OCaml Peano Fold

peano_fold.ml

type nat = O | S of nat

let rec fold succ acc n =
    match n with
    | O -> acc
    | S n' ->
        let acc = succ acc in 
        fold succ acc n'

let add x y = fold (fun n -> S n) y x
let to_int = fold (fun n -> n + 1) 0
let two = S (S O)
let three = add (S O) two
let five = add three two

let () = Format.eprintf "%d\n%!" (to_int five)

https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers
https://en.wikipedia.org/wiki/Peano_axioms