Type classes: expose super class functions in sub classes. (WIP)

 Also ensure inheritance-based implementations via seal of type class.
 This avoid going through no-op invoke virtuals in most cases.

 WIP: Monoid/Semigroup/Functor->Monad only.

base/shared/src/main/scala/scalaz/BaseHierarchy.scala

@@ -7,8 +7,8 @@ object BaseHierarchy {
     implicit def choiceProfunctor[P[_, _]](implicit P: Choice[P]): Profunctor[P] = P.profunctor
     implicit def monadBind[M[_]](implicit M: Monad[M]): Bind[M] = M.bind
     implicit def monadApplicative[M[_]](implicit M: Monad[M]): Applicative[M] = M.applicative
-    implicit def monadApply[M[_]](implicit M: Monad[M]): Apply[M] = M.applicative.apply
-    implicit def monadFunctor[M[_]](implicit M: Monad[M]): Functor[M] = M.applicative.apply.functor
+    implicit def monadApply[M[_]](implicit M: Monad[M]): Apply[M] = M.apply
+    implicit def monadFunctor[M[_]](implicit M: Monad[M]): Functor[M] = M.functor
     implicit def monoidSemigroup[A](implicit A: Monoid[A]): Semigroup[A] = A.semigroup
     implicit def traversableFoldable[T[_]](implicit T: Traversable[T]): Foldable[T] = T.foldable
     implicit def categoryComposable[=>:[_,_]](implicit C: Category[=>:]): Compose[=>:] = C.compose
@@ -17,13 +17,13 @@ object BaseHierarchy {
 
   trait BH1 extends BH2 {
     implicit def bindApply[M[_]](implicit M: Bind[M]): Apply[M] = M.apply
-    implicit def bindFunctor[M[_]](implicit M: Bind[M]): Functor[M] = M.apply.functor
+    implicit def bindFunctor[M[_]](implicit M: Bind[M]): Functor[M] = M.functor
     implicit def strongProfunctor[P[_, _]](implicit P: Strong[P]): Profunctor[P] = P.profunctor
   }
 
   trait BH2 extends BH3 {
     implicit def applicativeApply[M[_]](implicit M: Applicative[M]): Apply[M] = M.apply
-    implicit def applicativeFunctor[M[_]](implicit M: Applicative[M]): Functor[M] = M.apply.functor
+    implicit def applicativeFunctor[M[_]](implicit M: Applicative[M]): Functor[M] = M.functor
   }
 
   trait BH3 extends BH4 {

base/shared/src/main/scala/scalaz/Prelude.scala

@@ -2,48 +2,49 @@ package scalaz
 
 trait BaseTypeclasses {
   type Applicative[F[_]] = typeclass.Applicative[F]
+  val Applicative = typeclass.Applicative
   type Apply[F[_]] = typeclass.Apply[F]
+  val Apply = typeclass.Apply
   type Bind[M[_]] = typeclass.Bind[M]
+  val Bind = typeclass.Bind
   type Category[=>:[_,_]] = typeclass.Category[=>:]
   type Choice[P[_,_]] = typeclass.Choice[P]
   type Cobind[F[_]] = typeclass.Cobind[F]
   type Comonad[F[_]] = typeclass.Comonad[F]
   type Compose[P[_,_]] = typeclass.Compose[P]
   type Foldable[T[_]] = typeclass.Foldable[T]
+  val Foldable = typeclass.Foldable
   type Functor[F[_]] = typeclass.Functor[F]
+  val Functor = typeclass.Functor
   type InvariantFunctor[F[_]] = typeclass.InvariantFunctor[F]
   type IsContravariant[F[_]] = typeclass.IsContravariant[F]
   type IsCovariant[F[_]] = typeclass.IsCovariant[F]
   type Monad[M[_]] = typeclass.Monad[M]
+  val Monad = typeclass.Monad
   type Monoid[T] = typeclass.Monoid[T]
+  val Monoid = typeclass.Monoid
   type Phantom[F[_]] = typeclass.Phantom[F]
   type Profunctor[F[_,_]] = typeclass.Profunctor[F]
   type Semigroup[T] = typeclass.Semigroup[T]
+  val Semigroup = typeclass.Semigroup
   type Show[A] = typeclass.Show[A]
   type Strong[F[_,_]] = typeclass.Strong[F]
   type Traversable[T[_]] = typeclass.Traversable[T]
+  val Traversable = typeclass.Traversable
+
 
-  def Applicative[F[_]](implicit F: Applicative[F]): Applicative[F] = F
-  def Apply[F[_]](implicit F: Apply[F]): Apply[F] = F
-  def Bind[F[_]](implicit F: Bind[F]): Bind[F] = F
   def Category[=>:[_,_]](implicit P: Category[=>:]): Category[=>:] = P
   def Choice[P[_,_]](implicit P: Choice[P]): Choice[P] = P
   def Cobind[F[_]](implicit F: Cobind[F]): Cobind[F] = F
   def Comonad[F[_]](implicit F: Comonad[F]): Comonad[F] = F
   def Compose[P[_,_]](implicit P: Compose[P]): Compose[P] = P
-  def Foldable[F[_]](implicit F: Foldable[F]): Foldable[F] = F
-  def Functor[F[_]](implicit F: Functor[F]): Functor[F] = F
   def InvariantFunctor[F[_]](implicit F: InvariantFunctor[F]): InvariantFunctor[F] = F
   def IsContravariant[F[_]](implicit F: IsContravariant[F]): IsContravariant[F] = F
   def IsCovariant[F[_]](implicit F: IsCovariant[F]): IsCovariant[F] = F
-  def Monad[M[_]](implicit M: Monad[M]): Monad[M] = M
-  def Monoid[T](implicit T: Monoid[T]): Monoid[T] = T
   def Phantom[F[_]](implicit F: Phantom[F]): Phantom[F] = F
   def Profunctor[P[_,_]](implicit P: Profunctor[P]): Profunctor[P] = P
-  def Semigroup[T](implicit T: Semigroup[T]): Semigroup[T] = T
   def Show[A](implicit A: Show[A]): Show[A] = A
   def Strong[P[_,_]](implicit P: Strong[P]): Strong[P] = P
-  def Traversable[T[_]](implicit T: Traversable[T]): Traversable[T] = T
 }
 
 trait BaseData {

base/shared/src/main/scala/scalaz/data/ConstInstances.scala

@@ -1,50 +1,61 @@
 package scalaz
 package data
 
-import typeclass.{FoldableClass, TraversableClass}
-
-import Prelude._
-import FoldableClass._
-import TraversableClass._
 
 trait ConstInstances {
-  implicit def constTraverse[R]: Traversable[Const[R, ?]] = new TraversableClass[Const[R, ?]] with FoldRight[Const[R, ?]] with Traverse[Const[R, ?]] {
-    def map[A, B](ma: Const[R, A])(f: A => B): Const[R, B] = ma.retag
+  implicit def constTraverse[R]: Traversable[Const[R, ?]] = new Traversable.Template[Const[R, ?]] with Traversable.DeriveSequence[Const[R, ?]] with Foldable.DeriveFoldMap[Const[R, ?]] with ConstFunctor[R] {
 
-    def traverse[F[_], A, B](ta: Const[R, A])(f: A => F[B])(implicit F: Applicative[F]): F[Const[R, B]] =
+    override def traverse[F[_], A, B](ta: Const[R, A])(f: A => F[B])(implicit F: Applicative[F]): F[Const[R, B]] =
       F.pure(ta.retag)
 
-    def foldLeft[A, B](fa: Const[R, A], z: B)(f: (B, A) => B): B = z
+    override def foldLeft[A, B](fa: Const[R, A], z: B)(f: (B, A) => B): B = z
 
-    def foldRight[A, B](fa: Const[R, A], z: => B)(f: (A, => B) => B): B = z
+    override def foldRight[A, B](fa: Const[R, A], z: => B)(f: (A, => B) => B): B = z
 
     override def toList[A](fa: Const[R, A]): List[A] = Nil
   }
 
-  implicit def constFunctor[R]: Functor[Const[R, ?]] = new Functor[Const[R, ?]] {
-    def map[A, B](fa: Const[R, A])(f: A => B): Const[R, B] =
+  private trait ConstFunctor[R] extends Functor.Template[Const[R, ?]] {
+    final override def map[A, B](fa: Const[R, A])(f: A => B): Const[R, B] =
       fa.retag[B]
   }
 
-  implicit def constApply[R](implicit R: Semigroup[R]): Apply[Const[R, ?]] = new Apply[Const[R, ?]] {
-    def functor: Functor[Const[R, ?]] = Const.constFunctor[R]
-    def ap[A, B](fa: Const[R, A])(f: Const[R, A => B]): Const[R, B] =
+  private trait ConstApply[R] extends Apply.Template[Const[R, ?]] with ConstFunctor[R] {
+    def R: Semigroup.Class[R]
+    final override def ap[A, B](fa: Const[R, A])(f: Const[R, A => B]): Const[R, B] =
       Const(R.append(fa.getConst, f.getConst))
   }
 
-  implicit def constApplicative[R](implicit R: Monoid[R]): Applicative[Const[R, ?]] = new Applicative[Const[R, ?]] {
-    def apply: Apply[Const[R, ?]] = Const.constApply[R]
-    def pure[A](a: A): Const[R, A] = Const(R.empty)
+  private trait ConstApplicative[R] extends Applicative.Template[Const[R, ?]] with ConstApply[R]  {
+    override def R: Monoid.Class[R]
+    final override def pure[A](a: A): Const[R, A] = Const(R.empty)
   }
 
-  implicit def constSemigroup[A, B](implicit A: Semigroup[A]): Semigroup[Const[A, B]] = new Semigroup[Const[A, B]] {
-    def append(a1: Const[A, B], a2: => Const[A, B]): Const[A, B] =
+  private trait ConstSemigroup[A, B] extends Semigroup.Template[Const[A, B]] {
+    def A: Semigroup.Class[A]
+    final override def append(a1: Const[A, B], a2: => Const[A, B]): Const[A, B] =
       Const(A.append(a1.getConst, a2.getConst))
   }
 
-  implicit def constMonoid[A, B](implicit A: Monoid[A]): Monoid[Const[A, B]] = new Monoid[Const[A, B]] {
-    def semigroup: Semigroup[Const[A, B]] = implicitly
-    def empty: Const[A, B] = Const(A.empty)
+  private trait ConstMonoid[A, B] extends Monoid.Template[Const[A, B]] with ConstSemigroup[A, B] {
+    override def A: Monoid.Class[A]
+    final override def empty: Const[A, B] = Const(A.empty)
+  }
+
+  implicit def constApply[R: Semigroup]: Apply[Const[R, ?]] = new ConstApply[R] {
+    override val R = implicitly
+  }
+
+  implicit def constApplicative[R: Monoid]: Applicative[Const[R, ?]] = new ConstApplicative[R] {
+    override val R = implicitly
+  }
+
+  implicit def constSemigroup[A: Semigroup, B]: Semigroup[Const[A, B]] = new ConstSemigroup[A, B] {
+    override val A = implicitly
+  }
+
+  implicit def constMonoid[A: Monoid, B]: Monoid[Const[A, B]] = new ConstMonoid[A, B] {
+    override val A = implicitly
   }
 
   implicit def constShow[A, B](implicit A: Show[A]): Show[Const[A, B]] =

base/shared/src/main/scala/scalaz/data/DisjunctionInstances.scala

@@ -1,10 +1,8 @@
 package scalaz
 package data
 
-import typeclass.MonadClass
-
 trait DisjunctionInstances {
-  implicit def disjunctionMonad[L]: Monad[L \/ ?] = new MonadClass.Template[L \/ ?] {
+  implicit def disjunctionMonad[L]: Monad[L \/ ?] = new Monad.Template[L \/ ?] with Bind.DeriveFlatten[L \/ ?] {
 
     override def map[A, B](ma: L \/ A)(f: A => B): L \/ B =
       ma.fold[L \/ B](l => -\/(l))(r => \/-(f(r)))

base/shared/src/main/scala/scalaz/data/IdentityInstances.scala

@@ -1,12 +1,10 @@
 package scalaz
 package data
 
-import typeclass.MonadClass
-
 trait IdentityInstances {
-  implicit val monad: Monad[Identity] = new MonadClass[Identity] {
+  implicit val monad: Monad[Identity] = new Monad.Template[Identity] {
     override def map[A, B](fa: Identity[A])(f: A => B): Identity[B] = Identity(f(fa.run))
-    override def ap[A, B](fa: Identity[A])(f: Identity[A => B]): Identity[B] = Identity(f.run.apply(fa.run))
+    override def ap[A, B](fa: Identity[A])(f: Identity[A => B]): Identity[B] = Identity(f.run(fa.run))
     override def pure[A](a: A): Identity[A] = Identity(a)
     override def flatMap[A, B](oa: Identity[A])(f: A => Identity[B]): Identity[B] = f(oa.run)
     override def flatten[A](ma: Identity[Identity[A]]): Identity[A] = ma.run

base/shared/src/main/scala/scalaz/data/Maybe.scala

@@ -1,9 +1,6 @@
 package scalaz
 package data
 
-import typeclass.{MonadClass, TraversableClass}
-import typeclass.FoldableClass._
-
 sealed trait MaybeModule {
   type Maybe[A]
 
@@ -60,7 +57,7 @@ private[scalaz] object MaybeImpl extends MaybeModule {
   }
 
   private val instance =
-    new MonadClass.Template[Maybe] with TraversableClass[Maybe] with FoldRight[Maybe] {
+    new Monad.Template[Maybe] with Bind.DeriveFlatten[Maybe] with Traversable.Template[Maybe] with Foldable.DeriveFoldMap[Maybe] {
 
       override def ap[A, B](ma: Maybe[A])(mf: Maybe[A => B]): Maybe[B] =
         mf match {
@@ -79,13 +76,13 @@ private[scalaz] object MaybeImpl extends MaybeModule {
 
       override def traverse[F[_], A, B](ma: Maybe[A])(f: A => F[B])(implicit F: Applicative[F]): F[Maybe[B]] =
         ma match {
-          case Some(a) => F.apply.functor.map(f(a))(just)
+          case Some(a) => F.map(f(a))(just)
           case None    => F.pure(None)
         }
 
       override def sequence[F[_], A](ma: Maybe[F[A]])(implicit F: Applicative[F]): F[Maybe[A]] =
         ma match {
-          case Some(fa) => F.apply.functor.map(fa)(just)
+          case Some(fa) => F.map(fa)(just)
           case None     => F.pure(None)
         }
 

base/shared/src/main/scala/scalaz/data/These.scala

@@ -96,8 +96,8 @@ sealed abstract class These[L, R] {
   /* Traversable (on the right) */
   final def traverse[F[_], B](f: R => F[B])(implicit F: Applicative[F]): F[These[L, B]] = this match {
     case thiz @ This(_)    => F.pure(thiz.pmap[B])
-    case That(right)       => F.apply.functor.map(f(right))(That(_))
-    case Both(left, right) => F.apply.functor.map(f(right))(Both(left, _))
+    case That(right)       => F.map(f(right))(That(_))
+    case Both(left, right) => F.map(f(right))(Both(left, _))
   }
 
   /* Semigroup */

base/shared/src/main/scala/scalaz/data/TheseInstances.scala

@@ -1,22 +1,19 @@
 package scalaz
 package data
 
-import typeclass.{ BindClass, FoldableClass, MonadClass, SemigroupClass, TraversableClass }
-
 trait TheseInstances {
   // implicit def bifunctor: Bifunctor[These] = ...
 
   implicit final def theseMonad[L: Semigroup]: Monad[These[L, ?]] =
-    new MonadClass.Template[These[L, ?]] with BindClass.Ap[These[L, ?]] {
+    new Monad.Template[These[L, ?]] with Bind.DeriveAp[These[L, ?]] with Bind.DeriveFlatten[These[L, ?]] {
       override def map[A, B](ma: These[L, A])(f: A => B) = ma.rmap(f)
       def flatMap[A, B](ma: These[L, A])(f: A => These[L, B]) = ma.flatMap(f)
       def pure[A](a: A) = That(a)
     }
 
   implicit final def theseTraversable[L]: Traversable[These[L, ?]] =
-    new TraversableClass[These[L, ?]]
-        with TraversableClass.Traverse[These[L, ?]]
-        with FoldableClass.FoldMap[These[L, ?]] {
+    new Traversable.Template[These[L, ?]]
+        with Traversable.DeriveSequence[These[L, ?]] with Foldable.DeriveToList[These[L, ?]] {
       def traverse[F[_]: Applicative, A, B](ta: These[L, A])(f: A => F[B]) = ta.traverse(f)
       def foldMap[A, B: Monoid](fa: These[L, A])(f: A => B) = fa.foldMap(f)
       def map[A, B](ma: These[L, A])(f: A => B) = ma.rmap(f)
@@ -27,7 +24,7 @@ trait TheseInstances {
     }
 
   implicit final def theseSemigroup[L: Semigroup, R: Semigroup]: Semigroup[These[L, R]] =
-    new SemigroupClass[These[L, R]] {
+    new Semigroup.Template[These[L, R]] {
       def append(a1: These[L, R], a2: => These[L, R]) = a1.append(a2)
     }
 

base/shared/src/main/scala/scalaz/typeclass/Applicative.scala

@@ -1,7 +1,23 @@
 package scalaz
 package typeclass
 
-trait Applicative[F[_]] {
-  def apply: Apply[F]
-  def pure[A](a: A): F[A]
-}
+sealed trait Applicative[F[_]] extends Applicative.Class[F]
+
+object Applicative {
+
+  trait Class[F[_]] extends Apply.Class[F] {
+    def pure[A](a: A): F[A]
+
+    def applicative: Applicative[F]
+  }
+
+  trait Template[F[_]] extends Apply.Template[F] with Applicative[F]  {
+    final override def applicative = this
+  }
+
+  trait DeriveMap[F[_]] extends Monad.Alt[DeriveMap[F]] { self: Class[F]  =>
+    final override def map[A, B](ma: F[A])(f: (A) => B): F[B] = ap(ma)(pure(f))
+  }
+
+  def apply[F[_]](implicit F: Applicative[F]): Applicative[F] = F
+}

base/shared/src/main/scala/scalaz/typeclass/Apply.scala

@@ -1,7 +1,19 @@
 package scalaz
 package typeclass
 
-trait Apply[F[_]] {
-  def functor: Functor[F]
-  def ap[A, B](fa: F[A])(f: F[A => B]): F[B]
-}
+sealed trait Apply[F[_]] extends Apply.Class[F]
+
+object Apply {
+
+  trait Class[F[_]] extends Functor.Class[F] {
+    def ap[A, B](fa: F[A])(f: F[A => B]): F[B]
+
+    def apply: Apply[F]
+  }
+
+  trait Template[F[_]] extends Functor.Template[F] with Apply[F] {
+    final override def apply = this
+  }
+
+  def apply[F[_]](implicit F: Apply[F]): Apply[F] = F
+}

base/shared/src/main/scala/scalaz/typeclass/Bind.scala

@@ -1,8 +1,32 @@
 package scalaz
 package typeclass
 
-trait Bind[M[_]] {
-  def apply: Apply[M]
-  def flatMap[A, B](ma: M[A])(f: A => M[B]): M[B]
-  def flatten[A](ma: M[M[A]]): M[A]
-}
+sealed trait Bind[M[_]] extends Bind.Class[M]
+
+object Bind {
+
+  trait Class[M[_]] extends Apply.Class[M] {
+    def flatMap[A, B](ma: M[A])(f: A => M[B]): M[B]
+    def flatten[A](ma: M[M[A]]): M[A]
+
+    def bind: Bind[M]
+  }
+
+  trait Template[M[_]] extends Apply.Template[M] with Bind[M] {
+    final override def bind = this
+  }
+
+  trait DeriveAp[M[_]] extends Monad.Alt[DeriveAp[M]] { self: Class[M] =>
+    final override def ap[A, B](fa: M[A])(f: M[A => B]): M[B] = flatMap(f)(map(fa))
+  }
+
+  trait Alt[D <: Alt[D]]
+  trait DeriveFlatten[M[_]] extends Alt[DeriveFlatten[M]] { self: Class[M] =>
+    final override def flatten[A](ma: M[M[A]]): M[A] = flatMap(ma)(identity)
+  }
+  trait DeriveFlatMap[M[_]] extends Alt[DeriveFlatMap[M]] { self: Class[M] =>
+    final override def flatMap[A, B](ma: M[A])(f: (A) => M[B]): M[B] = flatten(map(ma)(f))
+  }
+
+  def apply[F[_]](implicit F: Bind[F]): Bind[F] = F
+}