Higher-order function in Ocaml

Higher-order functions

There is no restriction on functions, which may thus be passed as arguments to other functions. Let us define a function sigma that returns the sum of the results of applying a given function f to each element of a list:

let rec sigma f = function
    | [] -> 0
    | x :: l -> f x + sigma f l;;
val sigma : ('a -> int) -> 'a list -> int = 

Anonymous functions may be defined using the function construct:

sigma (function x -> x * x) [1; 2; 3];;
- : int = 14

Polymorphism and higher-order functions allow defining function composition in its most general form:

let compose f g = function x -> f (g x);;
val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = 
let square_o_fact = compose square fact;;
val square_o_fact : int -> int = 
square_o_fact 5;;
- : int = 14400

Ref: http://caml.inria.fr/about/taste.en.html