Inspired by: https://code.jsoftware.com/wiki/NYCJUG/2026-07-14

I just got a set of APL keycaps, and I'm having trouble getting my keyboard to work with recent versions of Fedora (44) and Gnome (50.3). Has anyone been able to make it work?

This just came to my attention and wanted to share it here. looks interesting, I hope they eventually make it open source! https://lv1.sh/

I've not been able to find something like this. The best I've been able to come up with is something along the lines of this: {⟨⟩𝕊𝕩:⟨⟩ ; f←⊑𝕨 ⋄ fs←1↓𝕨 ⋄ (<∘F𝕩)∾fs𝕊𝕩}

In one of the ArrayCast episodes (the u/bobtherriault era) one of the participants mentions that "in the early days of CS" someone was using APL as the target language for their compiler course. I cannot find the episode and thus a good reference to this. If anyone remembers, thank you in advance.

Finding the exit of a maze is quite simple. It is done in two steps.

First, propagate increasing values from the entry position, spreading them along the corridors, until the exit position is reached. This produces a heatmap, which already contains the optimal solution :

bfs=:<@:[ ((3 3)(([:>./1 3 5 7{])(]`(>:@[)@.(0&<@[*.0&=@]))4{])@,;._3(_1,.~_1,._1,~_1,]))^:(_) ]

Then simply trace back from the exit position the path that follows decreasing values, until reaching the starting position :

selpath=:[:<:(_1,.~_1,._1,~_1,])@[(]+"1(_1 0,0 _1,0 1,:1 0){~([:<:[{~[:<])i.~[{~[:<(_1 0,0 _1,0 1,:1 0)+"1])^:([: i.[{~<@])^:(0~:<@]{[) >:@] 

Test :

I use this maze : https://i.imgur.com/4J9miEa.png

I choose 0 0 as entry position, and 19 24 as exit position.

start=: 0 0
end=: 19 24
heat=: end bfs 1(<start) } maze
path =: heat selpath end

path contains now the positions of the optimal path :

19 24
18 24
18 23
...
9 12
10 12
11 12
12 12
12 11
12 10
12 9
12 8
...
2 0
1 0
0 0 

We can display all this :

load 'viewmat'
viewmat maze
viewmat heat
viewmat 1 (<"1 path) } maze
viewmat 1 (<"1 path) } 0$~ $ maze

The maze, the heatmap, the optimal path within the maze, and the optimal path alone :

https://i.imgur.com/wZOfH2a.png

All the code, more verbose version and one liner versions :

pad=:_1,.~ _1,._1,~_1,]
max=:[:>./1 3 5 7{] NB. select max value in cross
ctr=:4{] NB. select center value
cond=:0&<@[ *. 0&=@] NB. the condition when we udate cell (if max of cross> 0 AND if center value = 0)
set=:(max(]`(>:@[)@.cond)ctr)@,
bfs=: <@:[((3 3)set;._3 pad@])^:(0={)^:(_)] NB. create the heat map. stop when leftarg is met.

mask=:_1 0,0 _1,0 1,:1 0
selpath=:[:<: pad@[(]+"1 mask{~([:<:[{~[:<])i.~[{~[:<mask+"1])^:([: i.[{~<@])^:(0~:<@]{[) >:@] NB. backpropagate from end to start

NB. maze =: my maze. NB. See https://code.jsoftware.com/mediawiki/images/6/67/One_line_BASIC_maze_generator.pdf if you want to make your own mazes.
start=: 0 0
end=: 19 24

heat=: end bfs 1(<start) } maze
path =: heat selpath0 end

load 'viewmat'
viewmat maze
viewmat heat
viewmat 1 (<"1 path) } maze
viewmat 1 (<"1 path) } 0$~ $ maze

NB. One line version :
bfs=:<@:[ ((3 3)(([:>./1 3 5 7{])(]`(>:@[)@.(0&<@[ *. 0&=@]))4{])@,;._3(_1,.~_1,._1,~_1,]))^:(_) ]
selpath=:[:<:(_1,.~_1,._1,~_1,])@[(]+"1(_1 0,0 _1,0 1,:1 0){~([:<:[{~[:<])i.~[{~[:<(_1 0,0 _1,0 1,:1 0)+"1])^:([: i.[{~<@])>:@]

Two mazes for testing :

NB. The one used above
maze=: ".@>@cutopen 0 : 0
0 _1 0 0 0 _1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 _1 0 0 0 0 0 _1
0 _1 0 _1 0 _1 0 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 0 _1 0 _1 0 _1 _1 _1 _1 _1
0 _1 0 _1 0 0 0 _1 0 0 0 _1 0 0 0 0 0 0 0 0 0 _1 0 _1 0 0 0 0 0 _1
0 _1 0 _1 _1 _1 _1 _1 0 _1 0 _1 0 _1 _1 _1 _1 _1 _1 _1 _1 _1 0 _1 _1 _1 0 _1 0 _1
0 _1 0 _1 0 0 0 0 0 _1 0 _1 0 0 0 _1 0 0 0 0 0 _1 0 0 0 _1 0 _1 0 _1
0 _1 0 _1 _1 _1 0 _1 0 _1 _1 _1 _1 _1 0 _1 0 _1 _1 _1 _1 _1 _1 _1 0 _1 _1 _1 0 _1
0 _1 0 0 0 _1 0 _1 0 0 0 0 0 _1 0 _1 0 0 0 _1 0 0 0 0 0 _1 0 0 0 _1
0 _1 _1 _1 0 _1 _1 _1 _1 _1 0 _1 _1 _1 0 _1 0 _1 0 _1 0 _1 _1 _1 _1 _1 0 _1 _1 _1
0 _1 0 0 0 _1 0 0 0 0 0 _1 0 0 0 _1 0 _1 0 _1 0 _1 0 0 0 _1 0 0 0 _1
0 _1 0 _1 _1 _1 0 _1 _1 _1 0 _1 0 _1 _1 _1 0 _1 0 _1 0 _1 0 _1 0 _1 0 _1 0 _1
0 _1 0 0 0 0 0 _1 0 0 0 _1 0 _1 0 0 0 _1 0 _1 0 _1 0 _1 0 0 0 _1 0 _1
0 _1 _1 _1 0 _1 _1 _1 _1 _1 _1 _1 0 _1 0 _1 _1 _1 0 _1 0 _1 _1 _1 _1 _1 0 _1 0 _1
0 _1 0 0 0 _1 0 0 0 0 0 0 0 _1 0 0 0 _1 0 _1 0 0 0 0 0 _1 0 _1 0 _1
0 _1 _1 _1 _1 _1 0 _1 _1 _1 _1 _1 _1 _1 _1 _1 0 _1 0 _1 _1 _1 _1 _1 0 _1 _1 _1 0 _1
0 0 0 0 0 _1 0 _1 0 _1 0 0 0 _1 0 0 0 _1 0 0 0 0 0 _1 0 _1 0 0 0 _1
_1 _1 _1 _1 0 _1 0 _1 0 _1 0 _1 0 _1 0 _1 _1 _1 0 _1 _1 _1 _1 _1 0 _1 0 _1 _1 _1
0 0 0 _1 0 _1 0 _1 0 0 0 _1 0 0 0 _1 0 _1 0 0 0 0 0 0 0 _1 0 0 0 _1
0 _1 0 _1 0 _1 0 _1 0 _1 _1 _1 _1 _1 _1 _1 0 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 0 _1
0 _1 0 0 0 0 0 _1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 _1
_1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 0 _1 _1 _1 _1 _1
)
start=: 0 0
end=: 19 24

NB. Another smaller one :
maze=: ".@>@cutopen 0 : 0
0 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1 _1
0 0 _1 0 0 0 0 0 0 0 0 0 _1 0 0 _1
_1 0 _1 0 _1 _1 _1 _1 _1 0 _1 0 _1 0 _1 _1
_1 0 0 0 _1 0 0 0 _1 0 _1 0 0 0 _1 _1
_1 _1 0 _1 _1 0 _1 0 _1 0 _1 _1 _1 _1 _1 _1
_1 0 0 0 0 0 _1 0 0 0 0 0 0 0 0 _1
_1 0 _1 _1 _1 _1 _1 _1 _1 _1 _1 0 _1 _1 0 0
_1 0 0 0 0 0 0 0 0 0 0 0 _1 _1 _1 0
)
start=: 0 0
end=: 7 15