:PROPERTIES:
:ID:       10eb4672-19ab-4275-a110-5446c96e7e24
:END:
#+title: Applicative

In [[id:9e68d422-cced-4177-96d1-90f777b9a493][Software Development]], this refers to a [[id:7a19b34d-c4bb-462b-8fae-581bf06dfdc4][Functor]] that provides a method for
applying a function wrapped in such a type to a value wrapped in the same type.

In [[id:9ac78677-2602-4a06-af0a-4ed82e98a9b6][Haskell]], the function for applying a wrapped function to a value wrapped in
the same type is available as the infix operator =<*>=, and facilitates the
application of a function taking an arbitrary number of arguments over multiple
wrapped values. An applicative must also implement the =pure= function, which
takes a single argument and returns it wrapped.

#+caption: Applicative functions in Haskell
#+begin_src haskell :exports code
  pure :: Applicative f => a -> f a
  (<*>) :: Applicative f => f (a -> b) -> f a -> f b
#+end_src

In the following example, =fmap= (=<$>=) first applies the =add= function to the
value =Just 1=, resulting in a function of the type =Just (Int -> Int)=. The
applicative infix operator (=<*>=) then applies that function to the remaining
value =Just 2=, resulting in =Just 3=.

#+caption: Applying a function over multiple wrapped values
#+begin_src haskell :cache yes :exports both
  add :: Int -> Int -> Int
  add x y = x + y

  add <$> Just 1 <*> Just 2
#+end_src

#+RESULTS[10751e7c3100f27569974ee18b3f34498166dfc5]:
: Prelude> Just 3