OCaml Higher Order Functions Composition operators

Example

Two useful higher-order functions are the binary application (@@) and reverse-application or "pipe" (|>) operators. Although since 4.01 they're available as primitives, it might still be instructive to define them here:

let (|>) x f = f x
let (@@) f x = f x

Consider the problem of incrementing the square of 3. One way of expressing that computation is this:

(* 1 -- Using parentheses *)
succ (square 3)
(* - : int = 10 *)

(* where `square` is defined as: *)
let square x = x * x

Note that we couldn't simply do succ square 3 because (due to left-associativity) that would reduce to the meaningless (succ square) 3. Using application (@@) we can express that without the parentheses:

(* 2 -- Using the application operator *)
succ @@ square 3
(* - : int = 10 *)

Notice how the last operation to be performed (namely succ) occurs first in the expression? The reverse-application operator (|>) allows us to, well, reverse this:

(* 3 -- Using the reverse-application operator *)
3 |> square |> succ
(* - : int = 10 *)

The number 3 is now "piped" through square and then succ, as opposed to being applied to square to yield a result that succ is applied to.