Hypercascading Hyper Notation (HpCHN) is the 13th 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

Y = X_Y<1>. Any X_Y<0> can be removed.

X<X_Y<A-1>,B> (for B < X_Y<A>) = X<X_Y<A-1>> = X_(X_Y<A-1>) = X_Y<A-1>

Define # is rest of array.

If A is a sequence array:

X<X_Y<A-1>,N+X_Y<A>> (where N is any array) is the cascader of X<X_Y<A-1>,N+A> (where A < X_Y<A>), that means it copies X<X_Y<A-1>,N+A> and not [A].

X<X_Y<A-1>,B> (where B is sequence array) is the cascader of X<X_Y<A-1>+C,B-1> (where C is an array), that means it copies X<X_Y<A-1>+C,B-1> and not [C].

Now, Define X_Y<A>is a Y-cascader of X<X_Y<A-1>,N>, that means it uses X<X_Y<A-1>,N> and not X<N>.

If A is a limit array:

X_Y<A> is a Y-cascader of X<X_Y<FS(A,x)>>, that means it uses X<X_Y<FS(A,x)>> and not X<N>.