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copied!<p>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.</p> <pre><code>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]] = _ </code></pre> <p>this is where we're starting out - b1 is equivalent to your vv situation</p> <pre><code>val b1: V[O[V[Int]]] = v.map(_.map(checkInt)) </code></pre> <p>so let's sequence the option to flip over the V[O[V[Int]]] into a V[V[O[Int]]]</p> <pre><code>val b2: V[V[O[Int]]] = v.map(_.map(checkInt)).map(_.sequence[V, Int]) </code></pre> <p>or if you're feeling lambda-y it could have been</p> <pre><code>sequence[({type l[x] = Validation[String, x]})#l, Int] </code></pre> <p>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.</p> <pre><code>implicit val monad = Validation.validationMonad[String] val b3: V[O[Int]] = v.map(_.map(checkInt)).map(_.sequence[V, Int]).join </code></pre> <p>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</p> <p>By the second functor law we know that:</p> <pre><code>X.map(_.f).map(_.g) = X.map(_.f.g) => val i1: V[O[Int]] = v.map(_.map(checkInt).sequence[V, Int]).join </code></pre> <p>and by the definition of a monad:</p> <pre><code>X.map(f).join = X.flatMap(f) => val i2: V[O[Int]] = v.flatMap(_.map(checkInt).sequence[V, Int]) </code></pre> <p>and then we apply the free theorem of traversal:<br> (I struggled with that bloody paper so much, but it looks like some of it sunk in!):</p> <pre><code>X.map(f).sequence = X.traverse(f andThen identity) = X.traverse(f) => val i3: V[O[Int]] = v.flatMap(_.traverse[V, Int](checkInt)) </code></pre> <p>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.</p>

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