Higher Hypercascading Hyper Notation (HHpCHN) is the 15th 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

Definitions from HHCHN apply.

X{1} = X, X{2} = Y, X{3} = Z.

H_A<B,C> is the first H-function.

X_A<B,C> is the second H-function.

Y_A<B,C> is the third H-function, that means it uses X_A<B,C> instead of H_A<B,C>.

Z_A<B,C> is the fourth H-function, that means it uses Y_A<B,C> instead of H_A<B,C>.

If N is sequence array:

X{N}_A<B,C> is the H-function of X{N-1}_A<B,C>, that means it uses X{N-1}_A<B,C> instead of H_A<B,C>.

If N is limit array:

X{N}_A<B,C> is the H-function of....WIP.

To compare arrays, first compare the Ns inside of X{N}, and if they are the same then compare the A inside of X{N}_A<B,C>, and if they are the same then compare the B,C inside of X{N}_A<B,C>, and if they are the same, use HHCHN rules.