Composing Kleisli and Reader monad in Scala

Suppose I have functions like this:

val fooXAB: X => A => Try[B] = ...
val fooXBC: X => B => Try[C] = ...
val fooXCD: X => C => Try[D] = ...

I'd like to compose them to make a new function fooXAD: X => A => Try[D], which calls fooXAB, fooXBC, and fooXCD sequentially and pass the X argument to all of them.

Suppose I use scalaz and have a monad instance for scala.util.Try. Now I can do it this way:

type AB = Kleisli[Try, A, B]
type BC = Kleilsi[Try, B, C]
type CD = Kleisli[Try, C, D]

type XReader[T] = Reader[X, T]

val fooXAB: XReader[AB] = ...
val fooXBC: XReader[BC] = ...
val fooXCD: XReader[CD] = ...

val fooXAC: XReader[AC] =
  for {
    ab <- fooXAB
    bc <- fooXBC
    cd <- fooXCD
  } yield (ab andThen bc andThen cd)

Does it make sense? Is it possible to simplify it ?

Solution

So I don't think the Reader Monad on the outer function helps here. once you apply and X to your threee XReaders, you can use Kleisli composition on the results (assuming you have a Monad instance for Try). Here's your example reworked this way, and it compiles for me:

import scala.util.{Try,Success}

import scalaz._
import Scalaz._

object A
object B
object C
object D
trait X

object Main {
  implicit val pretendTryIsAMonad: Monad[Try] = new Monad[Try] {
    def point[A](a: => A): Try[A] = Success(a)
    def bind[A,B](fa: Try[A])(f: A => Try[B]): Try[B] = fa flatMap f
  }

  type AB = Kleisli[Try, A.type, B.type]
  type BC = Kleisli[Try, B.type, C.type]
  type CD = Kleisli[Try, C.type, D.type]
  type AD = Kleisli[Try, A.type, D.type]

  type XReader[T] = X => T

  val fooXAB: XReader[AB] = (x: X) => Kleisli((a: A.type) => Success(B))
  val fooXBC: XReader[BC] = (x: X) => Kleisli((b: B.type) => Success(C))
  val fooXCD: XReader[CD] = (x: X) => Kleisli((c: C.type) => Success(D))

  val fooXAD: XReader[AD] = (x: X) =>
    fooXAB(x) >=> fooXBC(x) >=> fooXCD(x)
}