A higher-order function in Haskell is a function that either takes in a function as its argument or returns a function as its result. We have already seen how functions can return other functions as their result when we introduced curried functions, so we will focus on functions that take other functions as arguments in this chapter. First, let's look at a simple example of a higher-order function that takes in a function and applies it twice to an argument:

applyTwice :: (a -> a) -> a -> a
applyTwice f x = f (f x)

ghci> applyTwice (++ " two") "one"
"one two two"

The function we passed in (++ "two ") simply appends the string "two " to the argument passed in (in this case, it must be a string), and it is applied twice when the higher-order function applyTwice is called.

Now let's take a closer look at two higher-order functions that are defined in the Prelude for working with lists, map and filter.

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