Add another compose variant with composes inside

(Implementation is really just identity functions, but Scala can't seem to figure that out)

Author: Katrix

dotty/perspective/src/main/scala/perspective/ApplicativeK.scala

@@ -45,6 +45,18 @@ object ApplicativeK:
     extension [A[_]](a: ValueK[A]) override def pure[C]: F[Compose2[G, A]] = F.pure([X] => () => G.pure(a[X]()))
   }
 
+  given composeCatsInsideRight[F[_[_]], G[_]](
+    using F: ApplicativeKC[F],
+  ): ApplicativeKC[[H[_]] =>> F[Compose2[H, G]]] with {
+    extension [A[_], C](fag: F[Compose2[A, G]])
+      override def mapK[B[_]](f: A :~>: B): F[Compose2[B, G]] = F.mapK(fag)([X] => (ag: A[G[X]]) => f(ag))
+
+      override def map2K[B[_], Z[_]](fgb: F[Compose2[B, G]])(f: [X] => (A[X], B[X]) => Z[X]): F[Compose2[Z, G]] =
+        F.map2K(fag)(fgb)([X] => (ag: A[G[X]], bg: B[G[X]]) => f(ag, bg))
+
+    extension [A[_]](a: ValueK[A]) override def pure[C]: F[Compose2[A, G]] = F.pure([X] => () => a[G[X]]())
+  }
+
 /**
   * A version of [[ApplicativeK]] without a normal type as well as a higher
   * kinded type.

dotty/perspective/src/main/scala/perspective/ApplyK.scala

@@ -42,6 +42,14 @@ object ApplyK:
         F.map2K(fga)(fgb)([X] => (ga: G[A[X]], gb: G[B[X]]) => G.map2(ga, gb)((a, b) => f(a, b)))
   }
 
+  given composeCatsInsideRight[F[_[_]], G[_]](using F: ApplyKC[F]): ApplyKC[[H[_]] =>> F[Compose2[H, G]]] with {
+    extension [A[_], C](fag: F[Compose2[A, G]])
+      override def mapK[B[_]](f: A :~>: B): F[Compose2[B, G]] = F.mapK(fag)([X] => (ag: A[G[X]]) => f(ag))
+
+      override def map2K[B[_], Z[_]](fbg: F[Compose2[B, G]])(f: [X] => (A[X], B[X]) => Z[X]): F[Compose2[Z, G]] =
+        F.map2K(fag)(fbg)([X] => (ag: A[G[X]], bg: B[G[X]]) => f(ag, bg))
+  }
+
 /**
   * A version of [[ApplyK]] without a normal type as well as a higher kinded
   * type.

dotty/perspective/src/main/scala/perspective/ContravariantK.scala

@@ -23,4 +23,10 @@ object ContravariantK:
         F.mapK(fga)([X] => (ga: G[A[X]]) => G.contramap[A[X], B[X]](ga)(b => f(b)))
   }
 
+  given composeCatsInsideRight[F[_[_]], G[_]](using F: ContravariantKC[F]): ContravariantKC[[H[_]] =>> F[Compose2[H, G]]] with {
+    extension [A[_], C](fga: F[Compose2[A, G]])
+      override def contramapK[B[_]](f: B :~>: A): F[Compose2[B, G]] =
+        F.contramapK(fga)([X] => (ga: B[G[X]]) => f(ga))
+  }
+
 type ContravariantKC[F[_[_]]] = ContravariantK[IgnoreC[F]]

dotty/perspective/src/main/scala/perspective/DistributiveK.scala

@@ -53,6 +53,17 @@ object DistributiveK:
 
   }
 
+  given composeCatsInsideRight[F[_[_]], G[_]](
+    using F: DistributiveKC[F],
+  ): DistributiveKC[[H[_]] =>> F[Compose2[H, G]]] with {
+    extension [A[_], C](fag: F[Compose2[A, G]])
+      override def mapK[B[_]](f: A :~>: B): F[Compose2[B, G]] = F.mapK(fag)([X] => (ag: A[G[X]]) => f(ag))
+
+    extension [H[_] : Functor, A[_], C](hfag: H[F[Compose2[A, G]]])
+      override def cosequenceK: F[Compose3[H, A, G]] = F.cosequenceK(hfag)
+
+  }
+
 /**
   * A version of [[DistributiveK]] without a normal type as well as a higher
   * kinded type.

dotty/perspective/src/main/scala/perspective/FoldableK.scala

@@ -52,4 +52,15 @@ object FoldableK:
         )
   }
 
+  given composeCatsInsideRight[F[_[_]], G[_]](
+      using F: FoldableKC[F]
+  ): FoldableKC[[H[_]] =>> F[Compose2[H, G]]] with {
+    extension [A[_], C](fag: F[Compose2[A, G]])
+      override def foldLeftK[B](b: B)(f: B => A :~>#: B): B =
+        F.foldLeftK(fag)(b)(bacc => [Z] => (ag: A[G[Z]]) => f(bacc)(ag))
+
+      override def foldRightK[B](b: B)(f: A :~>#: (B => B)): B =
+        F.foldRightK(fag)(b)([Z] => (ag: A[G[Z]]) => (bacc: B) => f(ag)(bacc))
+  }
+
 type FoldableKC[F[_[_]]] = FoldableK[IgnoreC[F]]

dotty/perspective/src/main/scala/perspective/FunctorK.scala

@@ -46,6 +46,11 @@ object FunctorK:
       override def mapK[B[_]](f: A :~>: B): F[Compose2[G, B]] = F.mapK(fga)([X] => (ga: G[A[X]]) => ga.map(a => f(a)))
   }
 
+  given composeCatsInsideRight[F[_[_]], G[_]](using F: FunctorKC[F]): FunctorKC[[H[_]] =>> F[Compose2[H, G]]] with {
+    extension [A[_], C](fag: F[Compose2[A, G]])
+      override def mapK[B[_]](f: A :~>: B): F[Compose2[B, G]] = F.mapK(fag)([X] => (ag: A[G[X]]) => f(ag))
+  }
+
 /**
   * A version of [[FunctorK]] without a normal type as well as a higher kinded
   * type.

dotty/perspective/src/main/scala/perspective/InvariantK.scala

@@ -30,4 +30,14 @@ object InvariantK:
         F.imapK(fga)(f2)(g2)
   }
 
+  given composeCatsInsideRight[F[_[_]], G[_]](
+    using F: InvariantKC[F],
+  ): InvariantKC[[H[_]] =>> F[Compose2[H, G]]] with {
+    extension [A[_], C](fag: F[Compose2[A, G]])
+      override def imapK[B[_]](f: A :~>: B)(g: B :~>: A): F[Compose2[B, G]] =
+        val f2: Compose2[A, G] :~>: Compose2[B, G] = [X] => (ag: A[G[X]]) => f(ag)
+        val g2: Compose2[B, G] :~>: Compose2[A, G] = [X] => (bg: B[G[X]]) => g(bg)
+        F.imapK(fag)(f2)(g2)
+  }
+
 type InvariantKC[F[_[_]]] = InvariantK[IgnoreC[F]]

dotty/perspective/src/main/scala/perspective/TraverseK.scala

@@ -67,6 +67,20 @@ object TraverseK:
         F.traverseK(fga)[H, Compose2[G, B]]([Z] => (ga: G[A[Z]]) => G.traverse[H, A[Z], B[Z]](ga)(a => f(a)))
   }
 
+  given composeCatsInsideRight[F[_[_]], G[_]](
+      using F: TraverseKC[F]
+  ): TraverseKC[[H[_]] =>> F[Compose2[H, G]]] with {
+    extension [A[_], C](fag: F[Compose2[A, G]])
+      override def foldLeftK[B](b: B)(f: B => A :~>#: B): B =
+        F.foldLeftK(fag)(b)(bacc => [Z] => (ag: A[G[Z]]) => f(bacc)(ag))
+
+      override def foldRightK[B](b: B)(f: A :~>#: (B => B)): B =
+        F.foldRightK(fag)(b)([Z] => (ag: A[G[Z]]) => (bacc: B) => f(ag)(bacc))
+
+      def traverseK[H[_]: Applicative, B[_]](f: A :~>: Compose2[H, B]): H[F[Compose2[B, G]]] =
+        F.traverseK(fag)[H, Compose2[B, G]]([Z] => (ag: A[G[Z]]) => f(ag))
+  }
+
 /**
   * A version of [[TraverseK]] without a normal type as well as a higher kinded
   * type.