Partial application

Partial application in Haskell involves passing less than the full number of arguments to a function that takes multiple arguments.

Examples

Simple introduction

For example:

add     :: Int -> Int -> Int
add x y = x + y

addOne = add 1

In this example, addOne is the result of partially applying add. It is a new function that takes an integer, adds 1 to it and returns that as the result.

The important property here is that the -> operator is right associative, and function application is left associative, meaning the type signature of add actually looks like this:

add :: Int -> (Int -> Int)

This means that add actually takes one argument and returns a function that takes another argument and returns an Int.

Slightly more complicated

What if you have a higher order function?

For example:

comp2 :: (a -> b) -> (b -> b -> c) -> (a -> a -> c)
comp2 f g = (\x y -> g (f x) (f y))

Remembering the maxim that: Functions are not partial, you can partially apply a function.

So, is this a partial definition of comp2'?

comp2' f = (\x y -> add (f x) (f y))

Not really, this is the definition of another function. But you can achieve the desired result by partially applying comp2, like so:

comp2' f = comp2 f add