[juliangoldsmith]

The array languages aren't super popular because of the sharp learning curve. They're a lot different than most other languages, and they have a lot of operators that simply don't exist in something like C++.

A few years ago there was an article about K's use in high-frequency trading. I'm not sure about usage of APL and J, though. BQN is still fairly new, so it will take a while to see much production usage.

If you've ever written code using NumPy, Tensorflow, or PyTorch, you're doing array programming. Those libraries are heavily influenced by the array languages, including taking a lot of terminology (rank, etc.). I've personally found that playing with J and BQN helped me understand Tensorflow, and vice versa.

[behnamoh]

> including taking a lot of terminology (rank, etc.).

AFAIK that's a linear algebra term for matrices, not something array programming or Pytorch or TF invented.

[ssfrr]

it's an unfortunate terminology collision.

- array languages: rank is the dimensionality of an array, i.e. a vector is rank-1, a matrix is rank-2, a N-D array is rank-N

- linear algebra: rank is the number of linearly-independent columns (and also rows)

So for example, if you have a 5x5 matrix where 4 of the columns are linearly independent, it would be rank-4 in the linear algebra sense, and rank-2 in the array language sense.

I guess (though I've never really thought of it before) that you could say that the array-language definition is the rank (in the linear algebra sense) of the index space. Not sure if that's intentional.

[juliangoldsmith]

Rank in the array language terminology seems to be synonymous with tensor order (sometimes called tensor rank). Ken Iverson (APL's creator) was a mathematician, so I'm not that surprised to learn the term came from a branch of math.