Scala: Applicative with scalaz example

I’ve talked on Functor previously, will repeat myself that construction is very useful in the Scala's world. We covered Comonad as well, it is extending Functor and adds functionality for the extraction value or the wrapping of already wrapped.

This post is related to Applicative. Applicative is coupled with Functor, even has an alternative name: Applicative Functor. At first let look into class hierarchy for Applicative in scalaz library:

Scala: Comonad (scalaz example)

When we were talking on Functor - we described it as a construction that can apply function to incapsulated value and return a new instance of the same container with function result value inside. Quite useful construction, it is even implemented by scala library's classes: like Option, List and others. To be honest Scala's standart library classes mixing Functor and Monad, but lets do not concentrate on this now.

Scala: Functor (scalaz example)

Function programming got a proven handy in structuring the code, from where we have common structures/classes presented in many functional languages. All this magic comes from mathematic and in the most parts aren't so easy to get for regular developers with imperative experience. I've been googling a lot to get essence and still getting a lot of "news". Looks like the best way to review FP types in Scala is using examples from scalaz library. Let try to start from the Functor.

Functor 

Functor is a something you can map over, it has only one method map (called fmap scalaz). Class diagram is very simple: