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
#