Higher order function

From HaskellWiki

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

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

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 defn 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.

Categories: Glossary | Idioms