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Wed, 25 Aug 2010

Pascal's Triangle in Perl 6


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Today on IRC, Larry Wall showed this piece of Perl 6 code, which he wrote for Rosetta Code:

sub pascal { [1], -> @p { [0, @p Z+ @p, 0] } ... * };
say pascal[^10].perl
# output (reformatted for easy readbility):
# ([1],
#  [1, 1],
#  [1, 2, 1],
#  [1, 3, 3, 1],
#  [1, 4, 6, 4, 1],
#  [1, 5, 10, 10, 5, 1],
#  [1, 6, 15, 20, 15, 6, 1],
#  [1, 7, 21, 35, 35, 21, 7, 1],
#  [1, 8, 28, 56, 70, 56, 28, 8, 1],
#  [1, 9, 36, 84, 126, 126, 84, 36, 9, 1])

That's Pascal's triangle, generated in one line of Perl 6.

The ... is the series operator, which generates lists by feeding the previous value(s) (here always one array) to the generating block on its left, until it reaches the goal on the right (in this case "whatever", which means it returns a lazy, infinite list).

So for example if the previous item was the array [1, 2, 1], the code block evaluates 0, 1, 2, 1 Z+ 1, 2, 1, 0.

Z is the zip operator, Z+ is pairwise addition (ie adding the pairs that the zip operator produced). In our example that leads to 0+1, 1+2, 2+1, 1+0 or 1, 3, 3, 1.

It takes a while to get used to the meta operators and the series operator, but once you've understood them, you can do pretty neat things with them.

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