Problem Statement

It is known that the set of finite lists of positive integers is   countable.
This means that there exists a subset of natural integers which can be mapped to the set of finite lists of positive integers.

Implement such a mapping:

Demonstrate your solution by:

There are many ways to do this.   Feel free to choose any one you like.

Make the   rank   function as a   bijection   and show   unrank(n)   for   n   varying from   0   to   10.

Let's start with the solution:

rank: function [arr][
    if empty? arr -> return 0
    from.binary "1" ++ join.with:"0" map arr 'a -> repeat "1" a
]

unrank: function [rnk][
    if rnk=1 -> return [0]
    bn: as.binary rnk 
    map split.by:"0" slice bn 1 dec size bn => size
]

l: [1, 2, 3, 5, 8]

print ["The initial list:" l]

r: rank l
print ["Ranked:" r]

u: unrank r
print ["Unranked:" u]