant[Lambda[A => F[G[A]]]] =
+  override def composeContravariant[G[_]: Contravariant]: Contravariant[λ[α => F[G[α]]]] =
     new ComposedCovariantContravariant[F, G] {
       val F = self
       val G = Contravariant[G]

core/src/main/scala/cats/MonoidK.scala

@@ -38,7 +38,7 @@ import simulacrum.typeclass
       def combine(x: F[A], y: F[A]): F[A] = self.combineK(x, y)
     }
 
-  override def compose[G[_]]: MonoidK[Lambda[A => F[G[A]]]] =
+  override def compose[G[_]]: MonoidK[λ[α => F[G[α]]]] =
     new ComposedMonoidK[F, G] {
       val F = self
     }

core/src/main/scala/cats/Reducible.scala

@@ -107,7 +107,7 @@ import simulacrum.typeclass
   def sequence1_[G[_], A](fga: F[G[A]])(implicit G: Apply[G]): G[Unit] =
     G.map(reduceLeft(fga)((x, y) => G.map2(x, y)((_, b) => b)))(_ => ())
 
-  def compose[G[_]: Reducible]: Reducible[Lambda[A => F[G[A]]]] =
+  def compose[G[_]: Reducible]: Reducible[λ[α => F[G[α]]]] =
     new ComposedReducible[F, G] {
       val F = self
       val G = Reducible[G]

core/src/main/scala/cats/SemigroupK.scala

@@ -36,7 +36,7 @@ import simulacrum.typeclass
       def combine(x: F[A], y: F[A]): F[A] = self.combineK(x, y)
     }
 
-  def compose[G[_]]: SemigroupK[Lambda[A => F[G[A]]]] =
+  def compose[G[_]]: SemigroupK[λ[α => F[G[α]]]] =
     new ComposedSemigroupK[F, G] {
       val F = self
     }

core/src/main/scala/cats/Traverse.scala

@@ -49,7 +49,7 @@ import simulacrum.typeclass
   def sequenceU[GA](fga: F[GA])(implicit U: Unapply[Applicative,GA]): U.M[F[U.A]] =
     traverse(fga)(U.subst)(U.TC)
 
-  def compose[G[_]: Traverse]: Traverse[Lambda[A => F[G[A]]]] =
+  def compose[G[_]: Traverse]: Traverse[λ[α => F[G[α]]]] =
     new ComposedTraverse[F, G] {
       val F = self
       val G = Traverse[G]

core/src/main/scala/cats/data/Cokleisli.scala

@@ -58,7 +58,7 @@ private[data] sealed abstract class CokleisliInstances extends CokleisliInstance
       fa.map(f)
   }
 
-  implicit def catsDataMonoidKForCokleisli[F[_]](implicit ev: Comonad[F]): MonoidK[Lambda[A => Cokleisli[F, A, A]]] =
+  implicit def catsDataMonoidKForCokleisli[F[_]](implicit ev: Comonad[F]): MonoidK[λ[α => Cokleisli[F, α, α]]] =
     new CokleisliMonoidK[F] { def F: Comonad[F] = ev }
 }
 
@@ -69,7 +69,7 @@ private[data] sealed abstract class CokleisliInstances0 {
   implicit def catsDataProfunctorForCokleisli[F[_]](implicit ev: Functor[F]): Profunctor[Cokleisli[F, ?, ?]] =
     new CokleisliProfunctor[F] { def F: Functor[F] = ev }
 
-  implicit def catsDataSemigroupKForCokleisli[F[_]](implicit ev: CoflatMap[F]): SemigroupK[Lambda[A => Cokleisli[F, A, A]]] =
+  implicit def catsDataSemigroupKForCokleisli[F[_]](implicit ev: CoflatMap[F]): SemigroupK[λ[α => Cokleisli[F, α, α]]] =
     new CokleisliSemigroupK[F] { def F: CoflatMap[F] = ev }
 }
 
@@ -118,13 +118,13 @@ private trait CokleisliProfunctor[F[_]] extends Profunctor[Cokleisli[F, ?, ?]] {
     fab.map(f)
 }
 
-private trait CokleisliSemigroupK[F[_]] extends SemigroupK[Lambda[A => Cokleisli[F, A, A]]] {
+private trait CokleisliSemigroupK[F[_]] extends SemigroupK[λ[α => Cokleisli[F, α, α]]] {
   implicit def F: CoflatMap[F]
 
   def combineK[A](a: Cokleisli[F, A, A], b: Cokleisli[F, A, A]): Cokleisli[F, A, A] = a compose b
 }
 
-private trait CokleisliMonoidK[F[_]] extends MonoidK[Lambda[A => Cokleisli[F, A, A]]] with CokleisliSemigroupK[F] {
+private trait CokleisliMonoidK[F[_]] extends MonoidK[λ[α => Cokleisli[F, α, α]]] with CokleisliSemigroupK[F] {
   implicit def F: Comonad[F]
 
   def empty[A]: Cokleisli[F, A, A] = Cokleisli(F.extract[A])

core/src/main/scala/cats/data/Func.scala

@@ -32,41 +32,41 @@ object Func extends FuncInstances {
 }
 
 private[data] abstract class FuncInstances extends FuncInstances0 {
-  implicit def catsDataApplicativeForFunc[F[_], C](implicit FF: Applicative[F]): Applicative[Lambda[X => Func[F, C, X]]] =
+  implicit def catsDataApplicativeForFunc[F[_], C](implicit FF: Applicative[F]): Applicative[λ[α => Func[F, C, α]]] =
     new FuncApplicative[F, C] {
       def F: Applicative[F] = FF
     }
 }
 
 private[data] abstract class FuncInstances0 extends FuncInstances1 {
-  implicit def catsDataApplyForFunc[F[_], C](implicit FF: Apply[F]): Apply[Lambda[X => Func[F, C, X]]] =
+  implicit def catsDataApplyForFunc[F[_], C](implicit FF: Apply[F]): Apply[λ[α => Func[F, C, α]]] =
     new FuncApply[F, C] {
       def F: Apply[F] = FF
     }
 }
 
 private[data] abstract class FuncInstances1 {
-  implicit def catsDataFunctorForFunc[F[_], C](implicit FF: Functor[F]): Functor[Lambda[X => Func[F, C, X]]] =
+  implicit def catsDataFunctorForFunc[F[_], C](implicit FF: Functor[F]): Functor[λ[α => Func[F, C, α]]] =
     new FuncFunctor[F, C] {
       def F: Functor[F] = FF
     }
 }
 
-sealed trait FuncFunctor[F[_], C] extends Functor[Lambda[X => Func[F, C, X]]] {
+sealed trait FuncFunctor[F[_], C] extends Functor[λ[α => Func[F, C, α]]] {
   def F: Functor[F]
   override def map[A, B](fa: Func[F, C, A])(f: A => B): Func[F, C, B] =
     fa.map(f)(F)
 }
 
-sealed trait FuncApply[F[_], C] extends Apply[Lambda[X => Func[F, C, X]]] with FuncFunctor[F, C] {
+sealed trait FuncApply[F[_], C] extends Apply[λ[α => Func[F, C, α]]] with FuncFunctor[F, C] {
   def F: Apply[F]
   def ap[A, B](f: Func[F, C, A => B])(fa: Func[F, C, A]): Func[F, C, B] =
     Func.func(c => F.ap(f.run(c))(fa.run(c)))
   override def product[A, B](fa: Func[F, C, A], fb: Func[F, C, B]): Func[F, C, (A, B)] =
     Func.func(c => F.product(fa.run(c), fb.run(c)))
 }
 
-sealed trait FuncApplicative[F[_], C] extends Applicative[Lambda[X => Func[F, C, X]]] with FuncApply[F, C] {
+sealed trait FuncApplicative[F[_], C] extends Applicative[λ[α => Func[F, C, α]]] with FuncApply[F, C] {
   def F: Applicative[F]
   def pure[A](a: A): Func[F, C, A] =
     Func.func(c => F.pure(a))
@@ -78,11 +78,11 @@ sealed trait FuncApplicative[F[_], C] extends Applicative[Lambda[X => Func[F, C,
 sealed abstract class AppFunc[F[_], A, B] extends Func[F, A, B] { self =>
   def F: Applicative[F]
 
-  def product[G[_]](g: AppFunc[G, A, B]): AppFunc[Lambda[X => Prod[F, G, X]], A, B] =
+  def product[G[_]](g: AppFunc[G, A, B]): AppFunc[λ[α => Prod[F, G, α]], A, B] =
     {
       implicit val FF: Applicative[F] = self.F
       implicit val GG: Applicative[G] = g.F
-      Func.appFunc[Lambda[X => Prod[F, G, X]], A, B]{
+      Func.appFunc[λ[α => Prod[F, G, α]], A, B]{
         a: A => Prod(self.run(a), g.run(a))
       }
     }
@@ -97,11 +97,10 @@ sealed abstract class AppFunc[F[_], A, B] extends Func[F, A, B] { self =>
   def andThen[G[_], C](g: AppFunc[G, B, C]): AppFunc[Nested[F, G, ?], A, C] =
     g.compose(self)
 
-  def map[C](f: B => C): AppFunc[F, A, C] =
-    {
-      implicit val FF: Applicative[F] = self.F
-      Func.appFunc(a => F.map(self.run(a))(f))
-    }
+  def map[C](f: B => C): AppFunc[F, A, C] = {
+    implicit val FF: Applicative[F] = self.F
+    Func.appFunc(a => F.map(self.run(a))(f))
+  }
 
   def traverse[G[_]](ga: G[A])(implicit GG: Traverse[G]): F[G[B]] =
     GG.traverse(ga)(self.run)(F)
@@ -110,13 +109,13 @@ sealed abstract class AppFunc[F[_], A, B] extends Func[F, A, B] { self =>
 object AppFunc extends AppFuncInstances
 
 private[data] abstract class AppFuncInstances {
-  implicit def appFuncApplicative[F[_], C](implicit FF: Applicative[F]): Applicative[Lambda[X => AppFunc[F, C, X]]] =
+  implicit def appFuncApplicative[F[_], C](implicit FF: Applicative[F]): Applicative[λ[α => AppFunc[F, C, α]]] =
     new AppFuncApplicative[F, C] {
       def F: Applicative[F] = FF
     }
 }
 
-private[data] sealed trait AppFuncApplicative[F[_], C] extends Applicative[Lambda[X => AppFunc[F, C, X]]] {
+private[data] sealed trait AppFuncApplicative[F[_], C] extends Applicative[λ[α => AppFunc[F, C, α]]] {
   def F: Applicative[F]
   override def map[A, B](fa: AppFunc[F, C, A])(f: A => B): AppFunc[F, C, B] =
     fa.map(f)