XExelxebar·May 24, 2026
> At some point you get what APL is all about, and you can move on with life without too many regrets.
Unfortunately, this seems to be a common experience. A lot of smart people only engage with APL via toy puzzles, like you did, and bounce off because that gives no insight about how to use the language in real life. IME, to really start getting APL you need to write and rewrite a full application 20 times.
It helps to read code from the masters, too [0, 1, 2, 3, 4]. These all approach architecture in different ways: pedagogical FP style, OOP heavy, data-oriented design, event-driven state-machine, or a mix of the above.
[0]:https://dfns.dyalog.com/
[1]:https://github.com/Co-dfns/MicroUI-APL
[2]:https://github.com/Dyalog/ewc
[3]:https://github.com/Co-dfns/Co-dfns
[4]:https://github.com/Dyalog/Jarvis/blob/master/Source/Jarvis.d...
> As you
Read the rest
can see, the famous prime generator is not even the Eratostenes' sieve, but a simple N^2 divisor counting computation.
Well, that's because you wrote a divisor function, not a seive. Arguably, the ease of typing an outer product (i.e ∘.|⍨⍳N) can tempt us into writing quadratic algorithms unnecessarily, but this is just an experience issue, IMO.
If we want a seive, we can just write one directly:
p⊣{ω~n×1+⍳⌊N÷p⍪←n←ω↑⍨1⌊≢ω}⍣≡1↓1+⍳N⊣p←⍬
The algorithm is O(N log log N) as expected of a naive Eratosthenes implementation. You'll need ⎕IO←0 if you want to try it out.
There's also a faster seive by Roger Hui [0] in the dfns workspace as well as a family of prime number functions [1] for things more than just prime generation.
[0]:https://dfns.dyalog.com/n_sieve.htm
[1]:https://dfns.dyalog.com/n_pco.htm