A higher-order function receives another function as an argument or returns a function. It separates an algorithm’s general structure from the specific behavior supplied by the caller. section 2.5.1
A list transformation demonstrates the pattern: traverse the list once, apply the supplied function to each element, and construct the result. The same transformation can increment numbers, test values, or replace characters. section 2.5.1
A reusable list transformation
transform :: (t -> a) -> [t] -> [a] transform fun [] = [] transform fun (x : xs) = fun x : transform fun xs transform (\x -> x + 1) [1..10] produces [2,3,4,5,6,7,8,9,10,11]. Applying a predicate produces [Bool], while applying a character replacement produces "Hullo World!".
Parametric polymorphism makes higher-order functions reusable across element types. The type variable t allows transform to consume one kind of element while a may differ for the produced elements. section 2.5.2
Functions are values, so a program can select behavior by storing one of several functions in a variable. A line-numbering tool uses this technique to choose between numbering all lines and numbering only nonempty lines. section 4.4.1
Use higher-order functions to:
- Describe a general operation over a data structure. section 2.5.1
- Replace repeated, type-specific implementations with one polymorphic function. section 2.5.2
- Generalize similar graph operations over lists, such as adding edges and building a directed graph. section 5.3.1
