What is the purpose of `pure` in Applicative Functor

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Meet the Applicative typeclass. It lies in the Control.Applicative module and it defines two methods, pure and <*>. It doesn't provide a default implementation for any of them, so we have to define them both if we want something to be an applicative functor.

I am trying to understand who is using pure function. I do use (<*>) function for which applicative functors are most useful for. But I am not sure who really uses pure.

I read something like pure (+3) <*> Just 10 but it can be written as Just (+3) <*> Just 10 too.

Above is just one confusion of too many I have. What is the true purpose of defining pure and when do I get to use it (or) who is already using it?

 


<*> :: f (a -> b) -> f a -> f b, this operator accepts a function in the applicative type, as well as a value in the applicative type. The first argument of this operator can not thus be simply a function, but it has to be residing within an applicative.

The pure function solves problems that might occur here (e.g wanting to apply a function that is not residing in the applicative). It accepts a function that is not currently residing in the applicative, and lifts it into the applicative.pure :: a -> f a

(+3) :: Int -> Int, and Just 10 :: Maybe Int, you can not thus evaluate (+3) <*> Just 10 as the types do not work; the (+3) has to be promoted to a value in the Maybe applicative.

For Maybe a, the definition of pure is pure = Just, which is why you can write either pure (+3) or Just (+3)

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I'll leave it to you to look into the <$> operator :-) Remember, every Applicative is a Functor.

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