Applicative Functors

Like Functors, Applicative Functors are a sort of container and defines two operations:

(defprotocol Applicative
  (pure [av v])
  (fapply [ag av]))

The pure function is a generic way to put a value inside an Applicative Functor. So far, we have been using the option helper function for this purpose. We will be using it a little later.

The fapply function will unwrap the function contained in the Applicative ag and apply it to the value contained in the applicative av.

The purpose of both the functions will become clear with an example, but first, we need to promote our Option Functor into an Applicative Functor:

(extend-protocol fkp/Applicative
  Some
  (pure [_ v]
    (Some. v))

  (fapply [ag av]
    (if-let [v (:v av)]
      (Some. ((:v ag) v))
      (None.)))

  None
  (pure [_ v]
    (Some. v))

  (fapply [ag av]
    (None.)))

The implementation of pure is the simplest. All it does is wrap the value v into an instance of Some. Equally simple is the implementation of...