Applicative functor

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An applicative functor has more structure than a functor but less than a monad. See the Haddock docs for Control.Applicative.


It has turned out that many applications do not require monad functionality but only those of applicative functors. Monads allow you to run actions depending on the outcomes of earlier actions.

do text <- getLine
   if null text
     then putStrLn "You refuse to enter something?"
     else putStrLn ("You entered " ++ text)

This is obviously necessary in some cases, but in other cases it is disadvantageous.

Consider an extended IO monad which handles automated closing of allocated resources. This is possible with a monad.

openDialog, openWindow :: String -> CleanIO ()

liftToCleanup :: IO a -> CleanIO a

runAndCleanup :: CleanIO a -> IO a

runAndCleanup $
   do text <- liftToCleanup getLine
      if null text
        then openDialog "You refuse to enter something?"
        else openWindow ("You entered " ++ text)

The (fictive) functions openDialog and openWindow could not only open dialogs and windows but could also register some cleanup routine in the CleanIO. runAndCleanup would first run the opening actions and afterwards the required cleanup actions. I.e. if the dialog was opened, the dialog must be closed, but not the window. That is, the cleanup procedure depends on the outcomes of earlier actions.

Now consider the slightly different task, where functions shall register initialization routines that shall be run before the actual action takes place. (See the original discussion started by Michael T. Richter in Haskell-Cafe: Practical Haskell Question) This is impossible in the monadic framework. Consider the example above where the choice between openDialog and openWindow depends on the outcome of getLine. You cannot run initialization code for either openDialog or openWindow, because you do not know which one will be called before executing getLine. If you eliminate this dependency, you end up in an applicative functor and there you can do the initialization trick. You could write

initializeAndRun $
  (liftToInit getLine)
  (writeToWindow "You requested to open a window")

where writeToWindow registers an initialization routine which opens the window.


If you have the variables

f :: a -> b -> c
a :: f a
b :: f b

you can combine them in the following ways with the same result of type f c:

pure f <*> a <*> b

liftA2 f a b

But how to cope with let and sharing in the presence of effects? Consider the non-functorial expression:

x :: x
g :: x -> y
h :: y -> y -> z

let y = g x
in  h y y

Very simple. Now we like to generalize this to

fx :: f x
fg :: f (x -> y)
fh :: f (y -> y -> z)

However, we note that

let fy = fg <*> fx
in  fh <*> fy <*> fy

runs the effect of fy twice. E.g. if fy writes something to the terminal then fh <*> fy <*> fy writes twice. This could be intended, but how can we achieve, that the effect is run only once and the result is used twice?

Actually, using the liftA commands we can pull results of applicative functors into a scope where we can talk exclusively about functor results and not about effects. Note that functor results can also be functions. This scope is simply a function, which contains the code that we used in the non-functorial setting.

   (\x g h -> let y = g x in h y y)
   fx fg fh

The order of effects is entirely determined by the order of arguments to liftA3.

Some advantages of applicative functors

  • Code that uses only on the Applicative interface are more general than ones uses the Monad interface, because there are more applicative functors than monads.
  • Programming with Applicative has a more applicative/functional feel. Especially for newbies, it may encourage functional style even when programming with effects. Monad programming with do notation encourages a more sequential & imperative style.

How to switch from monads

  • Start using liftM, liftM2, etc or ap where you can, in place of do/(>>=).
  • When you notice you're only using those monad methods, then import Control.Applicative and replacereturn with pure, liftM with (<$>) (or fmap or liftA), liftM2 with liftA2, etc, and ap with (<*>). If your function signature was Monad m => ..., change to Applicative m => ... (and maybe rename m to f or whatever).

See also