Ken Iverson, 1920–2020
Let's implement his favourite expression:
Given a row of Pascal's triangle, compute the next row.
This can for example be computed by taking the input padded with a zero on the left, and the input padded with a zero on the right, and then adding the two element...
@ngn ;-) But in all seriousness, lots of challenges use non-golfed code to help specify the task, and the snippet (not a valid answer, since it is neither a function, nor a full program) is obviously not golfed.
How can I center (in leading axis) an array (or scalar) a of rank n in an array b of rank n+1? So if a is 5 and b is 0 0 0 0 0 → 0 0 5 0 0. Or if a is 1 2 3 and b is 3 3⍴0 → 3 3⍴0 0 0 1 2 3 0 0 0. Or another way to think of it is to raise rank and pad.
I created b, found the non-zero locations ⍸a and added half, and pre-pended half to the list of coordinates, sort of big[half,¨¯1+half+⍸a]←1. I'll try your suggestions now.
Input
A string S of length between 2 and 30. The only letters in the string will be a or b.
Output
All strings within Levenshtein distance 2 of S. You must output all the strings without duplicates but in any order you like.
Example
If S = aaa then the output would be (in any order):
aa
abab
ab
a...
@Konrad'Unrooted'Klawikowski For sure. I took the freedom of looking briefly at your website. You're functional programmer, interested in mathematics. Does that mean that you're comfortable with mathematics up to and including linear algebra?
Perfect. Now, because you've already done some programming (even if functional) we need to start with you discarding the notion that APL is a programming language (despite the initialism).
APL was invented by a mathematician (who loved matrices…) who intended a better alternative to traditional mathematical notation (TMN).
(Coincidentally, he would have turned 100 today, had he still been alive.)
So, APL doesn't try to be like other programming language. Instead, takes the best from TMN but generalises and harmonises concepts to yield a more consistent, and therefore machine-executable, notation.
We use × and ÷ (not * and /) for multiplication and division, just like it is taught to kids in school (well, in America, at least).
But APL is also array-oriented. You don't need to specify a loop to add one number to each element of a list: 1+(10,20,30) works.
@Konrad'Unrooted'Klawikowski Can you guess what (1,2,3)+(10,20,30) does?
One of the things APL generalises compared to TMN is the position of symbols. TMN is all over the place… prefix: –a, suffix: a!, omnifix:|a|, superscript: a², none: ab, etc.
APL takes the usage from – and applies it universally: Two-argument functions are between their arguments, while one-argument functions are on the left of their arguments.
@Konrad'Unrooted'Klawikowski Yeah, I've suggested that too.
@rak1507 hm, maybe from one Discord? I'm @KamilaSzewczyk friend, maybe we do share some servers or something, I'm not very active, but maybe you've seen me somewhere there
APL has a rather large vocabulary of symbols (we call them primitive functions ― operators are something else, that we'll get to soon), so having a precedence order like TMN's × before + etc. wouldn't be reasonable.
Instead, we generalise the rule from repeated exponentiation ― ₂3⁴ is ₂(3⁴) ― i.e. right-to-left.
The first thing you have to evaluate is "car", then you can specify that it is "red", and "crashed". Only finally, can you "look" at it. The sentence cannot be understood from the left!
So APL (like English) is written from the left and evaluated from the right. It can often be read both ways for various effects.
in Haskell, I would make a list of n, then I'd check if `mod` 2 == 0, if True, add it to list and then print out that list, or something like that dunno about arithmetic approach tbh, I'd say something around the same, to check if dividing by 2 does produce natural number or something
(dunno if this is called like that in English, we call it like that here, I hope it's the same, and by natural, I mean numbers that don't have 'something.other_something' form)
@Konrad'Unrooted'Klawikowski Think about how to map1 2 3 4 5 6 7 8 9 10 → 2 4 6 8 10 12 14 16 18 20. What is the relationship, i.e. the mapping function?
The reason I'm drilling this, is because I want you to get used to the concept of working on whole arrays, rather than their elements. So, now, can you make the bot print those even numbers from 2…20?
@rak1507 You guys :-D Slow down, we've not even introduced operators yet! I know it is all very obvious and easy for you, but it is very alien for a newcomer within their first two hours.
I'll have to eat and drink something because I have more lessons at 4pm (Python lessons, sadly), but maybe in the evening I can come back for a while if that's not a problem, I also can try being there on that online event this evening
Well, Python lessons in my schools are only for those who think about Matura Or Abitur (auf Deutsch) from IT, so for people who additionaly, to extended maths and extended physics have 'extended' IT added
cmc (fastest code): neighbours sums (of the 3^n neighbours, including self) for an any-dimensional array. neighbours outside the array are treated as 0s.
I have this strange idea of working through and reviewing several older texts on APL. Partly the idea is to show how stable the underlying fundamentals of the language have been over time. Another is to provide updated examples from some of these texts to use trains/rank operator/etc. Is that something others here would be interested in reading?
@Razetime You don't want to do 3*n rotations, so you'd want to decompose it to work on a smaller number of axes at a time. One at a time gives you the smallest number of rotations to perform, but if boolean rotation is 8x faster than integer rotation then you'd probably prefer to do to axes together first.
@Adám Cool! Sometimes a little external motivation is helpful :) .. At least two of these books have appendices with instructions about using acoustic couplers. It makes me nostalgic for a time during which I didn't live. So there is a certain extent of general computing history involved too.
@Razetime Okay, before I forget about this, the CMC was to find ((⍵[0]≤⍺)∧(⍺<⍵[1]))∨((⍵[2]≤⍺)∧(⍺<⍵[3])) for a vector ⍵ and number ⍺ (can swap the argument order), and two APL solutions are 2|⍸ and ≠/≤. Here's a translated BQN example.
another day, another question about implementing a bqn runtime (i should have some time over xmas break to put in some work).
so, as I understand it, in the reference bqn implementation, environments can be nested. get/1, ge/2, and set/2 work on references to environments/slots in this nested structure. what I think i need to do, is flatten the environments into a key-value structure (the "heap" for lack of a better term), where the key is a unique reference, and the value is the environment itself (array of slots & parent environment reference).
Ken Iverson, 1920–2020
Let's implement his favourite expression:
Given a row of Pascal's triangle, compute the next row.
This can for example be computed by taking the input padded with a zero on the left, and the input padded with a zero on the right, and then adding the two element...
