Add NonEmptyTraverse docs (typelevel#1787)

* Add NonEmptyTraverse documentation

* Initial version of nonEmptyTraverse docs

* Add menu entry

* Add links to other typeclasses

* Remove misplaced backtick

docs/src/main/resources/microsite/data/menu.yml

@@ -96,6 +96,11 @@ options:
     url: typeclasses/show.html
     menu_type: typeclasses
 
+
+  - title: NonEmptyTraverse
+    url: typeclasses/nonemptytraverse.html
+    menu_type: typeclasses
+
   - title: Arrow
     url: typeclasses/arrow.html
     menu_type: typeclasses

docs/src/main/tut/typeclasses/nonemptytraverse.md

@@ -0,0 +1,47 @@
+---
+layout: docs
+title:  "NonEmptyTraverse"
+section: "typeclasses"
+source: "core/src/main/scala/cats/NonEmptyTraverse.scala"
+scaladoc: "#cats.NonEmptyTraverse"
+---
+
+# NonEmptyTraverse
+
+`NonEmptyTraverse` is a non-empty version of the [Traverse](traverse.html) type class, just like [Reducible](reducible.html) is a non-empty version of [Foldable](foldable.html).
+As such, it extends both `Reducible` and `Traverse` in the type class hierarchy.
+It provides the `nonEmptyTraverse` and `nonEmptySequence` methods that require an instance of `Apply` instead of `Applicative`:
+
+```scala
+def nonEmptyTraverse[G[_]: Apply, A, B](fa: F[A])(f: A => G[B]): G[F[B]]
+
+def nonEmptySequence[G[_]: Apply, A](fga: F[G[A]]): G[F[A]]
+```
+
+In the [Applicative tutorial](applicative.html) we learned of `Apply` as a weakened `Applicative` lacking the `pure` method.
+One example type lacking an `Applicative` instance is `Map[K, ?]`, it's impossible to implement a `pure` method for it.
+
+Knowing this, we can make use of `NonEmptyTraverse`, to traverse over a sequence of `Map`s.
+One example application one could think of is, when we have a list of text snippets,
+count the occurrence of each word in each snippet and return all the common words and their occurrences in each snippet:
+
+```tut:book
+import cats.implicits._
+import cats.data.NonEmptyList
+
+val snippets = NonEmptyList.of("What do you do", "What are you doing")
+
+def countWords(text: String): Map[String, Int] =
+  text.split(" ").groupBy(identity).mapValues(_.length)
+
+snippets.nonEmptyTraverse(countWords)
+```
+
+Note that, just like `traverse`, `nonEmptyTraverse(f)` is equivalent to `map(f).nonEmptySequence`, so the above could be rewritten as:
+
+```tut:book
+snippets.map(countWords).nonEmptySequence
+```
+
+`NonEmptyTraverse` also offers `flatNonEmptyTraverse` and `flatNonEmptySequence` methods that are analogous to `flatTraverse` and `flatSequence` in `Traverse`.
+Just like with `nonEmptyTraverse` these methods don't require a `Monad` instance, but only a `FlatMap`, which is the weakened version of `Monad` without `pure`.