A further informal APL learning session is taking place this evening at 18:30 UTC - you can join Adam at https://chat.stackexchange.com/rooms/52405/apl Reading along is open to everyone, but 20 StackExchange reputation points are required to contribute messages to the chat.
@Potato44 If you want to try things locally on your own computer, you should install Dyalog APL. However, there is an bot in this chat room which will evaluate any APL expression that begins with ⎕← or ⍞← (just don't put backticks around your code). You may want to have an APL keyboard layout set up. You can also use the on-screen keyboard found on TryAPL.
Will do, just got to see if I can find how to quick swap back to english, currently I have to go all the way back to keyboard settings to change layout
@J.Sallé I chose win-space for that reason, I used to use a Japanese IME as my normal keyboard on windows, but sometimes I needed to swap back to the normal US keyboard to use the WSL bash prompt without typing japanese
@Potato44 I see. Took me ages to figure out why sometimes my keyboard layouts changed without me doing anything, turns out I was pressing win-space by accident when I typed too fast
@Potato44 a quick and dirty way to set up the "windows key" as APL key is setxkbmap -layout us,apl -variant ,dyalog -option grp:win_switch (replace "us" with the layout you normally use and optionally include its variant before ",dyalog")
okay, I finished reading the first part of that stuff Adam linked, ⍴ reshapes (dyadic), ⍴ gets the shape(monadic). ≢ gets the number of items in a vector. ≡ gets the depth of a vector. , concatenates vectors. ↑ and ↓ exchange depth and rank (monadically). ↑ and ↓ are take and drop (dyadically). Is that all correct?
@EriktheOutgolfer dvorak is a subclass of en (US )in the XFCE keyboard dialog
@EriktheOutgolfer Dvorak has a good reason to be under US - Mr Dvorak who designed it was an American. Why would APL be? If anything, it should be under CA :)
@Potato44 Tradfns need a header line to indicate their syntax. e.g. r←function rarg indicates a monadic function which returns a result. In the body of the function the right argument can be references with rarg and the result with r.
@Potato44 In an APL session (REPL) ∇ opens and closes the ancient line editor (called the "Del Editor"). In an APL object script, it marks beginning and end of tradfns and tradops, so that you can have multiple in a single script.
@Potato44 I should mention that due to TIO being strictly non-interactive, the Code field is an object script representing the workspace (environment) wherein the Input field's content will be "typed" into the REPL.
@Pavel Monadic it gives you the shape of its argument, i.e. the length of each axis. Dyadic it makes a new array with shape indicated by left argument, filled with elements taken from right argument.
@Adám You can evaluate an APL expression by typing it into chat prefixed by ⍞←. Use ⎕← instead for boxed display and multi-line results. Do not use markdown. Commands: #lb for language bar, #help for table of language elements, #docs for full documentation, #ref for PDF reference card.
That's really all there is to say about ∘. However a warning is in place: (f g)Y is the same as f∘g Y which may fool you into thinking that X(f g)Y is the same as X f∘g Y. However, they are not the same!
And a nice golfing trick using ∘ is having the left operand (which we've called f) be ⊢. This allows using a monadic function on the right argument while ignoring the left argument.
@cairdcoinheringaahing Input is the immediate execution mode. Each line will get executed by itself. You can also use it to "respond" to ⎕ and ⍞ prompts. The Code field will let you define multi-line functions and objects.
@cairdcoinheringaahing To prevent losing your code and data, APL will not let you use the name of a function for data or vice versa without you explicitly erasing them first.
@cairdcoinheringaahing The absolute value is the magnitude (ignoring the sign). It has to be called that due to complex numbers.
@Potato44 This means the dyadic function ⍳ but "pre-populate" the right argument with 1. So that gives you a new monadic (prefix) function: (⍳∘1)x is x⍳1 (which is the index of the leftmost 1.
@EriktheOutgolfer Yes, all monadic functions are prefix.
Btw, for operators you can "curry" their right operand. So WithTwo←∘2 is a new monadic operator which can in turn modify a dyadic function to become monadic (using 2 as its right argument). E.g. + WithTwo 3 will give 5.
This is especially useful with the f⍣n "power operator" which applies its f operand functionn times.
So twice←⍣2 is an operator which applies a function twice. E.g. 2+twice 3 is 7.
@Potato44 No, but surprisingly many do. And if you derive new functions tacitly using only operators and invertible functions, then the resulting function can also (generally) be inverted automatically.
So what happened here is that we applied the function 'x'∘, which prepends the letter x, and then we applied its inverse, which removes an x from the left side.
@Potato44 Yes, e.g. ↓ drops elements and its inverse pads elements (it will use the default fill element):
@Potato44 The specific function 'x'∘, is not hardcoded. Instead the interpreter has a bunch of rules which lets it determine the inverse of various compositions.
@EriktheOutgolfer You mean ×∘× (A times the direction of B) and ×∘+ (A times the conjugate of B)?
One of the most useful inverted functions is ⊥⍣¯1 (inverse of convert-from-base) which will use as many positions as needed to represent a number in a given base:
Now we have been using an array right operand. If we use a function right operand it gets applied to the right argument, and the result must be a Boolean mask instead of a list of indices.
∊ is membership, so the derived function ∊∘⎕A gives a Boolean for where elements of the right (and only) argument are members of the uppercase alphabet:
APL (Dyalog), 83 82 bytes
Anonymous infix function taking current as left argument and total as right argument.
{('prev '/⍨⍺>1),('x+'⎕R'...'⍕∊(⊂1⌽'][',⍕)@⍺⊢'x'@(~∊∘(1,⍵,⍺+3-⍳5))⍳⍵),' next'/⍨⍺<⍵}
Try it online!
{…} explicit lambda where ⍺ and ⍵ represent the left and right arguments:
⍺<⍵ ...
Some of the numbers are a little bit mnemonic. E.g. 819 looks a bit like BIg. It takes a Boolean left argument which says whether the right argument should be made big (uppercase) or not (lowercase):
APL (Dyalog), 83 82 bytes
Anonymous infix function taking current as left argument and total as right argument.
{('prev '/⍨⍺>1),('x+'⎕R'...'⍕∊(⊂1⌽'][',⍕)@⍺⊢'x'@(~∊∘(1,⍵,⍺+3-⍳5))⍳⍵),' next'/⍨⍺<⍵}
Try it online!
{…} explicit lambda where ⍺ and ⍵ represent the left and right arguments:
⍺<⍵ ...
