Introduction to J

Written by Ben Wendt

I tried using j for some of my advent of code puzzles. I found it wasn’t totally suitable for a lot of the challenges, but I had fun learning about J nonetheless.

J is a declarative and functional array programming language. I like this quote from J’s new user guide:

J isn’t just another way to declare variables and write loops. J is a way of thinking big: describing an algorithm by looking at it as a whole and breaking it into its natural parts. You’re going to have to spend some time learning what those natural parts are. Your skill as a program designer will help, but it will be fighting against your learned tendency to think small.

But I won’t be giving an example of that. I’ll just show how some of J’s vocabulary works.

Here’s how to multiply two numbers in J:

   4 * 4
16

But let’s look at a silly way of doing the same multiplication:

   NB. note that comments in J start with NB., for nota bene
   1
1
   NB. commands read right to left.

   NB. $ is the reshape operator it will take the input and
   NB. change it into an array with the size on the left.
   4 $ 1
1 1 1 1
   NB. you can reshape to multiple dimensions
   4 4 $ 1
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
   NB. now we have 4 * 4 = 16 ones above, we need to add them up.

   NB. / is the insert operator. It adds it's left operand between
   NB. everything in the right operand.
   NB. So this shows the sum of all of the columns:
   + / 4 4 $ 1
4 4 4 4
   NB. So, to get the result of 4 * 4, we need to apply the + insert twice:
   + / + / 4 4 $ 1
16

Now, let’s imagine Guass knew J when he was in school, he could have done this:

   +/ 1 + i.100
5050

Which probably isn’t as fun as the original story.

And for day of of 2017 advent of code, the question was very well suited for J. It gives you a 16 x 16 array of numbers, and asks for the sum of the max of each column minus the minus of each column. So in J, that was:

e =: 790 ... NB. tonnes of numbers
NB. reshape the input.
f =: 16 16 $ e

NB. insert the minimum into the list
max =: >./
NB. insert the maximum into the list
min =: <./

NB. sum of maxes minus mins. (|: is transpose)
+/ (max |: f - min |: f) NB. answer

And that’s it. I really love J but I doubt I’ll get any chance to use it professionally.