Transform typeclass

[leandrob13]

There has been some discussion about adding a typeclass for dealing with F ~> G transformations in #1644. The original proposal was made by @kailuowang in this gist and I materialized it by the name of Transform. The example below includes only instances for EitherT and Kleisli.

import cats.arrow.FunctionK
import cats.data.{EitherT, Kleisli}
import cats.~>

trait Transform[H[_[_], _]] {
  def map[F[_], G[_], A](ha: H[F, A])(f: F ~> G): H[G, A]

  def lift[F[_], G[_]](f: F ~> G): H[F, ?] ~> H[G, ?] =
    new FunctionK[H[F, ?], H[G, ?]] {
      def apply[A](fa: H[F, A]): H[G, A] = map(fa)(f)
    }
}

object Transform {

  implicit def eitherTTransform[E]: Transform[EitherT[?[_], E, ?]] =
    new Transform[EitherT[?[_], E, ?]] {
      def map[F[_], G[_], A](ha: EitherT[F, E, A])(f: F ~> G): EitherT[G, E, A] =
        EitherT[G, E, A](f(ha.value)) //This should be EitherT's transformF
    }

  implicit def kleisliTransform[E]: Transform[Kleisli[?[_], E, ?]] =
    new Transform[Kleisli[?[_], E, ?]] {
      def map[F[_], G[_], A](ha: Kleisli[F, E, A])(f: F ~> G): Kleisli[G, E, A] =
        ha.transform(f)
    }
}

The pattern is apparent in Kleisli since it already implements transform. For the rest of the monad transformers it is not defined as a F ~> G and it is confusing given that for EitherT and OptionT transform means to bimap/map the inner types. This might be an opportunity to make standard the F ~> G operations in MonadTs and solve the confusion for the actual use of transform.

[edmundnoble]

I can empathize with this requirement, and I would approve a PR that renames the methods to only be transform for higher-kinded mapping. However, cats-mtl has something very close to this in the form of cats.mtl.monad.TransFunctor and cats.mtl.monad.LayerFunctor.

[wedens]

This typeclass is better known as Hoist or MFunctor.

[leandrob13]

@edmundnoble where can I see code for cats.mtl.monad.TransFunctor?

Sure thing about the PR for defining transform accordingly in monad transformers.

[edmundnoble]

This unfortunately is not implementable for StateT. See https://github.com/edmundnoble/cats-mtl/issues/1.