User blog:GamesFan2000/PAN (Part 3)

Rules: Hyper-Nested Arrays

Rule 22: (1’#, …) = 1

Rule 23: (a’1, …) = (a[[[…a brackets…[[[[ [a, a, a, …a a’s…a] ]]…]]]]], …a[[[…a brackets…[[[[ [a, a, a, …a a’s…a] ]]…]]]]] a[[[…a brackets…[[[[ [a, a, a, …a a’s…a] ]]…]]]]]’s…a[[[…a brackets…[[[[ [a, a, a, …a a’s…a] ]]…]]]]], …)

Rule 24: (a’#, …) = (a’#-1, a’#-1, …a’#-1 a’#-1’s…a’#-1, …)

Rule 25: (a’(b, c), …) = (a’(b→b→b…c b’s…b), …)

Rule 26: (a’(b, c, …), …) = (a’((b, c, …), (b, c, …), …), …)

Rule 27: (a’#’1, …) = (a’(#, #, …# #’s…#), …a’(#, #, …#) a’(#, #, …#)’s…a’(#, #, …#), …)

Rule 28: (a’b’c’…n ‘s…d, …) = (a’b’c’…d-1, …a’b’c’…d-1 a’b’c’…d-1’s…a’b’c’…d-1, …)

Rule 29: (a’’1, …) = (a’(a, a, …a a’s…a)’…a ‘s…(a, a, …a), …a’(a, a, …a a’s…a)’…a ‘s…(a, a, …a) a’(a, a, …a a’s…a)’…a ‘s…(a, a, …a)’s…a’(a, a, …a a’s…a)’…a ‘s…(a, a, …a), …)

Rule 30: (a’’#, …) = (a’’#-1, a’’#-1, …a’’#-1 a’’#-1’s…a’’#-1, …)

Rule 31: (a’’’…n ‘s…’’’1, …) = (a’’’…n-1 ‘s…’’’(a, a, …a a’s…a)…a ‘ groups…(a, a, …a), …a’’’…n-1 ‘s…’’’(a, a, …a a’s…a)…a ‘ groups…(a, a, …a) a’’’…n-1 ‘s…’’’(a, a, …a a’s…a)…a ‘ groups…(a, a, …a)’s a’’’…n-1 ‘s…’’’(a, a, …a a’s…a)…a ‘ groups…(a, a, …a), …)

Rule 32: (a’’…’’#, …) = (a’’…’’#-1, …a’’…’’#-1 a’’…’’#-1’s…a’’…’’#-1, …)

Examples

(3’1) = (3[ [ [3, 3, 3] ] ], …3[ [ [3, 3, 3] ] ] 3[ [ [3, 3, 3] ] ]’s…3[ [ [3, 3, 3] ] ])

(3’’3, 3’’’4’’7) = (3’’2, …3’’2 3’’2’s…3’’2, 3’’’4’’6, …3’’’4’’6 3’’’4’’6’s…3’’’4’’6)