Yearly APL Problem Solving Competition

@Phoenix Try it online!

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

@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).

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

@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.

Drop makes sense

@Phoenix ? is random numbers.

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

Why is ⍳ range

@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.

It makes sense if you know APL

@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.

/ is map?

@Phoenix reduce

But +/ is total.

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

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

So it is like map

@Phoenix Except mapping is always implied for scalar functions.

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

@Phoenix . is dot product.

running sum means it returns a listt?

~ 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

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

this one: ∅

@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.

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

@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.

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

@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).

those last two commands are the same

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

so I assume there's a typo there somewhere?

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

do any of the I/O commands use →?

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

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

I'm not used to APL-alikes having variables

too much Jelly, I guess

→ is assignment in TI-Basic

Except it's e.g. 2→x

@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).

What is it, then?

And why isn't is superset?

@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 ≥.

Makes sense

@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).

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

@ais523 It isn't really uneval, though.

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

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

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

(because most languages write integer literals using decimal)

@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)

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

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

does APL have a policy of avoiding ASCII for operators?

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

# is the root namespace.

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

@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.

∧ 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

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

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)

@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"?

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

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

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→“€

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

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)

@ais523 é×±Ç→¨É

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"

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

right, left alt + left shift

most of Windows' keyboard layouts are really anemic though

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

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.

@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.