The APL Orchard

In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f ′, and an initial guess x0 for a root of f. If the function satisfies sufficient assumptions and the initial guess is close, then x 1 =...

Adám

12:55 AM

Slightly related: I saw the source for ⍣¯1 the other day. Apparently it gives up after 1000 iterations.

rak1507

How does ⍣¯1 work?

Other than magic, of course

Marshall

@rak1507 Maybe my BQN version is a little bit readable?

rak1507

Thanks I'll have a look

Marshall

Basically you just have a big lookup table for primitive inverses and a somewhat smaller table of methods to invert operators and so on based on the components. That's roughly how Dyalog and J work as well, although J uses magic functions mixed with C and Dyalog constructs a derived function with C.

Adám

And finally it tries a numeric solver.

Marshall

1:00 AM

In Dyalog's case.

rak1507

Clever

Adám

@Marshall what did you do about inversion of side-effecty functions?

Marshall

@Adám In BQN? Primitives don't have side effects, so that could only happen when you invert blocks. I don't invert blocks so it's a non-issue for now.

Adám

Ah, clever.

rak1507

Random question, does anyone have recommendations for syntax to mark a dfn as pure or impure? Was thinking that would be an interesting feature to have

Adám

1:07 AM

Any symbol immediately inside the opening brace.

@Marshall Did you get rid of ⍎?

Marshall

@Adám Yes, although it's still in dzaima/BQN and I'm using it in a few places that way. Probably needs a • name.

Adám

Is • only used as a prefix for system names?

Marshall

@Adám Yes.

Adám

I don't really like the choice of symbol. To me, it doesn't look like a character, more like a function symbol. And being small and centered, it doesn't "bind" with the character on its right.

Marshall

@Adám Primitives are all drawn with strokes though. I feel like it does a good job of sticking out in the right way in my code.

Adám

1:17 AM

Yeah, I realised the stroke thing, but still. It looks too separate to me. I get not wanting ⎕, nor a Greek letter like ∆ but how about ∇?

∇Out and ∇args.

Marshall

@Adám Are you looking at it in code though? For me it's working very well so I'm surprised you would object.

Adám

@Marshall Do you have a good example where it is used a lot?

Also, how would you name system operators?

Marshall

I don't think it should look like a character; it should look like some sort of special punctuation you'd put in shorthand.

Adám

But it isn't punctuation, it is just part of the name.

Unless, it is some sort of escape character.

Ah, that's it. That's why the letter after it determines syntactic role.

rak1507

Anyone have a clever way of compressing 2 3 ⍴ 1 ¯1 ¯1 2 ¯1 0

Marshall

1:22 AM

@Adám I guess md.bqn uses it the most.

Adám

fmtm ← ⟨"src/f.bqn"⟩ •Import "dzref"
Fmt ← ⟨•Type,•Decompose,•Glyph,⍕⟩ _fmtm

rak1507

⋄ {⍵-÷/⍵⊥⍤1⊢1-⍨2 3⍴⍎¨'200301'}⍣≡1

Dyalog APL

@rak1507 RANK ERROR

Adám

I dunno, it just sits uneasy with me.

fmtm ← ⟨"src/f.bqn"⟩ ⌂Import "dzref"
Fmt ← ⟨⌂Type,⌂Decompose,⌂Glyph,⍕⟩ _fmtm

fmtm ← ⟨"src/f.bqn"⟩ ¯Import "dzref"
Fmt ← ⟨¯Type,¯Decompose,¯Glyph,⍕⟩ _fmtm

Wezl

@Marshall It is very clear and entertaining. I especially agree with the remarks on type and booleans

I prefer not having a boolean type, but for some cases using church booleans is more convenient than numbers

(maybe just because I don't process numbers often)

Marshall

1:37 AM

@Wezl Huh. Any examples ready?

Wezl

@Wezl although this probably isn't true in the context of array languages

@Marshall In my functional language, I can implement pattern matching by just calling a condition. Actual code example in a minute

Marshall

@Adám Thinking about it some, I guess I'd find something like ▸ acceptable but the ones you've shown don't look right to me.

Adám

@Marshall Yes, that'd be better.

fmtm ← ⟨"src/f.bqn"⟩ ▸Import "dzref"
Fmt ← ⟨▸Type,▸Decompose,▸Glyph,⍕⟩ _fmtm

Wezl

@Marshall ermineii.github.io/…

Adám

Yes, that looks much better to me than the round blob does.

I like the idea of it being a filled symbol, to distinguish its role from primitives. And yes, I think it should be asymmetric, as it is a prefix/escape char.

Maybe a heavier variant:

fmtm ← ⟨"src/f.bqn"⟩ ▶Import "dzref"
Fmt ← ⟨▶Type,▶Decompose,▶Glyph,⍕⟩ _fmtm

Marshall

1:47 AM

@Adám ◥ could be okay except it's much too large. ▸ is too low in DejaVu but not that bad.

Adám

Ooh, how about:

fmtm ← ⟨"src/f.bqn"⟩ ➤Import "dzref"
Fmt ← ⟨➤Type,➤Decompose,➤Glyph,⍕⟩ _fmtm

Marshall

I'll pick one and see if I can find a way to try it out in the next few days.

@Adám Starting to look like a function but the alignment is good.

Adám

fmtm ← ⟨"src/f.bqn"⟩ ◖Import "dzref"
Fmt ← ⟨◖Type,◖Decompose,◖Glyph,⍕⟩ _fmtm

Marshall

@Wezl Ah, neat. What's the : doing here? Just grouping, or forming a list or lazy/macro-list of some description?

@Adám Amusingly enough I tried the half-circle too, but I really didn't like it.

Adám

@Marshall Agreed. I had to try it though ;-)

Wezl

1:52 AM

@Marshall that requires an explanation of half of my unspecified language, which I'd be glad to give :D

Marshall

@Wezl Go for it if it'll fit in a few paragraphs.

Wezl

Maybe it will. do you know any lisp?

Adám

▶►▸‣ What are Unicode thinking‽

Marshall

@Wezl Probably enough from general osmosis to follow along; I'll stop you if anything's unfamiliar.

@Adám Well, they all look different to me, and in fact ‣ is the one I wanted!

(not that I would describe whatever they're doing as thinking)

Dyalog APL

<moon-child> ⋄5 (6 6)

┌→────────┐
│   ┌→──┐ │
│ 5 │6 6│ │
│   └~──┘ │
└∊────────┘

<moon-child> it's boxing day!

Adám

2:04 AM

So you went for display over disp.

Marshall

moon-child: Nine days off, aren't you?

Dyalog APL

<moon-child> @Marshall close enough

Adám

I guess that's good for educational purposes, which is the main use case here.

What about dervs: ⋄ +⌿÷1⌈≢

Dyalog APL

@Adám
┌─────────────────────────────┐
│ #.[Namespace] .  +⌿ ÷ 1 ⌈≢  │
└∇────────────────────────────┘

<moon-child> (sadly no tree print for trains yet, as ⎕nc returns 2 for function results from Safe.Exec)

Wezl

@Marshall ermineii.github.io/…

but gtg now

Adám

2:05 AM

@DyalogAPL Ah, but check if the result is a ⎕OR.

Marshall

@Wezl Thanks!

Dyalog APL

<moon-child> ⋄+/÷≢

  ┌─┼─┐
  / ÷ ≢
┌─┘
+

Adám

Whoo!

⋄ ⍬ ⋄ 0 0⍴0 ⋄ '' ⋄ 0 0⍴''

Dyalog APL

@Adám (no output)

Adám

moon-child: ^?

Dyalog APL

2:17 AM

<moon-child> hmmm

Adám

Now that you have full boxing on, you don't need to special-case empty arrays.

I think you used to do ⎕SE.Dyalog.Utils.repObj on them.

Dyalog APL

<moon-child> right, I took out the special casing

Adám

⋄ 1 ⋄ a←2 ⋄ 3

Dyalog APL

@Adám (no output)

Adám

Wat?

⋄ 1 ⋄ 2

Dyalog APL

2:19 AM

@Adám (no output)

Adám

WAT.

Dyalog APL

<moon-child> go tthe check wrong. Here we go

<moon-child> ⋄5 (6 6)⋄⍬⋄f←+/÷≢⋄f⋄f 5 6 7 9 9

0x0.st/iFkK.txt

Adám

⋄ 1 ⋄ a←2 ⋄ 3

Dyalog APL

@Adám
1


3

Adám

moon-child: Why the blank line on assignment?

⋄ 'abc' ⋄ a←'defg' ⋄ 'hi'

Dyalog APL

2:27 AM

@Adám
┌→──┐
│abc│
└───┘
┌→─┐
│hi│
└──┘

<moon-child> not sure

<moon-child> oh, because display pads extra newlines around simple arrays

<moon-child> *simple scalars and vectors

Adám

Right, I see now that there's no blank line.

Dyalog APL

<moon-child> oh, just scalars

Adám

And SE chat doesn't allow leading or trailing empty lines.

Which actually works out nicely: ⋄ 2+3

Dyalog APL

@Adám 5

Adám

⋄ '5'

Dyalog APL

2:29 AM

@Adám 5

Adám

What? Why did it not underscore the digit?

Dyalog APL

<moon-child> ah, I made it use straight repr instead of display for simple scalars

<moon-child> though tbh, underscoring characters is a bit confusing

Adám

It only happens for scalar characters.

⋄ ⍕5

Dyalog APL

@Adám
┌→┐
│5│
└─┘

Adám

I think the underscore is good for educational purposes. It is a light-weight output type annotation.

I really should fix it so it uses ─ and not - though.

Dyalog APL

2:33 AM

<moon-child> perhaps ¯, so it's more like an actual underline?

Adám

Well, but that doesn't match the (invisible) annotation for non-scalars. Compare: ⋄ 1 2 ⋄ '1 2'

Dyalog APL

<moon-child> ⋄'5'⋄6

5
-
6

@Adám
┌→──┐
│1 2│
└~──┘
┌→──┐
│1 2│
└───┘

Adám

See, the character array uses ─ while the numeric uses ~.

Dyalog APL

<moon-child> that's fair

Adám

Still, you case where the line is exactly between the two digits does look a bit odd.

5
¯
6

is slightly better, but inconsistent.

Btw, you don't see edits, do you?

Dyalog APL

2:36 AM

<moon-child> ah, no. (I worry that posting them in irc could be spammy, for cases where they're just typo fixes)

Razetime

hello

Dyalog APL

<moon-child> could also repr as '5' or ⊃'5'

Adám

Right, but it does mean that actual extra content can be lost. E.g. after I wrote "is slightly better", I added "but inconsistent".

Razetime

new bot update?

Adám

Yeah, it got max boxing and trees.

⊃'5' doesn't make sense.

Dyalog APL

2:38 AM

<moon-child> maybe I can only send edits if levenshtein distance is high enough. (Or, levenshtein distance÷total message length)

Adám

I think it is good now. '-'

Razetime

is the bot written in APL?

Dyalog APL

<moon-child> raku

<moon-child> github.com/moon-chilled/seproxy

Adám

Or if code has changed. Those changes are critical.

Razetime

oh cool

Adám

2:40 AM

Well, but it uses APL to evaluate things.

Supposedly, one could make an ngn/apl evaluation bot as a userscript. It'd be able to react faster…

Razetime

Is the centenary today?

@Adám why a userscript?

Adám

@Razetime Depends on time zone. For you and me, it was yesterday.

@Razetime How else would you run 3rd party JavaScript on the page?

Dyalog APL

<moon-child> @Razetime all participating users would have to install the userscript, of course. But it would still be convenient for educational purposes

Adám

TopAnswers's APL site has built-in APL evaluation in chat.

Razetime

Oh I thought there's a possibility you could write a nodeJS bot

Adám

2:44 AM

It uses TIO, so it doesn't have this bot's limitations (but it does only use 17.1)

Razetime

with ngn/apl eval

Adám

Sure, but would that have any benefit over a Raku one?

Razetime

fair point

so how would you want the userscript to function?

maybe a REPL at the top of the page?

Adám

What's the point of that? Then you might as wall have an interpreter in a window.

No, basically the same; a chat bot.

Razetime

hmm interesting

I'll have a stab at it

Adám

2:51 AM

One odd side-effect of using Raku is: ⋄ 'Adám'≡⎕UCS 65 100 97 769 109 ⋄ ⎕UCS 65 100 97 769 109

Dyalog APL

@Adám
0
┌→────┐
│Adám│
└─────┘

Razetime

hmm

It doesn't match the a?

Adám

Raku does Unicode normalisation, so while my code constructs an a followed by a combining diacritic, Raku normalises the output by combining the two, so while APL can distinguish (hence the 0), when it tries to draw the box, it reserves space for 5 chars, not realising that Raku will change the text to only 4.

The arrows should line up in ⋄ ⎕UCS 2 4⍴8595 97 769 8595 8593 97 180 8593 but they won't.

Dyalog APL

@Adám
┌→───┐
↓↓á↓│
│↑a´↑│
└────┘

Adám

In this case, Raku's normalisation actually wouldn't matter, as the browser would visually combine them anyway.

↓á↓
↑a´↑

Hm, what does Raku do if it can't combine? ⋄ ⎕ucs 248 775

Dyalog APL

3:01 AM

@Adám
┌→─┐
│ø̇│
└──┘

Adám

⋄ ≢'ø̇'

Dyalog APL

@Adám 7

Adám

Wat.

⋄ ⎕UCS'ø̇'

Dyalog APL

@Adám
┌→────────────────────┐
│38 35 50 52 56 59 775│
└~────────────────────┘

Adám

⋄ ⎕UCS⎕UCS'ø̇'

Dyalog APL

3:02 AM

@Adám
┌→──────┐
│&#248;̇│
└───────┘

Adám

That's just wrong.

moon-child: is that your doing?

Razetime

@Adám cool

@DyalogAPL this is html escapes interfering right

Adám

Ah, maybe when scraping the chat, the bot gets fed escaped HTML for some characters, so it literally cannot know what I entered.

⋄ 'ø'≡'ø'

Dyalog APL

@Adám 1

Adám

That sure looks confusing the the APLer.

⋄ 'Ŗ'~'Ŧ'

Dyalog APL

3:07 AM

@Adám
┌→┐
│Ŗ│
└─┘

Adám

⋄ '¤¢'~'£¡'

Dyalog APL

@Adám
┌→─┐
│¤¢│
└──┘

Adám

'¡¢£¤¥¦§¨©ª«¬®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ'

⋄ '¡¢£¤¥¦§¨©ª«¬®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ'

Dyalog APL

@Adám
┌→──────────────────────────────────────────────────────────────────────────
│¡¢£¤¥¦§¨©ª«¬®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêë
└───────────────────────────────────────────────────────────────────────────

      ────────────────────┐
      ìíîïðñòóôõö÷øùúûüýþÿ│
      ────────────────────┘

Adám

I'm confused now.

⋄ 'ø'

Dyalog APL

3:10 AM

@Adám
ø
-

Adám

⋄ ⎕UCS 248

Dyalog APL

 @Adám
ø
-

Adám

\○/

Bubbler

⋄ ≢'¡¢£¤¥¦§¨©ª«¬®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ'

Dyalog APL

@Bubbler 95

Bubbler

3:13 AM

Looks good

Adám

⋄ 'Ŗ̇'~'Ŧ̇'

Dyalog APL

@Adám
┌→┐
│Ŗ│
└─┘

Adám

⋄ '¤̇¢̇'~'£̇¡̇'

Dyalog APL

@Adám
┌→─┐
│42│
└──┘

Adám

Yesss!

Razetime

3:18 AM

lmao

Bubbler

How did that even happen

Razetime

`⋄⎕UCS ⎕UCS '¤̇¢̇£̇¡̇'

⋄⎕UCS ⎕UCS '¤̇¢̇£̇¡̇'

Dyalog APL

@Razetime
┌→───────────────────────────┐
│&#164;̇&#162;̇&#163;̇&#161;̇│
└────────────────────────────┘

Razetime

that's how

Adám

⋄ '¤̇¢̇£̇¡̇'

Dyalog APL

3:19 AM

@Adám
┌→───────────────────────────┐
│&#164;̇&#162;̇&#163;̇&#161;̇│
└────────────────────────────┘

Adám

Somehow, for characters in the range (I guess) 128–255, the bot sees decimal escapes.

But only if followed but a combining character.

Bubbler

And only the 128-255 chars are affected, combining characters themselves are fine

Adám

The reason the box chars are misaligned is because each char is followed by a combining dot above.

Seems like it. And higher chars are unaffected too.

⋄ 'ÿ̇' 'Ā̇' ⍝ 255,dot-above,256,dot-above

Dyalog APL

@Adám
┌→───────────────┐
│ ┌→──────┐ ┌→─┐ │
│ │&#255;̇│ │Ā̇│ │
│ └───────┘ └──┘ │
└∊───────────────┘

Adám

Yup.

Bubbler

3:23 AM

That's... the weirdest character conversion bug I've ever seen

Adám

⋄ '̇̇̇' ⍝ 127 775 128 775 159 775

Dyalog APL

@Adám
┌→─────┐
│̇̇̇│
└──────┘

Adám

⋄ ' ̇' ⍝ 160 775

Dyalog APL

@Adám
┌→─┐
│ ̇│
└──┘

Adám

Right, so only 161–255 are affected.

Bubbler

3:25 AM

⋄ '¡̇̇'

Dyalog APL

@Bubbler
┌→───────┐
│&#161;̇̇│
└────────┘

Bubbler

⋄ '̇¡'

Dyalog APL

@Bubbler (no output)

Adám

Wat.

Bubbler

(The last one is ⎕UCS 775 161)

Adám

3:27 AM

Yes, I saw that.

Oh, if Raku tries to combine the combining char with the quote, maybe the quote isn't counted as a quote, and thus the APL statement fails?

Bubbler

⋄ ''̇¡'

Dyalog APL

@Bubbler
┌→──────┐
│&#39;̇¡│
└───────┘

Bubbler

Now it's weirder

quote is affected, 161 is not

Razetime

⋄' '

Adám

That was 39 775 161, right?

Dyalog APL

3:29 AM

@Razetime
┌→─────┐
│&nbsp;│
└──────┘

Bubbler

Uh, yeah

Razetime

wait amin

Bubbler

then 161 being fine is expected I guess

Adám

775 can only affect what's on its left. (Does that make 775 a monadic operator?)

Razetime

⋄'<>'

Dyalog APL

3:30 AM

@Razetime
┌→─┐
│<>│
└──┘

Razetime

so lt gt isnt happening

Bubbler

⋄ 12⍴' '

Dyalog APL

@Bubbler
┌→───────────┐
│            │
└────────────┘

Bubbler

⋄ ⎕UCS 31+⍳95

Dyalog APL

@Bubbler
┌→──────────────────────────────────────────────────────────────────────────
│ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghij
└───────────────────────────────────────────────────────────────────────────

      ────────────────────┐
      klmnopqrstuvwxyz{|}~│
      ────────────────────┘

Adám

3:31 AM

⋄ ⎕UCS 16 16⍴0,⍳255

Dyalog APL

@Adám 0x0.st/iFky.txt

Bubbler

I don't see any escapes there

Adám

No, it is some interaction with the combining char.

⋄ ⎕UCS 45 775

Dyalog APL

@Adám
┌→─┐
│-̇│
└──┘

Adám

⋄ ⎕UCS 255 775

Dyalog APL

3:33 AM

@Adám
┌→─┐
│ÿ̇│
└──┘

Adám

Ah, it only happens on input.

Bubbler

Yeah, I thought so

Adám

⋄ '-̇'

Dyalog APL

@Adám
┌→─┐
│-̇│
└──┘

Bubbler

⋄ 'ȦḂĊḊĖḞĠḢİJ̇K̇L̇ṀṄȮṖQ̇ṘṠṪU̇V̇ẆẊẎŻ'

Dyalog APL

3:33 AM

@Bubbler
┌→───────────────────────────────┐
│ȦḂĊḊĖḞĠḢİJ̇K̇L̇ṀṄȮṖQ̇ṘṠṪU̇V̇ẆẊẎŻ│
└────────────────────────────────┘

Adám

⋄ 1 '̇'̇ 2

Dyalog APL

@Adám Illegal code

Bubbler

⋄ ' ̇!̇"̇#̇$̇%̇&̇'̇(̇)̇*̇+̇,̇-̇.̇/̇0̇1̇2̇3̇4̇5̇6̇7̇8̇9̇:̇;̇<̇=̇>̇?̇@̇ȦḂĊḊĖḞĠḢİJ̇K̇L̇ṀṄȮṖQ̇ṘṠṪU̇V̇ẆẊẎŻ[̇\̇]̇^̇_̇

̇ȧḃċḋėḟġḣi̇j̇k̇l̇ṁṅȯṗq̇ṙṡṫu̇v̇ẇẋẏż{̇|̇}̇~̇'`

Dyalog APL

@Bubbler (no output)

Adám

Strange, but unlikely to affect anyone.

Bubbler

3:36 AM

⋄ '!̇"̇#̇$̇%̇&̇'̇(̇)̇*̇+̇,̇-̇.̇/̇0̇1̇2̇3̇4̇5̇6̇7̇8̇9̇:̇;̇<̇=̇>̇?̇@̇[̇\̇]̇^̇_̇̇{̇|̇}̇~̇'`

Dyalog APL

@Bubbler (no output)

Bubbler

Time to end bug chasing and write some documentation

> Caveats: Don't give a combining character directly into the Dyalog bot.

Adám

@Bubbler No, I think that's overly strict. Don't put combining characters after characters they cannot combine with.

Bubbler

That makes more sense I guess

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