Array Order Cascading Hyper Notation (AoCHN) is the 12th part of HN.

Rules

An expression is of the form H_m<n,A>, where n is the base, m is the secondary base, and A is an array.

1. If there is no array, H_m<n> = m^n
2. If there is no secondary base, H<n> = H_n<n>
3. If the array's first entry is 1, delete it.
4. If the array is a sequence array, decrease it by one, then nest the whole expression into the base n times.
5. If the array is a limit array, change the array into the nth member of it's FS.

Arrays

As always, the definitions from HCHN apply.

We can define X_n as X<n>, but we define X_A as X<(A)>. And if, in X<A>, A is a limit array, it will be the cascader of X<FS(A,x)>,that means it copies X<FS(A,x)> and not [A]. Else, if A is the sequence array, ignore A except for the first entry and solve like normal.

To compare arrays, use the rules from HCHN and when comparing X<A> and X<B>, compare A and B and that is the result.