User blog:GamesFan2000/Extreme Nesting Array Function (ENAF)

Well, my last attempt at an array notation was a failure. This time, I hope it goes better. I’m just going to call this the Extreme Nesting Array Function.

Definition
An array is a collection of positive integers. v(A) is the value of an array. {a, b, c, ...} is the shorthand for v(A).

Rule 1 – {0, ...}=0, {a}=a and {a, 1}=a↑aa

Rule 2 – {a, b+1}={{...{a, b} bracket pairs...{{a, b}, b}, ...b}, b}

Rule 3 – {a, ...x, 0, ...}={a, ...x}

Rule 4 – {a, b, c, ...x, 1}={{{{...{a, b, c, ...x} bracket pairs...{{{{...{a, b, c} bracket pairs...{{{{...{a, b} bracket pairs...{{{{a, b}, b}, b}, b}, ...b}, b}, b}, b}, ...b, c}, b, c}, b, c}, b, c}, ...b, c, ...x}, b, c, ...x}, b, c, ...x}, b, c, ...x}

Rule 5 – {a, b, c, ...z, x+1}={{{{...{a, b, c, ...z, x} bracket pairs...{{{{...{a, b, c, ...z} bracket pairs...{{{{...{a, b, c} bracket pairs...{{{{...{a, b} bracket pairs...{{{{a, b}, b}, b}, b}, ...b}, b}, b}, b}, ...b, c}, b, c}, b, c}, b, c}, ...b, c, ...z}, b, c, ...z}, b, c, ...z}, b, c, ...z}, ...b, c, ...z, x}, b, c, ...z, x}, b, c, ...z, x}, b, c, ...z, x}

Examples
{2, 2}={{{{2, 1}, 1}, 1}, 1}={{{4, 1}, 1}, 1}={{4^^^^4, 1}, 1}

{3, 3, 3}={{{{...{{{{3, 3}, 3}, 3}, 3}, ...3, 2}, 3, 2}, 3, 2}, 3, 2}