Functions

Introduction

Function application was introduced earlier and can be done with the space operator. The space operator cannot be re-used in setting where you want to avoid defining new functions.

Example

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applyOne :: (Int -> Int) -> Int
applyOne f = f 1 + 1

This function will apply the value 1 to whatever function is passed in as an input and then add 1 to the result.

Note that we couldn't express this function as the composition of other functions. We had to explicitly define how to use its input. What we need is a re-usable operator for function application.

Application Operator

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($) :: (a -> b) -> a -> b
($) f x = f x

The difference between ($) and the normal space operator is that it is right-associative. To see the difference:

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f x y z = ((f x) y) z
f $ x $ y $ z = f (x (y z))

Rewriting the Example

Now applyOne can be rewritten as:

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applyOne :: (Int -> Char) -> Char
applyOne = (+ 1) . ($ 1)

Note that we were able to define applyOne solely by composing existing functions.

Next Section

We will explore even futher methods of re-use by exploring higher-order functions.