Question

I have written the following code. I know that a higher order function is a function that takes in another function and returns a function as a result. But I can’t clearly distinguish a function if it is higher order or not. Is sort a higher order function? How do I find out if a function is higher order or not?

sortString :: String -> [String]
sortString x = sort (convertStringIntoList x)

Answer 1

A higher-order function is a function that takes another function as an argument, produces another function as a result, or perhaps both.

The function in your question has a single argument that is a string, not a function. When applied, your function’s value is an array of strings, not a function. Therefore, it is an ordinary function.

A similar function that is higher order is

sortString :: (Char -> Char -> Ordering) -> String -> [String]
sortString cmp s = map (:[]) $ sortBy cmp s

The power of higher-order functions is the flexibility they provide. Providing different functions produces different results:

ghci> sortString compare "slkdjfs"
["d","f","j","k","l","s","s"]

ghci> sortString (flip compare) "slkdjfs"
["s","s","l","k","j","f","d"]

In case you aren’t familiar, compare provides an Ordering relative to its arguments, e.g.,

ghci> compare 'a' 'b'
LT
ghci> compare 'b' 'a'
GT

As you may have noticed, flip is itself another higher-order function that reorders or flips the arguments to another function. Using flip as in the code above allows us to sort the list in descending rather than ascending order.