APL: An Array Oriented Programming Language (2018)
105 points by tailrecursion 2 years ago | 96 comments- jaygray0919 2 years agoOnce managed tech for an insurance actuarial department. We ran IBM DB2 for underwriting and claims apps. One day had lunch with the actuarials to make friends and make sure we were supporting them well. At one point in the conversation I foolishly asked whether they also would like to access DB2 to minimize data transfers. They laughed and said: "SQL is like drinking data through a straw. We use APL so we can drink it all at once." I felt like a rookie at spring training.
- zelphirkalt 2 years agoI intend to, at some point, learn a readable array oriented programming language. I heard that J fits that bill. Any other suggestions?
What I mean by "readable" is, that it uses ASCII strings and actual names, not merely 1 character (except for very few cases where 1 character might be appropriate, like "Y" or stuff like that) as function names, instead of symbols, of which I do not know their names. I should be able to not only write once, but read again easily. I should not need a special keyboard or special keyboard layout to write programs in the language.
- geocar 2 years ago> What I mean by "readable" is, that it uses ASCII strings and actual names, not merely 1 character
I urge you to reconsider: That they are 1-character is an extremely important feature of Iverson's work.
> instead of symbols, of which I do not know their names
Why do we write 5+5 and not five plus five? The symbols are important! Gosh, can you even remember not knowing how to do addition? Don't you remember how much easier adding things up became once you learned "+"?
Most of Iverson's ideas for symbols really good -- so good that if you do learn their names and everything about them you will have the most amazing ideas as significant a change in you as learning "+"
> I should not need a special keyboard or special keyboard layout to write programs in the language.
You don't need anything of the sort, but if you can't touch-type in APL you might want keycaps, because I think connecting the idea with a single symbol or unique idea is harder if you keep having to translate to English all the time.
- psychoslave 2 years ago>Why do we write 5+5 and not five plus five?
Because tradition is a very hard stuff to get rid of. Just like clocks with needles, with 12 sections.
If you assume addition as implicit juxtaposition syntactic operator ⁙⁙ or ⬠⬠ is also damn efficient to represent five plus five (/faɪv.plʌs.faɪv/ in IPA).
In Ruby:
Multiple letter "five" is a single symbol, just as the multiple pixel 5 glyph.class Fixnum alias_method :plus, :+;end five=5 five.plus fiveNow, there is some convenience in having scripturally short symbols when you do your math with paper and pencil, for example posing some additions in column. But that’s all there is to it, pencil convenience.
A concept is a single semantic idea whatever the length of the symbol used to refer to that concept.
- geocar 2 years ago> Now, there is some convenience in having scripturally short symbols when you do your math with paper and pencil, for example posing some additions in column. But that’s all there is to it, pencil convenience.
You say that like you can just say it, and it's so, but you've got no evidence all symbols are equal even if they are equal in some ways, and Iverson delivered such an utterly convincing argument to the contrary by showing example after example of the exact opposite. You should read it a few times:
https://dl.acm.org/doi/pdf/10.1145/1283920.1283935
> A concept is a single semantic idea whatever the length of the symbol used to refer to that concept.
No, symbols take up real space on the page, on the screen, and in our minds; there are only so many symbols you're going to be able to put in your mind in your career, or in your life, so if there's a way to say some symbols are better than others, then by knowing the better symbols you will among other things, be able to solve bigger problems faster and with fewer bugs. That may not be important to you, but it's important to me!
"+" is a really good symbol. That's why the tradition has been so hard to shake, and that "pencil convenience" has been with us for thousands of years, but "+" isn't that old! For a long time addition was performed with juxtaposition! Just a series of stroke marks like |||| but seriously 5+5 is better than ||||||||||| and nobody can convince me otherwise! I think though, if you aren't convinced by now, I'm not sure what else I can do.
- Koshkin 2 years agoMuch of the progress in mathematics over the past 500 years can be attributed to the development of a good, concise notation.
- Weebs 2 years agoI'm not the person you replied to, but symbols are easier to distinguish visually, tho they need careful balance. Too many are worse than too few
- codetrotter 2 years ago> ⁙⁙ or ⬠⬠ is also damn efficient to represent five plus five
Ok, now do a million plus a million.
- geocar 2 years ago
- abrudz 2 years agoAPL Mnemonics: https://dyalog.tv/APLSeeds23/?v=qZtb4XOLdkI
- gigatexal 2 years agoIf the symbols are just functions then they can have longer-than-one-character names. A(x,y) is no different than add(x,y) no?
- ruste 2 years agoThe advantage of single character concatenated symbols is that it allows your brain to group them rather than forcing you to read them separately. This means you almost unconsciously build up a bunch of set of instantly recognizable "chunks" of symbols that represent concepts you're familiar with. Each of these chunks can represent the equivalent of a huge amount of code in another language.
- t-3 2 years agoAs the other poster implied, it's the difference between a library of functions and an alphabet for composing functions. Concise symbols allow composition of "words" in a way that longer names really don't. There's a practical language design side too - I don't think the right-to-left evaluation and accompanying concision and logical reading order would work otherwise. Maps in other languages are so clumsy and clunky and backwards compared to the APL equivalent.
- ruste 2 years ago
- psychoslave 2 years ago
- xelxebar 2 years ago> I should be able to not only write once, but read again easily.
Once you overcome the admittedly very steep learning curve of APL, it tends to actually be more readable than Algol-likes in many respects.
In fact, counter-intuitively, the single-character symbols actually contribute a lot to its readability. This is, in part, similar to the reason that "a^2 + b^2 = c^2" is usually preferred over "The sum of the squares of the orthogonal sides of a right triangle is commensurate with the square of the hypotenuse," assuming you've done your homework and know basic algebra, equational reasoning, and all that.
In my experience, I see something like a 100X reduction in code size. This means that on my editor screen, right now, just by moving my eyeballs, I can read code that would be scattered over 10s of files in Python. This is the stronger sense in which APL is more readable, and by a large margin, to boot.
Seriously, APL is tons of fun. I feel like it would be tragic to let a few small preconceptions cut off the potential for you to give it an honest go. Also, the J and APL communities are each quite distinctive. FWIW, I've have a particularly good experience with the people using Dyalog APL.
- psychoslave 2 years ago>"a^2 + b^2 = c^2" is usually preferred over "The sum of the squares of the orthogonal sides of a right triangle is commensurate with the square of the hypotenuse,"
These two expression doesn’t carry the same level of information. At best the first, without additional contextual information can only be interpreted as into "The surface of two square equals to a third", or more directely "a·squared plus b·squared gives c·squared".
- xelxebar 2 years agoHehe. You are absolutely right. I was hoping someone would point that out because it highlights another strong point of APL, in my opinion.
APL expressions, just like mathematical formula, don't just float alone in a void in practice. They exist within a context, some problem domain, surrounding code and/or equations, etc. Just how the equation "a^2 + b^2 = c^2" can encode equivalence relations between different structures, depending on context, APL expressions take on interesting, semantically useful meanings when applied to a particular problem domains.
The reason I call this a strong point of APL is that, in "normal" languages we tend to re-encode that extra domain-specific information all over the place at the micro level—within function names, type signatures, and more pertinently in the abstractions we make. APL enables (but doesn't demand) us to let that information manifest directly at the macro level, without erasing the unused potential semantics of the raw algebraic expression.
This is something that practicing mathematicians get intuitively, I believe. Take category theory, for instance, where commutative diagrams in their most abstract form really are Abstract Nonsense™, but their power comes from instantiating them into specific categories, without having to erase the information about the fact that the same diagram also applies within other categories. That kind of thing really tickles the natural abilities of human pattern matching in a productive way.
- xelxebar 2 years ago
- psychoslave 2 years ago
- tluyben2 2 years agoAs said by others: you should reconsider and learn the symbols or k or j or Klong which use your normal keyboard. In k there are very few commands and it won’t take you long to learn them and in your head, at first, say things like 5 cut range 9 etc. You don’t notice after a while, like a natural language sinking in, that you don’t do this anymore and the symbols just ‘arrive’ instead; you will find patterns and type idioms faster than it would take you to look up (let alone learn how to use it etc) the npm in js let’s say. At that time you would not really enjoy not having mastered symbols but words instead.
Also, nothing keeps you from implementing names functions in k or j out of the 1 letter ones;
In k. You can make a readable lib, but I wouldn’t.3#!9 / original 0 1 2 take:{x#y} / or take:# take[3;!9] / 1 readable function 0 1 2 range:{!x} / or range:!: take[3;range[9]] / all readable functions 0 1 2 take[3] range[9] 0 1 2 - mseepgood 2 years agohttps://github.com/robpike/ivy
Documentation: https://pkg.go.dev/robpike.io/ivy#pkg-overview
Also see these Advent of Code 2021 solutions with Ivy: https://www.youtube.com/playlist?list=PLrwpzH1_9ufMLOB6BAdzO...
- sanjayjc 2 years agoAPL entered my consciousness when I wandered into a talk at a conference, where those cryptic symbols first confounded, then intrigued me. Now that I've learning a bit, here's how I explain it. While in elementary school we learned the symbol "-" is a very compact way to convey the powerful ideas of subtraction (when placed between operands: "3-2") and negation ("-5").
The insight underlying APL is that this idea can be extended further. When working with matrices (2d arrays), the operations of (a) checking the shape of an array and (b) reshaping arrays are so frequent that APL designates a single symbol for them: "⍴" (which to me looks like an iron bar whose end was "reshaped" into a loop).
In the same way as "-", compact symbols aid communication and also comprehension. Since the symbols aren't alphanumeric, whitespace separators aren't necessary to delimit tokens. Just as "10-7" means the same thing as "10 - 7", "3⍴4" and "3 ⍴ 4" are equivalent (it means a 1d array comprising 3 fours: 4 4 4).
What has helped me has been learning from the inventor himself: Iverson wrote books that introduced the symbols in a very natural way. The one I'm working through now (and which I highly recommend) is "Elementary Algebra", available for free download here:
https://www.softwarepreservation.org/projects/apl/Papers/Ele...
To try out your own expressions, you can use https://tryapl.org/
- skruger 2 years agoIf that’s what you really want, you end up with numpy, which — whilst efficient in its niche — ends up as a pale imitation of the real thing. I’d urge you to try a modern APL to really experience the power of the Iverson vision.
- HopenHeyHi 2 years agoSomebody always mentions BQN, so: https://mlochbaum.github.io/BQN/
I keep eyeballing that thing. But I am afraid that like only 7 people use it and it isn't a good longterm investment. No idea.
- icen 2 years agoI think if you're looking at learning an array language in order to learn an array language, because of the oft-discussed change in perspective and technique, then I think BQN meets that very handily.
BQN is, in my opinion, the most slick of the array languages; it consistently takes the best of the approaches to high-rank arrays and combinator (including tacit) programming from the others. Some things are unique, and amazing, like structural under.
It is small, it is new, so I would agree with your hesitation to start a business based on it, but to understand these languages or use it for the typical small calculations, it is more than capable.
- HopenHeyHi 2 years agoWell, I read:
http://nsl.com/papers/origins.htm
https://github.com/zserge/odetoj
And watched a few neat videos on the concepts of APL. There's a black and white one on YouTube of a British fellow introducing it using a typewriter. :)
I vaguely get it, my beef with BQN besides being slow is that it is fledgling. And so I have no real excuse to play with it. Otherwise it seems like a holy grail, like, woah finally an APL/J/K to rule them all.
I've seen enough wide eyed salty lispers telling tales of white whales to fear for my sanity going on this quest. Need some sort of lie to buy into like "BQN beyond a superior array language is so fast you could bang out half a page of code in a few minutes and get insane performance and functionality that no mere mortals with their aliensquiggles-less languages can hardly even conceive of".
What kind of half assed cult are you running, haha. No, I refuse to get sucked in. You will not nerd snipe me. Must. Resist.
- HopenHeyHi 2 years ago
- icen 2 years ago
- leprechaun1066 2 years agoSounds like you want q:
- testybesty2 2 years agoTo build on this:
k is a bit like APL, but more concerned with lists rather than multi-dimensional arrays. It uses normal symbols that are easily accessible on your keyboard like + and !, but they are seriously overloaded.
q is built on top of k, and take all the monadic overloads of the operators and gives them a name.
So instead of writing
to get a list of the first 5 integers, you write!5
This is sort of what the original comment is getting at (I think)til 5
- testybesty2 2 years ago
- rscho 2 years agoJ has a library for what you describe, but I doubt you'll like it given your description. What you described is another language called Nial.
- Y_Y 2 years agoI guess you're referring to this: https://github.com/danlm/QNial7
- Y_Y 2 years ago
- useerup 2 years ago> Any other suggestions?
Futhark: https://futhark-lang.org/
- jodrellblank 2 years ago> "a readable array oriented programming language. I heard that J fits that bill. What I mean by "readable" is, that it uses ASCII strings and actual names, not merely 1 character"
It definitely doesn't; J is ASCII symbols. See the vocabulary at https://code.jsoftware.com/wiki/NuVoc - those things in the coloured boxes like ": and ;. and {: are the J building blocks and the quotes and brackets don't pair up. If you want words and "actual names", you need something else.
- pasquinelli 2 years agosomeone already mentioned q, so i'll add nial
- geocar 2 years ago
- garyrob 2 years agoAPL was the first language I learned after IBM 360 Assembly in the 1970s while I was in college. I really liked it because I was a math major and it was extremely well-suited to math operations on arrays. I used it for finding objects on the 2D complex number plane for my Senior Thesis.
I really enjoyed creating clever combinations of the APL operators to get a ton of computation done in one line of code. However, this was the epitome of "read-only code". It was very difficult to read that kind of code after writing it.
After college I never used APL again, although I worked as a software developer (and still do). I miss the fun I had with it, but I wouldn't want to use it for code that I or anyone else would have to maintain, and I doubt that it would be a very expressive language for most commercial applications. For mathematical, array-oriented tasks, Python has appropriate libraries that would probably lead to more maintainable code. And of course there's Julia.
But I can imagine some people still having the expertise to use APL for exploratory calculations, enjoyably and more productively than any other language.
- mamcx 2 years agoIn a round-about fashion I get interested in array languages because the relational model.
I tough an array is "just a column" and somewhere I get to K and that leads me to my current attempt to build a language that make both paradigms work: https://tablam.org
I think each paradigm complement and "fill" the mission pieces the other has. For example, you can name columns, that is alone very useful!
BTW kdb+ is also on this direction but the combination is `array then SQL/Relational` and mine is `Relational then Array`.
- youssefabdelm 2 years agoI think APL is very beautiful as someone who has longed to learn it from afar and not yet had the time, would be very curious to get more insight into how it changes the way you approach problems in both APL and programming in general, and how it gets you to think differently.
If I recall correctly, the Dyalog branch of APL allows for variable names? I kind of like the idea of zero variable names and all strange symbols. The reasoning that after you learn those, you can read any program and understand what's going on at every step, without needing to check what each function actually does -- that sounded very intriguing to me.
And the reason that "checks out" (or may) I guess is that the language's primitives are very carefully chosen such that you have a kind of extreme economy of "words" - so your LOCs will be so low such that you may not need to abstract lines into mysterious function names to reduce the number of lines a person has to read to understand what a program does. Aka the economy of words more than compensates for the lack of abstraction.
- moonchild 2 years agoAs far as I know, every major dialect of APL has had support for variable names. Symbols are used to name primitive functions, but not user-defined terms; if you want to use any intermediate term more than once, you likely want to assign it a name. And even leaving this aside, you probably would not very much like to write an entire program as a single very long expression; intermediate variables are necessary to break lines up.
A few decades ago, j (an apl dialect) innovated a form of tacit programming—programming functions which do not refer to their arguments by name, and which do not need to name intermediate terms to share them—but you still must name your functions if you would like to compose them or if you would like to avoid the extremely-long-line problem.
Generally, I write J programs using a mix of small, tacit functions, and larger explicit functions. The latter primarily comprise a sequence of assignments, and generally use unnamed tacit functions heavily (alongside explicit applications and references to other defined functions) when constructing intermediate terms. Explicit control flow is rare, but usually accomplished using builtin combinators and recursion when necessary.
- youssefabdelm 2 years agoThanks for the correction! I haven't looked as deeply into J but now also curious to learn more. So many new and interesting terms to look up, thank you!
I agree maybe a little bit of variable and function naming is fine in some cases.
- abrudz 2 years ago
- abrudz 2 years ago
- youssefabdelm 2 years ago
- icen 2 years agoAll APL versions have had variable assignments, denoted by ←, e.g. `var ← 1 2 3`.
There is a concept of tacit, or point-free, programming, which avoids the variable names as parameters, for example the calculation of the mean `avg ← +⌿÷≢`. However this does become unwieldy pretty quickly, and it's easy to juggle too much. It is very useful for short snippets, where you avoid all of the ceremony and can just express the core thing you want to talk about (for the avg example, it's not improved by including a parameter: `{(+⌿ ⍵)÷≢⍵}` - the ⍵ parameter isn't informative at all, and nor would anything else, like `samples`). I think it is best to keep the tacit snippets short, and to assign good names to them.
- youssefabdelm 2 years agoOh! Thanks so much for the correction. I was sure my memory would fail me here. That's a great point too with naming. In cases like this it makes a lot of sense. There are many cases I'm thinking of where people sometimes have long function names that do lots of stuff so you're not quite sure what the implementation is like.
- youssefabdelm 2 years ago
- xelxebar 2 years agoThere are many styles of APL, not just due to its long history, but also because APL is somewhat agnostic to architecture paradigms. You can see heavily imperative code with explicit branching all over the place, strongly functional-style with lots of small functions, even object-oriented style.
However, given the aesthetic that you express, I think you might like https://github.com/Co-dfns/Co-dfns/. This is hands-down my favorite kind of APL, in which the data flow literally follows the linear code flow.
- abrudz 2 years agongn/apl is mostly a subset of Dyalog, but allows assigning to glyphs: https://abrudz.github.io/ngn-apl
- moonchild 2 years ago
- qwerty456127 2 years agoIs there a good book or whatever a resource to learn and train youself to efficiently think in APL?
APL seems beautiful to me and would probably help me with a number of tasks I do but it doesn't feel easy to actually practice.
- dybber 2 years agohttps://xpqz.github.io/learnapl/intro.html - is a good place to start. After that consider “Mastering Dyalog APL” it’s a freely available book by Dyalog
- leprechaun1066 2 years agoAnd Dyalog also has https://course.dyalog.com/
- leprechaun1066 2 years ago
- dybber 2 years ago
- eggy 2 years agoI love APL and I use J too as desktop calculators up to programming some quick mathy things for work and fun. My latest love is APRIL (Array Programming Re-Imagined in Lisp) [1]. It allows me to use the libraries and legacy of Lisp for a lot the drudgery in all programming and APL to sling numbers.
I dabble with BQN and Klong.
- CGamesPlay 2 years agoMy first and only experience with APL was on February 5, 2010, at the ACM ICPC world finals. I spent probably an hour and a half trying to figure out how to write a right-associative parser, and never ended up submitting a working solution.
Anybody here write a working solution to that problem? Or remember it, even?
- cl3misch 2 years agoIs there a comprehensive comparison between the strengths/weaknesses of APL and numpy?
I have been interested in APL and friends for some time, but have not yet seen an example which made me commit to taking the time to learn it. numpy (and JAX) have been doing everything I wanted, so far.
- yiyus 2 years agoI am not aware of such a comparison, but I hope this quote will encourage you to have a serious look at APL:
> i don't know one week of studying some APL i could just visualize how I would do that and I would just run and no error every time. Like one week of study APL did more for my expertise, you know, by then more than one year coding in JAX and NumPy.
João Araújo in The Array Cast: https://www.arraycast.com/episodes/episode33-joao-araujo
- cl3misch 2 years agoThanks for the suggestion! The quote indeed sounds promising. I was a bit disappointed by the episode though, because they don't really go into what exactly the learnings are. I guess that is to be expected from a podcast in which _each_ episode is about APL :D
- cl3misch 2 years ago
- yiyus 2 years ago
- 2 years ago
- finalfire 2 years agoI always wondered how one can start learning APL or similar array oriented language. Any suggestions? I'd like to give it a try!
- fishbacon 2 years agoI think BQN is a lot of fun, it is an array language like APL, but it does some things different https://mlochbaum.github.io/BQN/ the documentation is great.
Dyalog APL is more of an actual APL, https://www.dyalog.com/
There is also J https://www.jsoftware.com/#/
The array language community on discord "The Apl Farm" (https://discord.gg/SDTW36EhWF) is pretty active.
I also love the Arraycast podcast https://www.arraycast.com/ many amazing interviews and interesting discussions.
- skruger 2 years agoStart here (disclaimer: author) https://xpqz.github.io/learnapl/intro.html
- moonchild 2 years agoI think the j learning materials are best, particularly 'learning j' (https://www.jsoftware.com/help/learning/contents.htm), though others like 'j for c programmers' (https://www.jsoftware.com/help/jforc/contents.htm).
- j_not_j 2 years agoThere is a book on Klong https://t3x.org/klong/book.html
I've been using klong as it is small, quick to build and has good intro, reference and quick-reference.
One downside is somewhat memory limited.
- tluyben2 2 years agoTo add to the list, this one is pretty good;
- abrudz 2 years ago
- xelxebar 2 years agoHead on over to apl.chat! People are really friendly over there.
- fishbacon 2 years ago
- NeutralForest 2 years agoDo the people here of an opinion on cool projects made with or for APL?
- rscho 2 years agoThe obvious: Co-dfns. It's an APL compiler that generates GPU code. But the interesting thing is that it's also _hosted_ on the GPU!
- rscho 2 years ago
- IIAOPSW 2 years agoHas this guy not heard of Matlab? He's acting like the idea of everything as an array is some niche forgotten thing in a long dead language, meanwhile practically every Engineering department is choc o bloc of people who take the "everything is an array" idea way beyond its logical extent.
- juliangoldsmith 2 years agoArray programming languages are about more than just broadcasting. What you said is kind of like saying C is a functional language because you can pass function pointers around.
Also, Matlab's treatment of arrays is derived directly from APL.
- zackmorris 2 years agoCame here to say the same thing, and add that GNU Octave is pretty good too. Its libraries didn't seem as diverse as MATLAB's when I tried it, but since it's open source, maybe that's changed.
Also when I tried SSE and AltiVec about 20 years ago for SIMD, they were really fast, but I was flabbergasted that the instructions were fixed-length. I wanted something more like the x86 string instructions so that I could fused-multiply-add arrays of floats without having to manually unroll loops to process 4 elements at a time:
https://docs.oracle.com/cd/E19120-01/open.solaris/817-5477/e...
Looks like Arm is trying to do variable-length vectors with Scalable Vector Extension (SVE) but it's limited to 2048 bits, which is unfortunate IMHO:
https://developer.arm.com/documentation/101726/0400/Learn-ab...
https://alastairreid.github.io/papers/sve-ieee-micro-2017.pd...
- 7thaccount 2 years agoMatlab is pretty awesome for doing scientific work and building plots/graphs. It's array/matrix based, but very different than APL in how one goes about programming.
- keithalewis 2 years agoFortran on training wheels is not an array language. Put this in your pipe https://www.eecg.utoronto.ca/~jzhu/csc326/readings/iverson.p....
Matlab was created for people too dumb to use Fortran. APL was invented for people too smart to use Fortran.
- 7thaccount 2 years agoThis seems oversimplistic to say the least. Matlab is used over Fortran as a lot of scientific and numeric work doesn't need to be as fast as Fortran, so having something much easier and faster to develop in with a REPL and data inspector and top tier graphics and GUI building...etc is worth the performance cost as the overall time (including developer) time is much lower in a lot of cases. I've worked with a lot of brilliant academics and national labs folks and they all mostly use Python, Matlab, or Julia for their work. I doubt a single one of them can't learn Fortran. Indeed, some use it when needed on super computers after they've built a prototype in Matlab. Remember, there was a time when scientists thought anyone who needed to use Fortran over Assembly or Assembly over manually configuring the computer were just too dumb/spoiled.
Tldr: Fortran, C/C++, Matlab, Python, Julia are all great and serve different roles with pros and cons.
- 7thaccount 2 years ago
- canadianfella 2 years ago[dead]
- juliangoldsmith 2 years ago