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01:13
yea. ive been thunking bout the thread too. makes me wonder about what tangible things motivate a community beyond curiosity
sortve a chicken and egg problem
at some point it requires businesses to promote and take the risk, but the only business willing to go that route are either large and established and can mitigate the risk
or small ones w leads v familiar w apl and willing to use it as a technical edge
like, i would have no problem introducing apl to a company i ran, but not to one i dont
which if there was a larger community on par w, i dunno, haskell, that might be different
bootstrapping that divide could be difficult
01:40
there does seem to be a lot of latent curiousity surrounding apl on hackernews at least
What problems (if any) could be cleanly solved with J's "Sequential machine" primitive that could not be solved using its regex utilities?
 
1 hour later…
02:49
@Jonah The expressive powers of a sequential machine and a regex are identical (mathematically). The only possible difference is the degree of conciseness, but regex will mostly win for common text-processing tasks.
So the short answer would be "there are none".
(Of course, when most people say "regex" they mean something more powerful than a mathematical regex)
For example a regex can have lookahead, and capturing groups
03:45
One possible practical use case for x;:y would be when a DFA is easy to construct but the equivalent regex is exponentially large. (IIRC, the shortest "basic regex" testing for multiple of 17 in binary was around 10k bytes.)
Or when dealing with a vector of numbers.
@Bubbler That's what I thought, so I was wondering why it even existed. Based on your last comment, it seems you're suggesting a possible reason is "performance"?
04:04
Performance is a possible reason too. Testing a string against DFA takes strictly linear time in the length of input, while a regex-based testing may involve lots of backtracking.
Thanks.
 
3 hours later…
07:23
@RGS Maybe one of these can help?
07:42
@Thrastylon Welcome. Interested in APL?
@Adám Yes, of course!
@user743253 If you want write access, send an email to adam@ with the domain of www.dyalog.com
07:58
Good morning.
Was wondering, is there a setting to tell the interpreter its current working directory?
RGS
RGS
08:10
@Adám are those related in any way to the IME things the Dyalog APL interpreter installed on my computer? prnt.sc/sajnz7
@RGS No, but I didn't realise you had installed. Ctrl should work as your APL shifting key then.
@xpqz You mean which dir it should start in?
RGS
RGS
@Adám and it does in most places; in the VS Code terminal it just works in a weird way...
Well, which directory it should start looking in for the file 'file' if I say ⎕NGET 'file' 1
@RGS Right. I strongly disagree with kidnapping Ctrl for text input. You can uninstall the Dyalog IME and instead install one of mine which uses AltGr.
@xpqz Right, that'd be the directory it starts in. You should be able to modify the shortcut or the mapl script, but if none of that works, ]cd wherever should work.
Ok, cool, that's what I was after.
08:42
@RGS First piece of feedback for you is from Roger Hui in reaction to your self-styling as a "Mathmagician and problem solver":
> In 1850, Carl Friedrich Gauss and Franz Nauck showed that it is possible to place eight queens on a chessboard such that no queen attacks any other queen. The problem of enumerating the 92 different ways there are to place 8 queens in this manner has become a standard programming example, and people have shown that it can be solved using many different search techniques.
> Now consider a variant of this problem: you must place an equal number of knights and queens on a chessboard such that no piece attacks any other piece. What is the maximum number of pieces you can so place on the board, and how many different ways can you do it?
09:05
Cool problem.
SJT
SJT
09:38
Anyone know when tryapl.org will be back up?
10:01
@SJT Looks back up now.
RGS
RGS
@Adám so the feedback is really a challenge, right?
@Adám I will try to do that, thanks.
@RGS So far, but he's in western Canada and had time Friday to react to my report. Europeans might not have had time yet.
RGS
RGS
10:19
@Adám That was not what I meant; I mean that Hui's feedback is not direct feedback to the notebook I wrote. He is just reacting to me as a person, isn't he? :-)
@RGS Not sure. Roger is like that; it isn't the first time he reacts to presented material with a challenge.
RGS
RGS
10:33
@Adám Challenge accepted!
10:54
Anyone here POP their mail from GMail/GoogleMail? Are you able to get in, or is GMail refusing your password from the POP client (but not a browser)?
@Adám @RGS following on from our converstion on Friday on graphs->adjacency matrices, with your suggestions I managed to solve the problem - gist.github.com/xpqz/19217b6aa3b08d27629770dfafc458a7
@JeffZeitlin - Never mind; there's definitely a problem with all "fat" (i.e., not browser) clients. Worldwide.
RGS
RGS
11:15
@xpqz nice! One thing you can do instead of mirroring the adj. matrix is to expand the edge list with the reverse of the edge list :)
 
1 hour later…
12:26
@RGS Just had a 2020-interns meeting. You are in principle accepted. Expect an email about practical/legal/monetary stuff, and well set up proper communication channels where you'll report to me. Besides for making more Jupyter Notebook docs, some projects that might be interesting for you to work on are a replacement for the current TryAPL, finishing an intro course we have, and creating an additional one. We're also interested to know what you might want to do.
RGS
RGS
@Adám oh wow
Let me step back just for a second here... I am very interested in that internship but I didn't commit to anything yet, correct?
Don't take me wrong
Your (apparent) enthusiasm is great and makes me even more excited about this; but I don't want to skip any steps here because nothing has been discussed yet
Or did I misunderstand something?
@RGS No you didn't. I should have made that more clear. It just means that we're willing and are now giving you an offer on how this can work.
RGS
RGS
oh great :D
Alright, can't wait for that e-mail
my day just got better ⍥
earlier today a random person tried scamming me hahaha
it was really easy to spot the scam if you are moderately proficient on how the internet works... but on the other hand it worries me that many people probably fall for this ⍨
@RGS It can be hard to keep the right balance of necessary scepticism. When I got an actual email claiming the FBI needed my help, I almost sent it to spam.
RGS
RGS
@Adám oh boy, that sounds like an interesting story!
13:24
@Adám After a couple hours of thinking, the maximum number of queens (and knights) must be 4 or 5 (6 is trivially impossible) and very likely 4. I'll need a program to verify it though
13:38
@Bubbler - I think the problem ends up being isomorphic to placing the maximum possible number of mutually non-attacking Amazons, where an Amazon is a fairy piece that moves/captures like either a queen or a knight.
@JeffZeitlin It only applies between a knight and a queen. My 4-pieces solution has four knights crowded at a corner of the board.
It is a stronger version of n black and n white Amazons though.
14:13
@RGS It may take a few days .. to say that people at Dyalog are busy at the moment would apparently be an understatement! Everyone today has said how busy they are. Well, apart from Adam :-)
@xpqz I would be careful using ]cd .. use it at the beginning of your session and try to refrain from using it thereafter .. it's quite intentionally not built into the interpreter and there is a bit of "here be dragons" about changing your current working directory, particularly if you have any sort of file open when you do it.
@AndyS Right, that's why I added it as the last thing with "but if none of that works".
@Bubbler Wait, do you also want to be an intern‽
 
1 hour later…
RGS
RGS
15:20
@AndyS I got it shortly after @Adám 's message ⍥
:-)
RGS
RGS
16:09
@Adám what is tomorrow's APL Cultivation on? I don't know if I'll be able to attend (the whole session)...
@RGS Nothing planned. Ideas? Requests?
@Adám have you covered matrix division before?
One of those concepts I was familiar with in school and since forgotten.
@JamesHeslip It is only mentioned very briefly in lesson 6 but I guess we could take up and "deconstruct" some of the fancier things it can be used for.
RGS
RGS
@Adám (+1)
@RGS But then I need you here to keep my maths right!
RGS
RGS
16:20
@Adám I think I'll be able to attend; I'll just have to go afk for short periods of time. [hopefully]
also, your maths is fine
and APL will help you :D
It has been two decades since I passed linear algebra…
RGS
RGS
@Adám hopefully you only became smarter!
This is the fanciest thing I've seen matrix divide used for: jsoftware.com/papers/50/50_02.htm
@JamesHeslip Funny you should mention it.
Haha
Awfully neat though
16:33
@JamesHeslip I once heard you could justify the words in a char mat with it. Not sure if that was nonsense or not.
RGS
RGS
16:56
Can I get a simple CMC?
smth to get my brain ticking
@RGS Justify a charmat.
RGS
RGS
What does that mean?
@RGS Given a character matrix with text, distribute trailing spaces evenly on each row between words.
RGS
RGS
so each column starts in the same place or ends in the same place?
@Adám starts, right?
In publishing and graphic design, Lorem ipsum is
a placeholder text commonly used to demonstrate
the visual form of a document or a typeface
without relying on meaningful content.
becomes
In publishing and graphic design, Lorem ipsum is
a  placeholder text commonly used to demonstrate
the  visual  form  of  a  document or a typeface
without relying on meaningful content.
RGS
RGS
17:04
oh
I was thinking of a different "data type"
Also, why isn't the 4th row justified?
@RGS Feel free to.
RGS
RGS
Because that'd mean too much whitespace, sure;
@Adám alright perfect
How can I define a charmat like the (un)justified text above?
charmat ← 'first line' 'second' 'third' 'fourth'?
@RGS )ed -name or charmat ← ↑ 'first line' 'second' 'third' 'fourth'
RGS
RGS
thanks :)
@Adám what is the APL Cart search term for "take a number N and divide it as evenly as possible in K buckets"?
17:21
@RGS I don't think there is one, but divide the range and round, no?
RGS
RGS
I mean that 20f3 gives 7 7 6
how do you do that by dividing the range and rounding?
@RGS ¯2-/0,⌈(⍳3)×20÷3
RGS
RGS
@Adám but then ¯2-/0,⌈(⍳5)×17÷5 doesn't give 4 4 3 3 3
I'll write it and come back soon
{v ← (⍳⍺), ⍺⍴0 ⋄ c ← ⌈⍺÷⍵ ⋄ +⌿ 0 < c ⍵⍴v↑⍨⍵×c}
I mistakenly hard-coded a value in my previous version:P
hey there @Sciencisco
17:37
hey !!!
RGS
RGS
@Sciencisco are you interested in APL?
@RGS Honestly I don't even know what APL is
RGS
RGS
APL stands for A Programming Language and well... It's a programming language :P
how did you get here?
Just stumbling through the site reading some interesting questions and I got here...
Just seeing things
RGS
RGS
nice nice
pretty much how I came across APL to be honest
do you know any programming?
17:42
@RGS :)
Not yet... Am planing to do in college, some months later
RGS
RGS
I see, I see
APL is really cool, you know?
looks weird with all its glyphs... but you get used to it
and you start to appreciate them hehe
Well... I would really love to know more about it but gotta go now
RGS
RGS
alright!
Drop by again and ping Adam; he is usually around and is really good at introducing APL to novices
@RGS {c ← ⌈⍺÷⍵ ⋄ v ← c ⍵ ⍴ (⍳⍺), 0⍴⍨ ⍺-⍵×⌊⍺÷⍵ ⋄ +⌿ 0 < v}
RGS
RGS
18:09
@Adám I don't know if this was supposed to be very straightforward but I think I'm almost done
@RGS {c ← ⌈⍺÷⍵ ⋄ v ← c ⍵ ⍴ (⍳⍺), 0⍴⍨ (c×⍵)-⍵×⌊⍺÷⍵ ⋄ +⌿ 0 < v}
Justify ← {
    ⍝ Takes a character matrix and justifies its text.
    lines ← {⍵↓⍨-⊥⍨' '=⍵}¨ ↓⍵
    maxcol ← ⌈/ ≢¨ lines

    JustifyLine ← {
        ⍝ Justifies a single line ⍵ to length ⍺
        mask ← ' '=⍵
        spaces ← 1⊥mask
        used ← spaces -⍨ ≢⍵
        sizes ← (⍺-used) BucketSplit spaces
        replications ← 1 + (sizes-1)@(=∘1) ⊢ mask
        replications/⍵
    }

    ↑maxcol∘JustifyLine¨ lines
}
18:34
@JamesHeslip Ive been doing linear algebra in APL recently. I believe matrix division is often done by QR decomposition nowadays:
https://en.wikipedia.org/wiki/QR_decomposition

I want to devote some more time to it when I have it.
check out 'matrix computations' by golub and van loan (pdf should be available online but i wont link to it)
id like to post a question to the folks here (also posting in k tree):
if you could design an APL successor, what are the "best parts" of other languages you would want to draw from? What would you fix? what paradigms would you use to guide your decision making?

Any preexisting papers, research, or discussions I could reference would be helpful.
19:03
@Adám will there be an APL problem solving competition this year?
@VladimirSotirov Yes, it opens tomorrow.
RGS
RGS
@Adám ⍥
19:19
As a matter of fact, I'll be the one to hit the launch button.
RGS
RGS
@Adám Is it a big red button?
Also serious question right now: I'll be competing and I wanna know what the policy is on asking questions here, on CR, etc;
and how can I know if an APL question I have, arising because of the comp but not directly to solve a problem, is appropriate here?
@Adám (it works :-) )
(btw I downloaded and installed V13 of the US layout but windows displays V12 when I change keyboards)
Cool! Does that mean Dyalog v18.0 will also be out tomorrow? :-)
RGS
RGS
(c.f. this screenshot imgur.com/bopdcU2)
RGS
RGS
20:05
@VladimirSotirov I don't think so
21:00
@RGS Oops, I have the same. I probably forgot to bump the internal version.
@RGS No, blue.
RGS
RGS
@Adám I figured, just wanted to let you know
@BartoszKaliszuk Welcome back.
@Adám @Adám interested A little as I come from the k4 background. However I changed professions some time ago and only keep a warm place in my heart for it
(Still figuring out this "chat")
@RGS New competition site says:
> If you have a generally applicable question (not a competition-specific one!), consider posting it on Stack Overflow. APL questions are usually answered very quickly there.
Use your best judgement.
@RGS Btw, if you do become an intern, you can't win a prize.
RGS
RGS
@Adám seems reasonable
21:11
Goodness, is it time for the next annual competition already? Maybe I'll know enough to attempt some of it this year, albeit I'm not a student.
RGS
RGS
@Adám that is a bummer! I am not sure if I'm up to par with the top competitors though
Would the competition have to end before the beginning of the internship?
@RGS I suppose. Even so, it'd look odd if we award an employee.
@RGS You're welcome to participate anyway.
ngn
ngn
@BartoszKaliszuk there's a k room too
RGS
RGS
@Adám will participate for sure
@TessellatingHeckler There's always the professional prize too.
RGS
RGS
21:13
@Adám but wouldn't it look natural to employ an awardee?
@RGS Yes, in that order, sure. Has happened multiple times.
RGS
RGS
@Adám (+1)
@BartoszKaliszuk I'd be happy to give you a quick overview of the differences between K and APL. Also know that there is a dedicated K chat room if you prefer that.
@Adám thanks. It's kind of late already today but I might join during the day. I will also check the k room. Thanks.
K room is more like k4 or k7(shakti)?
RGS
RGS
(btw @Adám was there a benchmark solution to the CMC earlier today?)
21:20
@BartoszKaliszuk My understanding is that all Ks are on-topic there, hobby as well as commercial.
@RGS Is it just me or is BucketSplit missing?
RGS
RGS
If you want to run the solution, yes
@RGS Not really, other than there being one in dfns.dws
RGS
RGS
BucketSplit ← {
⍝ Dyadic function expecting two integers.
⍝ Splits ⍺ into ⍵ buckets as evenly as possible; accumulates at the beginning.
⍝ e.g. 20 BucketSplit 3 gives 7 7 6.

c ← ⌈⍺÷⍵
v ← c ⍵ ⍴ (⍳⍺), 0⍴⍨ (c×⍵)-⍵×⌊⍺÷⍵
+⌿ 0 < v
}
Markdown is hard.
Now I have to try to implement this myself ;-)
RGS
RGS
@Adám markdown? or the "justify" function?
Markdown is probably funnier
21:24
There's already MarkAPL, which is what we use on TryAPL to render Jupyter Notebooks. No, I meant Justify
RGS
RGS
@Adám CMC: Implement justify without looping over lines
@RGS Not even using ?
RGS
RGS
@Adám I haven't learned how to use ⍤ so you are allowed to use it
@RGS Well, it is really easy to define ¨ in terms of
RGS
RGS
unless you think it goes against the spirit of the CMC; "Use your best judgement"
21:27
Actually, I have an idea that might work.
RGS
RGS
Go for it; I'll be expanding my APL calculator
(it only handles arithmetic expressions with simple scalars, ÷×+-¯ and parenthesizing)
@RGS Once you have that plus / you are well on your way.
RGS
RGS
@Adám but having / will only make sense when I have vectors, isn't it?
True.
RGS
RGS
21:44
@Adám how hard do you think it would be to change key bindings in your layout so that they match the Pt layout?
The symbols on my keyboard are those of a US keyboard but I use a Pt key binding because I know where the keys are. If I managed to change the bindings of your layout to match what I know by heart for the Pt layout, I could live without having to change to and fro
because I still need the accents to type proper portuguese
@RGS It isn't hard, but question is what to do to allow you to type @£§{[]}€
@RGS Is it really right that you have two ways to type \ ?
@RGS Maybe a variation of my overstrike keyboard is the most viable for Pt?
RGS
RGS
@Adám what do you mean?
@RGS Button to the left of 1 and also AltGr+<
RGS
RGS
@Adám to the left of 1, yes; the AltGr+< do you mean the key that has a < written on it?
@RGS Yes.
RGS
RGS
21:51
If yes, nope; AltGr + the key with a < printed on it does nothing when in my Pt layout
So much for trusting Wikipedia.
RGS
RGS
which is annoying because in my Pt layout I can't type <> because I am one key short
(by "does nothing" I mean it prints , which is what it prints without pressing AltGr)
Ah, right you have a US physical keyboard, so you don't have the 102nd key.
RGS
RGS
@Adám never counted them but I'll believe you
@RGS Hold on, which accented characters do you need for Portuguese?
RGS
RGS
21:54
@Adám ´ on top of aeiou for áéíóú, ~ on top of ao for ãõ and ` on top of a for à
Don't know if it counts but we also have ç
which i don't have in a US layout
But in the Pt layouts the ç has a key for itself, with shift+ç = Ç (of course, for some reason this took me by surprise for a second) and AltGr+ç = ç as well
@RGS Somehow I missed (but can easily add) õ. Other than that, my US layout can easily type all of those (and çÇ). That might be the best for you to match what it says on your keyboard, include APL, and have access to Portuguese letters. Of course, it does require re-learning some positions.
RGS
RGS
@Adám ôêâ forgot
@RGS It has those too. If you have it installed, try AltGr+Shift+A,a and AltGr+Shift+W,a and AltGr+Shift+S,a and AltGr+Shift+A,c and AltGr+Shift+Y,a
RGS
RGS
wow
It does have all of them
And it has AltGr+Shift+A,a twice :-P
But tbh I don't know if I'll stick to it, it is not nearly as practical as the single key version in the Pt layout
22:10
@RGS What does that mean?
RGS
RGS
@Adám It means you wrote that combo twice in your message ⍥
@RGS Uh, where?
RGS
RGS
Ah apparently I'm dyslexic
the second one is with ,c
Yup, which makes ç
RGS
RGS
Yup; I might use the shortcuts for short pt sentences
But I'll definitely keep the Pt layout around :/
This is quite impressive, nonetheless
Somewhere in your repo it said that as a side effect of installing this keyboard we'd gain access to writing the majority of european languages; now I understand
22:14
I've packed so much into this layout, I can't even remember it all:
┌────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬─────────┐
│~ ⌺ │! ⌶ │@ ⍫ │# ⍒ │$ ⍋ │% ⌽ │^ ⍉ │& ⊖ │* ⍟ │( ⍱ │) ⍲ │_ ! │+ ⌹ │Backspace│
│` ⋄ │1 ¨ │2 ¯ │3 < │4 ≤ │5 = │6 ≥ │7 > │8 ≠ │9 ∨ │0 ∧ │- × │= ÷ │         │
├────┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬─┴──┬──────┤
│Tab    │Q ⍰ │W ^@│E ⍷ │R ¨@│T ⍨ │Y ~@│U _@│I ⍸ │O ⍥ │P ⍣ │{ ⍞ │} ⍬ │| ⊣   │
│       │q ? │w ⍵ │e ∊ │r ⍴ │t ~ │y ↑ │u ↓ │i ⍳ │o ○ │p * │[ ← │] → │\ ⊢   │
├───────┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴┬───┴──────┤
RGS
RGS
That is way too much :P
Sorry, that doesn't render well.
RGS
RGS
@Adám I don't think it even needs to, I got the idea :P
what does the @ on the spacebar key represent?
@RGS That there are combos using AltGr+Shift+Space. Unfortunately there seems to be a bug in my kbd map program, so it doesn't list all those combos.
RGS
RGS
@Adám that just gave me an idea for a possible CG challenge
assume a keyboard with n keys
we can define k keys for combos that don't print anything when pressed alone, and we can have n-k keys to actually print stuff, depending on the combos
22:21
Most of the AltGr+Shift+Space combos wouldn't be interesting to see anyway, as they are all various space width and (non-)breaking space characters, plus dashes of such lengths when shifted.
RGS
RGS
Now I just have to ask something; like what is the k for which there are the most possibilities or how many possibilities there are for given n, k or something...
@RGS Ah, so given the total number of keys and number of dead keys, compute the maximum number of chars.
RGS
RGS
But it's just a combinatorics question
You have a similar thing with APL. Every glyph can be either 2 functions (monadic or dyadic) or two monadic operators (array and function operand) or 4 dyadic operators (array-array, fn-array, array-fn, fn-fn)…
RGS
RGS
@Adám yup
22:39
hi all, thought i'd drop by and say hello - i've been attempting to teach myself a bit of APL over the last couple of days for a bit of codegolfing fun
@Jarmex Welcome to the Orchard. By all means, feel free to participate here and ask anything. Myself and others are happy to give tips, advice, guidance, private lessons, etc.
RGS
RGS
(+1)
thanks both, i was actually going to ask some advice for how best to formulate a TIO link for my first APL answer that i should be posting soon, and i also don't think i've done it in a particularly optimal way so if either of you had any tips for alternative strategies i'm all ears! i've done it using branching (→) because i couldn't see a decent way of effectively looping via the other ways i've seen - (e.g. ⍣ ⍳ ∆) but i'm sure there must be a neater way
i'll write it up anyway!
RGS
RGS
@Jarmex I can offer all my (limited) expertise!
@Jarmex Sure, write your code here, and we'll give you feedback.
22:53
solution is:

n←⎕
k←0
k+←1
x←⌈.5*⍨k×n
→3/⍨(⌊≠⊢)y←.5*⍨(x*2)-k×n
w,k÷w←k∨x+y
@Jarmex btw, if you put your code in a separate message and press Ctrl+K before posting it, it'll look nicer.
n←⎕
k←0
k+←1
x←⌈.5*⍨k×n
→3/⍨(⌊≠⊢)y←.5*⍨(x*2)-k×n
w,k÷w←k∨x+y
thanks. i can try to explain it - it's basically just following the algorithm in the post
the k+←1 and → is making me unhappy as it's effectively mimicking a for loop in other 'normal' languages, but the difficulty is needing to keep values x, y and k for use outside of the 'loop'
@Jarmex Recursive version:
f←{
  x←⌈.5*⍨⍵×⍺
  (⌊≠⊢)y←.5*⍨(x*2)-⍵×⍺:⍺∇1+⍵
  w,⍵÷w←⍵∨x+y
}∘1
blimey that was quick
You may have trouble inputting that, but if you make it into a one-liner by substituting for line breaks, it should work.
23:03
thanks! give me a few minutes and i'll try to process it
@Jarmex Golfed:
f←{×1|y←.5*⍨(×⍨x←⌈.5*⍨⍵×⍺)-⍵×⍺:⍺∇1+⍵⋄w,⍵÷w←⍵∨x+y}∘1
ok, give me a few hours and i'll try to process it
:P
@Jarmex I just inlined the definition of x, replaced *2 (square) with ×⍨ (self-multiply), and mashed everything into a single line.
aha, nice!
still very much in the early stages of learning so i need to look up each new symbol, takes a while!
@Jarmex No problem. Also, you can hit the up array button to edit your messages for a few mins.
23:12
so you can, cheers
RGS
RGS
(gotta go for today, tired as hell ⍥ bye everyone; good luck Jarmex, APL can be really fun!)
○/
thanks @RGS! ciao
what's the ':' ? that's a new one on me, can't see it on aplcart
@Jarmex That's a dfn guard.
thank you
23:24
@Jarmex While it is, APLcart is primarily intended to find out how to do something, not what something does. In the real interpreter, you can always press F1 on a symbol.
aha, that's useful
clever, i think i roughly follow the solution - i think i was lacking the ability to see the use of currying to allow the recursive solution to work
but that's a helpful learning point, thanks for the help - appreciate it! i'll do some more reading and practicing
@Jarmex You might find something useful here.
cheers

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