Add IdT, the identity monad transformer

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

@@ -0,0 +1,93 @@
+package cats
+package data
+
+/**
+ * `IdT[F[_], A]` is the identity monad transformer.
+ */
+final case class IdT[F[_], A](value: F[A]) {
+
+  def map[B](f: A => B)(implicit F: Functor[F]): IdT[F, B] =
+    IdT(F.map(value)(f))
+
+  def flatMap[B](f: A => IdT[F, B])(implicit F: Monad[F]): IdT[F, B] =
+    IdT(F.flatMap(value)(f.andThen(_.value)))
+
+  def flatMapF[B](f: A => F[B])(implicit F: Monad[F]): IdT[F, B] =
+    IdT(F.flatMap(value)(f))
+
+  def foldLeft[B](b: B)(f: (B, A) => B)(implicit F: Foldable[F]): B =
+    F.foldLeft(value, b)(f)
+
+  def foldRight[B](lb: Eval[B])(f: (A, Eval[B]) => Eval[B])(implicit F: Foldable[F]): Eval[B] =
+    F.foldRight(value, lb)(f)
+
+  def traverse[G[_], B](f: A => G[B])(implicit F: Traverse[F], G: Applicative[G]): G[IdT[F, B]] =
+    G.map(F.traverse(value)(f))(IdT(_))
+
+  def ap[B](f: IdT[F, A => B])(implicit F: Apply[F]): IdT[F, B] =
+    IdT(F.ap(value)(f.value))
+
+}
+
+object IdT extends IdTInstances {
+
+  def pure[F[_], A](a: A)(implicit F: Applicative[F]): IdT[F, A] =
+    IdT(F.pure(a))
+}
+
+private[data] sealed trait IdTFunctor[F[_]] extends Functor[IdT[F, ?]] {
+  implicit val F0: Functor[F]
+
+  def map[A, B](fa: IdT[F, A])(f: A => B): IdT[F, B] =
+    fa.map(f)
+}
+
+private[data] sealed trait IdTMonad[F[_]] extends Monad[IdT[F, ?]] {
+  implicit val F0: Monad[F]
+
+  def pure[A](a: A): IdT[F, A] =
+    IdT.pure(a)
+
+  def flatMap[A, B](fa: IdT[F, A])(f: A => IdT[F, B]): IdT[F, B] =
+    fa.flatMap(f)
+}
+
+private[data] sealed trait IdTFoldable[F[_]] extends Foldable[IdT[F, ?]] {
+  implicit val F0: Foldable[F]
+
+  def foldLeft[A, B](fa: IdT[F, A], b: B)(f: (B, A) => B): B =
+    fa.foldLeft(b)(f)
+
+  def foldRight[A, B](fa: IdT[F, A], lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] =
+    fa.foldRight(lb)(f)
+}
+
+private[data] sealed trait IdTTraverse[F[_]] extends Traverse[IdT[F, ?]] with IdTFoldable[F] {
+  implicit val F0: Traverse[F]
+
+  def traverse[G[_]: Applicative, A, B](fa: IdT[F, A])(f: A => G[B]): G[IdT[F, B]] =
+    fa.traverse(f)
+}
+
+private[data] sealed abstract class IdTInstances {
+  implicit def idTFunctor[F[_]](implicit F: Functor[F]): Functor[IdT[F, ?]] =
+    new IdTFunctor[F] {
+      implicit val F0: Functor[F] = F
+    }
+
+  implicit def idTMonad[F[_]](implicit F: Monad[F]): Monad[IdT[F, ?]] =
+    new IdTMonad[F] {
+      implicit val F0: Monad[F] = F
+    }
+
+  implicit def idTTraverse[F[_]](implicit F: Traverse[F]): Traverse[IdT[F, ?]] =
+    new IdTTraverse[F] {
+      implicit val F0: Traverse[F] = F
+    }
+
+  implicit def idTEq[F[_], A](implicit F: Eq[F[A]]): Eq[IdT[F, A]] =
+    F.on(_.value)
+
+  implicit def idTShow[F[_], A](implicit F: Show[F[A]]): Show[IdT[F, A]] =
+    functor.Contravariant[Show].contramap(F)(_.value)
+}