The APL Orchard

Adám

12:43

Yearly APL Problem Solving Competition

4

Phoenix

21:54

@Adám What's =+/⍳

Adám

@Phoenix Try it online!

Phoenix

@Dennis I think that the obvious thing for you to do now is teach your daughter Jelly.

Adám

@Phoenix But Jelly uses Latin letters. Also, Jelly is a little less promising when it comes to career and applying the skills in school math.

@Dennis Maybe teach her J? But again, J uses Latin letters, and the "symbols" are much less mnemonic than APL's (if you don't know APL).

Phoenix

I don't know APL, the symbols make no sense at all.

Adám

@Phoenix Which ones do you have in mind?

@Phoenix ⌽ and ⊖ reverse or rotate horizontally and vertically. ⍉ is transpose.

@Phoenix ↑ is take (n first elements), and ↓ is drop.

Phoenix

22:00

Drop makes sense

Adám

@Phoenix ? is random numbers.

@Phoenix < ≤ = ≥ > ≠ ≡ ≢ are what you think.

Phoenix

Why is ⍳ range

Adám

@Phoenix ⍳ is Greek equivalent of i as in indices or index. (Which is why it is i. in J)

@Phoenix ⍋ and ⍒ are ascending and descending grading.

Phoenix

It makes sense if you know APL

Adám

@Phoenix * is to-the-power-of; ⍟ is its inverse, log, which looks like a slice of a tree log.

@Phoenix ∧ ∨ and or; ⍲ ⍱ nand nor.

× ÷ are the proper symbols like found on a calculator.

⌹ is matrix division/inversion.

Phoenix

22:06

/ is map?

Adám

@Phoenix reduce

Phoenix

But +/ is total.

ais523

if / is reduce, then +/ meaning sum would make sense

Adám

@Phoenix the slash indicates the reading "over", like the + over the list.

Phoenix

So it is like map

Adám

22:08

@Phoenix Except mapping is always implied for scalar functions.

Just as +/ is sum, so is +\ running sum.

@Phoenix . is dot product.

Phoenix

running sum means it returns a listt?

Adám

~ is not or without. ∩ ∪ do what you expect, but monadic ∪ is unique too.

@Phoenix yes, of as many elements. Try it online!

∊ is membership (or ∊psilon=E=Enlist)

⍴ is rho =R=Reshape

○ does all kinds of unit-circular/trig/complex things.

⍬ is the empty set

⊣ is left and ⊢ is right.

⌈ and ⌊ are ceiling/max and floor/min

ais523

why not use the mathematical empty set symbol for empty set?

this one: ∅

Adám

@ais523 Well, it's pretty much that, no? Just a style difference. ∅ is too similar to the Danish letter Øø and confusable with transpose ⍉. Ø and ø are valid identifier chars in Dyalog APL.

ais523

transpose in maths is normally a supserscript T, which is pretty distinctive

although APL's symbol makes sense if you want it to be analogous to reverse

I didn't realise APL tried to avoid letters though

Adám

22:17

@ais523 And T(ranspose) is just English.

Also ⊤ is the inverse of ⊥ which in turn is from-base-N conversion, i.e. to-base-N. ⊥ looks like the base of a pillar.

ais523

shouldn't they mean up and down, given the definitions of left and right?

Adám

@ais523 Yes, but APL expressions are 2D; there cannot be any top or bottom arguments, only left and right arguments.

@Phoenix ⎕ symbolises the box, i.e. the computer. ←⎕ is input (of numbers) and ⎕← is output (STDOUT). Since strings are marked with single quotes ', the ←⍞ is string input, and ⍞← is prompt/output to STDERR (i.e. messages).

ais523

those last two commands are the same

Adám

@Phoenix [ ] square brackets can be used for indexing, but there is also a real indexing function, ⌷ which is the composition of [ and ].

ais523

so I assume there's a typo there somewhere?

Phoenix

22:23

←⍞ and ⍞← both seem to be string input.

ais523

do any of the I/O commands use →?

Adám

@ais523 No, → is GoTo, e.g. →5 GoTo line 5 or →End GoTo the label "End".

@ais523 ← is assignment, so no confusion with equality (=).

ais523

I'm not used to APL-alikes having variables

too much Jelly, I guess

Phoenix

→ is assignment in TI-Basic

Except it's e.g. 2→x

Adám

@Phoenix Yes, but TI-Basic goes from left to right, so that makes sense. APL goes from right to left.

@Phoenix Version 16.0 will include one new glyph that I managed to get in; ⊆ (does not mean superset).

Phoenix

22:34

What is it, then?

And why isn't is superset?

Adám

@Phoenix The super and subset functions are pretty easy to write in APL anyway, so they barely need dedicated glyphs (although the NARS2000 dialect does provide a way to use them as such). Instead they have been repurposed for enclosing and disclosing arrays.

@Phoenix ⊂A is encloses A (makes it a self-contained scalar). ⊆A encloses A only if it isn't already enclose. You can see it as enclose-or-equal just like ≤ and ≥.

Phoenix

Makes sense

Adám

@Phoenix P⊆A encloses pieces of A according to the pattern P.

⊃ is the inverse, disclose.

Just like ⊥ converts from a base, so does ⍎ convert from a string, i.e. eval. ⍕ is the inverse; it converts numbers (or anything, really) to text.

@Phoenix | is division remainder and absolute value (like | x | in math).

ais523

if you have both eval and uneval, a quine should be really easy to write

Adám

@ais523 It isn't really uneval, though.

@Phoenix , is horizontal concatenation, while ⍪ is vertical concatenation.

ais523

22:44

ah, hmm

being able to take a string and produce the source code representation of that string is a really useful technique

and that's the analogy on strings of uneval on numbers, in most languages

Adám

⍝ is a comment to enlighten you (it is a stylised picture of a lamp/bulb).

ais523

(because most languages write integer literals using decimal)

Adám

@ais523 We have a util for that. I have it mapped to F11.

@ modifies values at certain locations.

! is factorial (beta and gamma functions)

⍨ swaps arguments. You can kind of see how the wavy line swaps the two dots... (and its cute too)

ais523

in Brachylog we just use ~ to swap arguments

although I've been trying to persuade Fatalize to make it a superscript letter instead, for consistency

Adám

@ais523 Also in J, but ~ is logical not/set difference.

ais523

22:49

does APL have a policy of avoiding ASCII for operators?

Adám

@ais523 No: +-*,^~<>=

# is the root namespace.

ais523

- isn't even a minus sign, though, it's a hyphen; minus sign is −

Adám

@ais523 Well, APL predates Unicode… And the confusion would be great if both had meaning. Originally, we used ^ for And. Now Dyalog APL uses ∧, but allow ^ for compatibility. APLX has loads of such equivalencies.

ais523

∧ is so frustrating because it's fairly important in Brachylog but doesn't seem to be anywhere on my keyboard layout

so I have to keep copying-and-pasting it from Brachylog docs

Adám

@ais523 Nah, AFAIK only APL keyboards have it. Why don't you just modify your layout if you use Brachylog a lot?

ais523

22:55

because I use other languages a lot too

(meanwhile, I've got fairly good at typing Jelly; its character set was designed to be mostly typable on standard Linux layouts; and there's a golfing language I'm working on whose character set is the common subset of "typable using level 1/2/3/4 shifts on the default Linux keyboard layout" and Windows-1252)

Adám

@ais523 That's man serving machine. I prefer the other way around; use the best glyphs and make the computer (keyboard) comply.

@Phoenix So what do you say? "the symbols make no sense at all"?

ais523

it's more to do with, if you stick with one language you can use a heavily customized keyboard

Adám

@ais523 You could have several custom layouts, one for each language.

ais523

but if you work in 54 different languages you want them to all have a common thread

I favour keyboard layouts that give me a lot of freedom in what I can type

é×±Ṣ→“€

Adám

@ais523 Wait, what‽ You cycle between 54 languages that all have unique character sets?

ais523

23:02

most of them use ASCII

also, 54 is as of right now an underestimate (it's the number of languages in the current polyglot, but I know plenty which aren't there)

Adám

@ais523 é×±Ç→¨É

ais523

I assume that was retyped?

several of the characters are different, after all

anyway, this is why I'm frustrated at things like not having a minus sign on the keyboard layout (it's a stock keyboard layout, just one with a lot of characters)

also it doesn't have Greek letters

at least, not all of them

I just feel like, if I want to type something, I shouldn't have to jump through hoops to type it

regardless of what language it's in

actually this topic's coming back round to TIO, in a way; it's likely eventually going to need understanding of character sets above simple "UTF-8/SBCS"

Adám

@ais523 On Windows you can switch language and have an onscreen keyboard layout for that langauge.

ais523

right, left alt + left shift

most of Windows' keyboard layouts are really anemic though

Adám

@ais523 Yes, and custom keyboards, like TryAPL's.

Phoenix

23:30

I really like the Windows mnemonic keyboard. The Linux one ends up binding letters to useful keys like [, `, =; the windows one binds letters to key combinations.

Adám

@Phoenix I use AltGr+Shift+AWSRYU as prefixes, then another (optionally shifted) key. AWS stand for ´^`. R and Y flank T. T is ⍨ in APL, so R is ¨ and Y is ~. U is for underscore. E.g. AltGr+Shift+U,Plus gives ±, and AltGr+Shift+R,Shift+A gives Ä.

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