Sudan function

Sudan function
You are encouraged to solve this task according to the task description, using any language you may know.

The Sudan function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. This is also true of the better-known Ackermann function. The Sudan function was the first function having this property to be published.

The Sudan function is usually defined as follows (svg):

  <big>
    :<math>\begin{array}{lll}
      F_0 (x, y) & = x+y \\
      F_{n+1} (x, 0) & = x & \text{if } n \ge 0 \\
      F_{n+1} (x, y+1) & = F_n (F_{n+1} (x, y), F_{n+1} (x, y) + y + 1) & \text{if } n\ge 0 \\
      \end{array}
    </math>
  </big>

Task

Write a function which returns the value of F(x, y).

Hoon

<lang Hoon> |= [n=@ x=@ y=@] ^- @ |- ?: =(n 0)

 (add x y)

?: =(y 0)

 x

$(n (dec n), x $(n n, x x, y (dec y)), y (add $(n n, x x, y (dec y)) y)) </lang>