# Higher order function

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## Contents |

## 1 Definition

A **higher order function** is a function that takes other functions as arguments.

## 2 Discussion

The major use is to abstract common behaviour into one place.

### 2.1 Examples

#### 2.1.1 In the libraries

Many functions in the libraries are higher order. The (probably) most commonly given examples aremap

fold

curry, uncurry

curry :: ((a,b)->c) -> a->b->c curry f a b = f (a,b) uncurry :: (a->b->c) -> ((a,b)->c) uncurry f (a,b)= f a b

curry

uncurry

curry

uncurry

#### 2.1.2 Simple code examples

Rather than writing

doubleList [] = [] doubleList (x:xs) = 2*x : doubleList xs

and

tripleList [] = [] tripleList (x:xs) = 3*x : tripleList xs

we can parameterize out the difference

multList n [] = [] multList n (x:xs) = n*x : multList n xs

and define

tripleList = multList 3 doubleList = multList 2

leading to a less error prone definition of each.

But now, if we had the function

addToList n [] = [] addToList n (x:xs) = n+x : addToList n xs

we could parameterize the difference again

operlist n bop [] = [] operlist n bop (x:xs) = bop n x : operlist n bop xs

and define doubleList as

doubleList = operList 2 (*)

but this ties us into a constant parameters

and we could redefine things as

mapList f [] = [] mapList f (x:xs) = f x : mapList f xs

and define doubleList as

doubleList = mapList (2*)

This higher order function "mapList" can be used in a wide range of areas to simplify code.

## 3 See also

Accumulator recursion where the accumulator is a higher order function is one interesting case of continuation passing style.