How to call a function with multiple arguments using the Y combinator in ocaml?

Question

I'm trying to understand the Y combinator in OCaml. I took some code from here, and I'm trying to use it to write the Ackermann function. In the examples in the link, the functions only require one argument. The Ackermann function requires two arguments, and I keep having syntax errors because of it. The code I have so far is

type 'a mu = Roll of ('a mu -> 'a);;

let unroll (Roll x) = x;;

let fix f = (fun x a -> f (unroll x x) a) (Roll (fun x a -> f (unroll x x) a));;

let acker f = function
  0, n -> n + 1
| m, 0 -> f (m-1) 1
| m, n -> f (m-1) (f m (n-1))
;;

print_int (fix (acker 2 2));;

What do I need to do to get it to work? Thanks.

Answer 1

You are mixing curried with uncurried function definitions.

Here is acker in a consistently uncurried form:

let acker f = function
  0, n -> n + 1
| m, 0 -> f (m - 1, 1)
| m, n -> f (m - 1, f (m, n - 1));;

Here is a call:

# fix acker (2, 2);;
- : int = 7
#