Applicative functors are more powerful than Functors but not as powerful as monads. They provide a way to partially apply a function inside an Applicative context to parameters also inside the same context.
Confused? Well hopefully after this article you won’t be.
As we saw earlier, a Functor is just a Haskell typeclass with the
class Functor f where fmap :: (a -> b) -> f a -> f b
We can apply a function from
a -> b to a value wrapped inside of a functor
Now what if we want to apply a function to multiple arguments that are all
wrapped inside of a context? Such as summing two numbers wrapped in a
(Just 1) + (Just 2) -- ?
If we apply
Just 1 with the
(+) function we get back another
function wrapped in the
ghci> :t (+) <$> Just 1 (+) <$> Just 1 :: Num a => Maybe (a -> a)
But now we are stuck. We need to apply a function inside of the Maybe context to a number inside the Maybe context.
This is where Applicatives come in!
They allow us to take a function which operates on normal unwrapped values, and apply it to parameters which are all wrapped in a context.
The typeclass definition requires all Applicatives to be Functors (meaning they
all implement the
class (Functor f) => Applicative f where pure :: a -> f a (<*>) :: f (a -> b) -> f a -> f b
An Applicative must implement the
pure just takes a normal unwrapped value and wraps it into an Applicative
(<*>) takes a function wrapped in an Applicative context and a parameter also
wrapped. It then unwraps both, applies
a to the function, and wraps the result
Lets see how it is implemented for the
instance Applicative Maybe where pure x = Just x (Just f) <*> (Just x) = Just (f x) _ <*> _ = Nothing
If either Maybe types are
Nothing is returned. Otherwise, each
value is unwrapped (via pattern matching), the function is applied to the
contents of second Maybe, and the result is wrapped back up as a Maybe.
Since all functions in Haskell are curried, we can partially apply a function of \(n\) arguments to \(n\) parameters wrapped in the Applicative context.
Using our above example, summing two numbers wrapped in a Maybe would look like this
ghci> (+) <$> Just 1 <*> Just 2 Just 3
We first use
<$> to partially apply
Just 1. Functor stuff. But then
<*> to take the wrapped function and apply it to the wrapped parameter.
Alternatively we can use the
pure function to wrap
(+) inside of an
ghci> pure (+) <*> Just 1 <*> Just 2 Just 3
What happens if one of the parameters is
ghci> (+) <$> Just 1 <*> Nothing Nothing
This is awesome! We don’t have to worry about checking whether or not our
parameters are valid. The
(<*>) function does that for us under the hood.