Index finite lists of positive integers

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. The purpose of this task is to implement such a mapping :

• write a function rank which assigns an integer to any finite, arbitrarily long list of arbitrary large integers.

Index finite lists of positive integers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

• write a function unrank which is rank 's inverse function.

Demonstrate your solution by picking a random-length list of random positive integers, turn it into an integer and get the list back.

Perl 6

<lang perl6>sub expand(Int $n is copy, Int $dimension where * > 1) {

   my @reversed-digits = gather while $n > 0 {

take $n % $dimension; $n div= $dimension;

   }
   return map {

reduce * * $dimension + *, 0, 0, reverse @reversed-digits[$_, * + $dimension ... *]

   }, ^$dimension;

}

sub compress(*@n is copy where @n > 1) {

   my $dimension = @n.elems;
   reduce * * $dimension + *, 0, 0
   reverse gather while @n.any > 0 {

(state $i = 0) %= $dimension; take @n[$i] % $dimension; @n[$i] div= $dimension; $i++;

   }

}

sub rank(@n) { compress compress(@n), +@n } sub unrank(Int $n) { expand |expand($n, 2) }

say my @list = (^10).roll((2..20).pick); say my $rank = rank @list; say unrank $rank;</lang>

Output:

4 5 7 9 0 8 8 7 4 8 8 4 1
406578125236287223374090483
4 5 7 9 0 8 8 7 4 8 8 4 1