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Partial application

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

1 Examples

1.1 Simple introduction

For example:

add     :: Int -> Int -> Int
add x y = x + y
addOne = add 1
In this example,
is the result of partially applying
. 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.

1.2 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' 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
, like so:
comp2' f = comp2 f add