How to compose function to applicatives with scalaz - validation

Question

While learning Scalaz 6, I'm trying to write type-safe readers returning validations. Here are my new types:
type ValidReader[S,X] = (S) => Validation[NonEmptyList[String],X]
type MapReader[X] = ValidReader[Map[String,String],X]
and I have two functions creating map-readers for ints and strings (*):
def readInt( k: String ): MapReader[Int] = ...
def readString( k: String ): MapReader[String] = ...
Given the following map:
val data = Map( "name" -> "Paul", "age" -> "8" )
I can write two readers to retrieve the name and age:
val name = readString( "name" )
val age = readInt( "age" )
println( name(data) ) //=> Success("Paul")
println( age(data) ) //=> Success(8)
Everything works fine, but now I want to compose both readers to build a Boy instance:
case class Boy( name: String, age: Int )
My best take is:
val boy = ( name |#| age ) {
(n,a) => ( n |#| a ) { Boy(_,_) }
}
println( boy(data) ) //=> Success(Boy(Paul,8))
It works as expected, but the expression is awkward with two levels of applicative builders. Is there a way, to get the following syntax to work ?
val boy = ( name |#| age ) { Boy(_,_) }
(*) Full and runnable implementation in: https://gist.github.com/1891147
Update: Here is the compiler error message that I get when trying the line above or Daniel suggestion:
[error] ***/MapReader.scala:114: type mismatch;
[error] found : scalaz.Validation[scalaz.NonEmptyList[String],String]
[error] required: String
[error] val boy = ( name |#| age ) { Boy(_,_) }
[error] ^

Answer 1

How about this?
val boy = (name |#| age) {
(Boy.apply _).lift[({type V[X]=ValidationNEL[String,X]})#V]
}
or using a type alias:
type VNELStr[X] = ValidationNEL[String,X]
val boy = (name |#| age) apply (Boy(_, _)).lift[VNELStr]
This is based on the following error message at the console:
scala> name |#| age apply Boy.apply
<console>:22: error: type mismatch;
found : (String, Int) => MapReader.Boy
required: (scalaz.Validation[scalaz.NonEmptyList[String],String],
scalaz.Validation[scalaz.NonEmptyList[String],Int]) => ?
So I just lifted Boy.apply to take the required type.

Answer 2

Note that since Reader and Validation (with a semigroup E) are both Applicative, their composition is also Applicative. Using scalaz 7 this can be expressed as:
import scalaz.Reader
import scalaz.Reader.{apply => toReader}
import scalaz.{Validation, ValidationNEL, Applicative, Kleisli, NonEmptyList}
//type IntReader[A] = Reader[Int, A] // has some ambigous implicit resolution problem
type IntReader[A] = Kleisli[scalaz.IdInstances#Id, Int, A]
type ValNEL[A] = ValidationNEL[Throwable, A]
val app = Applicative[IntReader].compose[ValNEL]
Now we can use a single |#| operation on the composed Applicative:
val f1 = toReader((x: Int) => Validation.success[NonEmptyList[Throwable], String](x.toString))
val f2 = toReader((x: Int) => Validation.success[NonEmptyList[Throwable], String]((x+1).toString))
val f3 = app.map2(f1, f2)(_ + ":" + _)
f3.run(5) should be_==(Validation.success("5:6"))