Scalaz Validation, validate inner value - validation

Question

I have a Validation object
val v = Validation[String, Option[Int]]
I need to make a second validation, to check if actual Integer value is equals to 100 for example. If I do
val vv = v.map(_.map(intValue => if (intValue == 100)
intValue.success[String]
else
"Bad value found".fail[Integer]))
I get:
Validation[String, Option[Validation[String, Int]]]
How is it possible to get vv also as Validation[String, Option[Int]] in most concise way
=========
Found possible solution from my own:
val validation: Validation[String, Option[Int]] = Some(100).success[String]
val validatedTwice: Validation[String, Option[Int]] = validation.fold(
_ => validation, // if Failure then return it
_.map(validateValue _) getOrElse validation // validate Successful result
)
def validateValue(value: Int): Validation[String, Option[Int]] = {
if (value == 100)
Some(value).success[String]
else
"Bad value".fail[Option[Int]]
}
Looks not concise and elegant although it works
==============
Second solution from my own, but also looks over-compicated:
val validatedTwice2: Validation[String, Option[Int]] = validation.flatMap(
_.map(validateValue _).map(_.map(Some(_))) getOrElse validation)
def validateValue(value: Int): Validation[String, Int] = {
if (value == 100)
value.success[String]
else
"Bad value".fail[Int]
}

Answer 1

Your solution is over-complicated. The following will suffice!
v flatMap (_.filter(_ == 100).toSuccess("Bad value found"))
The toSuccess comes from OptionW and converts an Option[A] into a Validation[X, A] taking the value provided for the failure case in the event that the option is empty. The flatMap works like this:
Validation[X, A]
=> (A => Validation[X, B])
=> (via flatMap) Validation[X, B]
That is, flatMap maps and then flattens (join in scalaz-parlance):
Validation[X, A]
=> (A => Validation[X, B]]
=> (via map) Validation[X, Validation[X, B]]
=> (via join) Validation[X, B]

Answer 2

First, let's set up some type aliases because typing this out repeatedly will get old pretty fast. We'll tidy up your validation logic a little too while we're here.
type V[X] = Validation[String, X]
type O[X] = Option[X]
def checkInt(i: Int): V[Int] = Validation.fromEither(i != 100 either "Bad value found" or i)
val v: V[O[Int]] = _
this is where we're starting out - b1 is equivalent to your vv situation
val b1: V[O[V[Int]]] = v.map(_.map(checkInt))
so let's sequence the option to flip over the V[O[V[Int]]] into a V[V[O[Int]]]
val b2: V[V[O[Int]]] = v.map(_.map(checkInt)).map(_.sequence[V, Int])
or if you're feeling lambda-y it could have been
sequence[({type l[x] = Validation[String, x]})#l, Int]
next we flatten out that nested validation - we're going to pull in the Validation monad because we actually do want the fastfail behaviour here, although it's generally not the right thing to do.
implicit val monad = Validation.validationMonad[String]
val b3: V[O[Int]] = v.map(_.map(checkInt)).map(_.sequence[V, Int]).join
So now we've got a Validation[String, Option[Int]], so we're there, but this is still pretty messy. Lets use some equational reasoning to tidy it up
By the second functor law we know that:
X.map(_.f).map(_.g) = X.map(_.f.g) =>
val i1: V[O[Int]] = v.map(_.map(checkInt).sequence[V, Int]).join
and by the definition of a monad:
X.map(f).join = X.flatMap(f) =>
val i2: V[O[Int]] = v.flatMap(_.map(checkInt).sequence[V, Int])
and then we apply the free theorem of traversal:
(I struggled with that bloody paper so much, but it looks like some of it sunk in!):
X.map(f).sequence = X.traverse(f andThen identity) = X.traverse(f) =>
val i3: V[O[Int]] = v.flatMap(_.traverse[V, Int](checkInt))
so now we're looking at something a bit more civilised. I imagine there's some trickery to be played with the flatMap and traverse, but I've run out of inspiration.

Answer 3

Use flatMap, like so:
v.flatMap(_.parseInt.fail.map(_.getMessage).validation)