How can I express a factorial n! with an F# function, recursive or otherwise?

Question

A factorial of a natural number (any number greater or equal than 0) is that number multiplied by the factorial of itself minus one, where the factorial of 0 is defined as 1.

For example:

0! = 1
1! = 1 * 0!
2! = 2 * 1!
3! = 3 * 2!
4! = 4 * 3!
5! = 5 * 4!

Another way of writing this is to multiply all natural numbers between 1 and n for n!:

5! = 1 * 2 * 3 * 4 * 5

How can I express this with a recursive function in F#? And should I do it with a recursive function?

//Factorials!
let factorial n = 
    result = ?

Answer 1

How, option 1:

let rec factorial n =
    match n with
    | 0 | 1 -> 1
    | _ -> n * factorial(n-1)

How, option 2 (tail recursive, compiled into a loop):

let factorial n =
    let rec loop i acc =
        match i with
        | 0 | 1 -> acc
        | _ -> loop (i-1) (acc * i)
    loop n 1

Should: no, see my answer to:

While or Tail Recursion in F#, what to use when?

where I advocate often avoiding both iteration and recursion in favor of higher-order functions. But if you're just getting started, maybe don't worry too much about that advice yet. (But then see e.g. @ChaosPandion's answer, or e.g.

let factorial n = [1..n] |> List.fold (*) 1

---

Or even:

let factorial n = [1..n] |> List.reduce (*) // doesn't require the 2nd parameter